Systems and methods for switchable magnetic circuits

Abstract

Disclosed herein are systems, devices, and methods for providing or generating switchable magnetic fields. In some cases, such a system may comprise a source of magnetic flux; a flux guide comprising a first portion, a second portion, and an air gap between the first portion and the second portion, wherein the first portion is configured to direct the magnetic flux from a first pole of the source toward the air gap; and an electromagnet, wherein an application of an electrical current to the electromagnet is configured to control a flow of magnetic flux from the first portion through the air gap and from the air gap to the second portion.

Description

SYSTEMS AND METHODS FOR SWITCHABLE MAGNETIC CIRCUITS CROSS-REFERENCE

[0001] This application claims the benefit of French Patent Application No. FR2412568, entitled “SYSTEMS AND METHODS FOR SWITCHABLE MAGNETIC CIRCUITS,” filed on November 18, 2024, which is incorporated by reference herein in its entirety.BACKGROUND

[0002] Quantum computing relies on the quantum mechanical properties of particles or matter to store data. The data may be represented by certain atomic ions, dubbed quantum bits or qubits, which provide a two-state quantum mechanical system. Unlike normal bits, which must be in a 0 or 1, off or on state, qubits can exist in a superposition of quantum states. However, ions used as qubits typically have degenerate electronic states for their outermost electron. To remove the degeneracy of these states and establish a useful two state quantum mechanical system, magnetic fields may be used to reveal Zeeman split states. These states may be leveraged to perform quantum logic gates and store information with the ion. When combined with entanglement of quantum states, quantum computers are able to gain significant advantage in certain problems over classical computers.SUMMARY

[0003] In an aspect, the present disclosure provides system, comprising: a source of magnetic flux; a flux guide comprising a first portion, a second portion, and an air gap between the first portion and the second portion, wherein the first portion is configured to direct the magnetic flux from a first pole of the source toward the air gap; and an electromagnet, wherein an application of an electrical current to the electromagnet is configured to control a flow of magnetic flux from the first portion through the air gap and from the air gap to the second portion.

[0004] In some embodiments, the second portion is configured to direct the magnetic flux to a second pole of the source. In some embodiments, the electromagnet comprises a shunt disposed between the first portion and the second portion. In some embodiments, the shunt is configured to direct the magnetic flux through the air gap upon an application of electrical current to the electromagnet. In some embodiments, the source of magnetic flux is configured to provide a magnetic flux density along the flux guide of about 0.1 Tesla (T) to about 2.5 T. In some embodiments, prior to the application of the electrical current, the magnetic flux is configured to flow along the shunt portion. In some embodiments, prior to the application ofthe electrical current, a density of the magnetic flux along the air gap is less than about 1 milliTesla (mT), 0.1 mT, 0.01 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, prior to the application of the electrical current, a reluctance of the air gap portion is greater than a reluctance of the shunt. In some embodiments, after the application of the electrical current, relative a magnetic permeability of the shunt is about 1. In some embodiments, after the application of the electrical current, a density of the magnetic flux along the air gap comprises a magnitude of at about 0.1 T to about 2.5 T. In some embodiments, after the application of the electrical current, the shunt is saturated with magnetic flux. In some embodiments, a reluctance of the shunt is increased upon application of the electrical current. In some embodiments, after the application of the electrical current the reluctance of the shunt is greater than the reluctance of the air gap. In some embodiments, the shunt comprises a toroid shape. In some embodiments, the electromagnet comprises at least one wire coiled around the shunt. In some embodiments, the electromagnet comprises at least two wires coiled around the shunt. In some embodiments, a first wire and a second wire are configured to generate opposing magnetic fields. In some embodiments, the shunt comprises a reluctance modulator. In some embodiments, the reluctance modulator is a screw. In some embodiments, the reluctance modulator is configured to adjust one or both of a reluctance of the shunt or a magnetic flux along the air gap. In some embodiments, the shunt comprises at least two shunt pieces. In some embodiments, a wire is coiled around a shunt piece of the at least two shunt pieces. In some embodiments, each shunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces. In some embodiments, the electromagnet comprises the coiled wire. In some embodiments, the coiled wire is a solenoid. In some embodiments, a first shunt piece and a second shunt piece are configured to generate opposing magnetic fields.

[0005] In another aspect, the present disclosure provides a system, comprising: (a) at least one magnetic circuit comprising a soft ferromagnetic material; and (b) an ion trap proximate to the at least one magnetic circuit, wherein the magnetic circuit is configured to provide a magnetic field quadrupole proximate to the ion trap and on an opposite side of the ion trap from the at least one magnetic circuit.

[0006] In some embodiments, the magnetic circuit comprises at least one system herein. In some embodiments, the magnetic field quadrupole comprises a magnetic field nil line along an axis extending away from a surface of the ion trap. In some embodiments, the magnetic field quadrupole comprises a magnetic field nil line along a surface of the ion trap. In someembodiments, a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some embodiments, the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some embodiments, the system further comprises a second magnetic circuit. In some embodiments, the first magnetic circuit and the second magnetic circuit form a quadrupole. In some embodiments, the first magnetic circuit is configured to provide a first magnetic field and the second magnetic circuit is configured to provide a second magnetic field. In some embodiments, the first magnetic field comprises a different magnetic field strength than second magnetic field. In some embodiments, the system is configured to shift a position of the magnetic field nil line. In some embodiments, the quadrupole is a ring quadrupole. In some embodiments, the ring quadrupole comprises four quadrants, the four quadrants comprising: (i) a first quadrant comprising a first magnetic pole of the first magnetic circuit, (ii) a second quadrant comprising a second magnetic pole of the first magnetic circuit, (iii) a third quadrant comprising a first magnetic pole of the second magnetic circuit, and (iv) a fourth quadrant comprising a second magnetic pole of the second magnetic circuit. In some embodiments, the quadrupole is a linear quadrupole. In some embodiments, the linear quadrupole comprises four sections. In some embodiments, the linear quadrupole comprises: (i) a first magnetic pole of the first magnetic circuit, (ii) a second magnetic pole of the first magnetic circuit, (iii) a first magnetic pole of the second magnetic circuit, and (iv) a second magnetic pole of the second magnetic circuit, wherein the first and second magnetic poles of the first magnetic circuit are arranged between the first and second magnetic poles of the second magnetic circuit. In some embodiments, the magnetic field nil line is about 20 pm to about 2000 pm above the linear quadrupole. In some embodiments, the linear quadrupole is configured to generate the magnetic field nil line along a surface of the ion trap. In some embodiments, the first magnetic circuit and the second magnetic circuit form a plurality of quadrupoles. In some embodiments, the conductive material is copper. In some embodiments, the soft ferromagnetic material comprises a relative permeability of about 10 to about 10 million. In some embodiments, the soft ferromagnetic material comprises Hiperco®50 or MuMetal®. In some embodiments, the ion trap is configured to trap an ion in a pseudopotential well. In some embodiments, the system further comprises a source of magnetic flux. In some embodiments, the magnetic circuit comprises a flux guide.

[0007] In another aspect, the present disclosure provides a system, comprising: (a) a source of magnetic flux; (b) a flux guide comprising a first path and a second path; and (c) an electromagnet, wherein the electromagnet is configured to switch a flow of the magnetic flux from the first path to the second path, and wherein the second path is configured to generate a magnetic field quadrupole.

[0008] In some embodiments, (a)-(c) form a portion of a magnetic circuit. In some embodiments, the magnetic field quadrupole is formed by the magnetic circuit and a second magnetic circuit. In some embodiments, the magnetic circuit comprises at least one system herein. In some embodiments, the system further comprises an ion trap, wherein the source of magnetic flux, the flux guide, and the electromagnet are proximate to a first side of the ion trap, and the magnetic field quadrupole is proximate to a second side of the ion trap. In some embodiments, the ion trap is configured to trap an ion on the second side of the ion trap. In some embodiments, the ion trap is configured trap the ion proximate to a nil line of the magnetic field quadrupole. In some embodiments, prior to application of an electrical current to the electromagnet, the first path comprises a first reluctance lesser than a second reluctance of the second path. In some embodiments, after an application of an electrical current to the electromagnet, the first path comprises a first reluctance greater than a second reluctance of the second path. In some embodiments, the electromagnet comprises a solenoid coiled around a shunt. In some embodiments, the flux guide comprises an air gap along the second path. In some embodiments, the system further comprises a current source configured to apply a biasing current to the electromagnet. In some embodiments, the biasing current is configured to decrease a remnant flux along the air gap. In some embodiments, a density of the remnant flux along the air gap is at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some embodiments, the flux guide comprises a material with a saturation of flux density of at least about 0 T to about 2.5 T. In some embodiments, the flux guide comprises a material with a saturation flux density of at least about 0.1 T. In some embodiments, the electromagnet comprises a shunt. In some embodiments, the shunt comprises a material with a saturation flux density of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some embodiments, the saturation flux density of the flux guide isgreater than a saturation flux density of the shunt. In some embodiments, the source of magnetic flux is configured to provide a magnetic flux density along the flux guide of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some embodiments, the source of magnetic flux is a permanent magnet. In some embodiments, the permanent magnet comprises Fe, Ni, Sm, Co, or any combination thereof. In some embodiments, the source of magnetic flux comprises a second electromagnet. In some embodiments, the second electromagnet is a solenoid. In some embodiments, the flux guide comprises a soft ferromagnetic material. In some embodiments, the flux guide comprises MuMetal® or Hiperco®50. In some embodiments, the flux guide comprises a coercivity of less than about 1000 A / m. In some embodiments, the shunt and the flux guide comprise the same material. In some embodiments, the shunt and the flux guide comprise a different material. In some embodiments, the electromagnet is a solenoid. In some embodiments, the electromagnet comprises a first electromagnet portion and a second electromagnet portion. In some embodiments, each of the first electromagnet portion and the second electromagnet portion are configured to receive an electrical current in both forward and reverse directions. In some embodiments, the permanent magnet is disposed between the shunt and the air gap portion. In some embodiments, a saturation flux density of the shunt is lower than a saturation flux density of the flux guide. In some embodiments, the saturation flux density of the shunt, the saturation flux density of the flux guide, or both, is at least about 0.5 T. In some embodiments, the electromagnet is configured to modulate residual magnetic flux through the air gap portion. In some embodiments, upon modulation of the residual flux through the air gap a magnetic flux density along the air gap is of less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, the electromagnet is in electrical communication with a diode.

[0009] In another aspect, the present disclosure provides a method for generating a magnetic field quadrupole, comprising: (a) providing a magnetic flux from a magnetic flux source, wherein the magnetic flux flows through a first path; (b) applying a current to an electromagnet, thereby causing the magnetic flux to flow through a second path; and (c) with the magnetic flux flowing through the second path, generating the magnetic field quadrupole.

[0010] In some embodiments, the magnetic field quadrupole is formed by at least two magnetic circuits. In some embodiments, a magnetic circuit of the at least two magnetic circuits comprises at least one system herein. In some embodiments, the method is performedby a system comprising at least one system herein. In some embodiments, the method further comprises transporting an ion to a position within the magnetic field quadrupole. In some embodiments, the method further comprises performing a quantum logic operation with the ion. In some embodiments, the method further comprises switching off the current to the electromagnet. In some embodiments, the magnetic field quadrupole comprises a magnetic field nil line. In some embodiments, prior to (b) the first path comprises a first reluctance lesser than a second reluctance of the second path. In some embodiments, (b) causes the first reluctance to increase to a value greater than the second reluctance. In some embodiments, the electromagnet comprises a solenoid coiled around a shunt. In some embodiments, the method further comprises applying a biasing current to the electromagnet, thereby modulating the magnetic flux. In some embodiments, the biasing current causes a decrease in a remnant flux along the air gap. In some embodiments, a density of the remnant flux along the air gap is at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, prior to (b), the magnetic flux density flowing through the second path is less than about 0.1 T 0.01T, 0.001 T, or 0.0001 T. In some embodiments, after (b), the magnetic flux density flowing through the second path is at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T In some embodiments, the second path comprises an air gap. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some embodiments, the magnetic flux source is a permanent magnet. In some embodiments, the magnetic flux source is a second electromagnet. In some embodiments, the second electromagnet is a solenoid. In some embodiments, one or both of the first or second paths comprise a material with a saturation of flux density of at least about 0.5 T.

[0011] In another aspect, the present disclosure provides a method for switching a magnetic circuit, the method comprising: (a) providing a source of magnetic flux; (b) directing magnetic flux from a first pole of the source of magnetic flux through a flux guide towards an air gap, wherein the flux guide comprises a first portion, a second portion, and the air gap; and (c) at an electromagnet, controlling a flow of the magnetic flux from the first portion through the air gap and from the air gap to the second portion by an application of an electrical current to the electromagnet.

[0012] In some embodiments, the method is performed by a system comprising at least one system disclosed herein. In some embodiments, the magnetic flux of (c) flows to a second pole of the source of magnetic flux. In some embodiments, the electromagnet comprises a shunt disposed between the first portion and the second portion. In some embodiments, prior to the application of the electrical current, the magnetic flux is configured to flow along the shunt. In some embodiments, prior to the application of the electrical current, a density of the magnetic flux along the air gap is less than about 1 mT, 0.1 mT, 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, prior to the application of the electrical current, a reluctance of the air gap portion is greater than a reluctance of the shunt. In some embodiments, after the application of the electrical current, a relative magnetic permeability of the shunt portion is about 1. In some embodiments, after the application of the electrical current, a density of the magnetic flux along the air gap comprises a magnitude of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some embodiments, after the application of the electrical current, the shunt is saturated with magnetic flux. In some embodiments, a reluctance of the shunt is increased upon application of the electrical current. In some embodiments, after the application of the electrical current the reluctance of the shunt is greater than the reluctance of the air gap. In some embodiments, the shunt comprises a toroid shape. In some embodiments, the electromagnet comprises at least one wire coiled around the shunt. In some embodiments, the electromagnet comprises at least two wires coiled around the shunt. In some embodiments, a first wire and a second wire are configured to generate opposing magnetic fields. In some embodiments, the shunt comprises a reluctance modulator. In some embodiments, the reluctance modulator is a screw. In some embodiments, the reluctance modulator is configured to adjust one or both of a reluctance of the shunt or a magnetic flux along the air gap. In some embodiments, the shunt comprises at least two shunt pieces. In some embodiments, a wire is coiled around a shunt piece of the at least two shunt pieces. In some embodiments, each shunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces. In some embodiments, the electromagnet comprises the coiled wire. In some embodiments, the coiled wire is a solenoid. In some embodiments, a first shunt piece and a second shunt piece are configured to generate opposing magnetic fields.

[0013] In another aspect, the present disclosure provides method, comprising: (a) directing magnetic flux from at least one magnetic circuit comprising a soft ferromagnetic material,wherein the at least one magnetic circuit is configured to flow the magnetic flux through the soft ferromagnetic material toward an ion trap; and (b) forming a magnetic field quadrupole proximate to the ion trap and on an opposite side than the at least one magnetic circuit, wherein the magnetic field quadrupole is formed at least in part by directing the magnetic flux in (a).

[0014] In some embodiments, the method is performed by a system comprising at least one system disclosed herein. In some embodiments, the magnetic field quadrupole comprises a magnetic field nil line. In some embodiments, the magnetic field nil line along an axis perpendicular to the ion trap. In some embodiments, the magnetic field nil line along an axis parallel to the ion trap. In some embodiments, a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some embodiments, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some embodiments, the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some embodiments, the method further comprises performing operations (a) and (b) for a second magnetic circuit. In some embodiments, the magnetic circuit and the second magnetic circuit form the magnetic field quadrupole. In some embodiments, the method further comprises trapping an ion in a pseudopotential well.

[0015] In another aspect, the present disclosure provides a method of suspending an ion in a magnetic field in an ion trap, the ion trap comprising: a first plurality of electrodes and a first plurality of DACs configured to apply a DC field configured to confine an ion along a first axis in first direction; a second plurality of electrodes and a second DAC configured to apply an RF field configured to confine an ion in second and third perpendicular directions, each of the first, second and third directions being perpendicular; and four soft ferromagnetic poles; the method comprising: (a) applying an RF field, by the second DAC to the second plurality of electrodes to position the ion at an ion position a first height above the four soft ferromagnetic poles; (b) applying DC fields, by the first plurality of DACs, to the first plurality of electrodes to position the ion in a position between the soft ferromagnetic poles in a first direction; (c) magnetising each of the four soft ferromagnetic poles using magnetic flux from at least one magnetic flux source to generate a magnetic field gradient in a first direction and a magnetic field of less than ImT at the ion position.

[0016] In some embodiments, the four soft ferromagnet poles are arranged in a line along the first axis. In some embodiments, the magnetic flux applied to each soft ferromagnetic polealong the line along the first axis has alternating magnetic polarity. In some embodiments, the magnitude of the magnetic flux applied to each soft ferromagnetic pole is equal and the zero magnetic field line is at a centre line of the soft ferromagnetic poles. In some embodiments, the magnitude of the magnetic flux applied to each of the soft ferromagnetic poles closest to a centre line of the soft ferromagnetic poles differs from than that applied to the outer ferromagnetic poles. In some embodiments, the four soft ferromagnetic poles are arranged in a quadrangle. In some embodiments, the magnetic flux applied to each soft ferromagnetic pole around the quadrangle has alternating magnetic polarity. In some embodiments, the magnitude of the magnetic field applied to each soft ferromagnetic pole is equal and the zero magnetic field line is at the centre line of the soft ferromagnetic poles. In some embodiments, the magnitude of the magnetic flux applied to one pair of oppositely polarised soft ferromagnetic poles is greater than the magnitude of the magnetic flux applied to another pair of oppositely polarised soft ferromagnetic poles. In some embodiments, each of the soft ferromagnetic poles has a first end and a second end, the first end being proximate the ion position and the second end being distal the ion position and wherein the distance between each of the soft ferromagnetic poles at the second ends is greater than the distance between each of the soft ferromagnetic poles at the first ends. In some embodiments, the cross section of each soft ferromagnetic pole at the second end is at least 5 times greater than the cross section of each soft ferromagnetic pole at the first end. In some embodiments, the method further comprises a non-magnetic base and wherein each of the four soft ferromagnetic poles are bonded to the non-magnetic base. In some embodiments, the height of the ion position above the first end of the ferromagnetic poles, proximate the ion position, is lOOum-lmm. In some embodiments, the magnetic poles are formed of Hiperco®50. In some embodiments, the flux source is one of a permanent magnet, a current source or a current in a superconductor. In some embodiments, the method further comprises a magnetic circuit, coupled to at least two of the magnetic poles, the magnetic circuit comprising: (i) a flux source; (ii) a first parallel circuit path comprising an air gap; (iii) a second parallel circuit path comprising a second path and a switchable shunt. In some embodiments, the switchable shunt comprises: (i) a loop forming a first shunt path and a second, parallel, shunt path along the second parallel circuit path; (ii) a winding around the first shunt path and around the second shunt path; (iii) a current source coupled to the winding. In some embodiments, the winding and the current source are configured to generate a magnetic field in a first direction along the first shunt path and a second direction, opposite the first direction along the second shunt path. In some embodiments, the method further comprises switching between a first state in which thecurrent through the winding is below a predetermined threshold and a second state in which the current through the winding is above a predetermined threshold. In some embodiments, the winding and the current source are configured to generate a magnetic field in a first direction along the first shunt path and a second direction, opposite the first direction along the second shunt path. In some embodiments, the first shunt path and the second shunt path form a toroid. In some embodiments, the first parallel circuit path and the second parallel circuit path are formed of the same material. In some embodiments, the first parallel circuit path and the second parallel circuit path are formed of a highly permeable soft ferromagnetic material. In some embodiments, the first shunt path and the second shunt path are formed of a material with a lower saturation flux density than the saturation flux density of the second path and first parallel circuit path. In some embodiments, the first shunt path and the second shunt path are formed of MuMetal®. In some embodiments, the second path and first parallel path is formed of Hiperco®50. In some embodiments, the first parallel circuit path is formed on a first side of the flux source and the second parallel circuit is formed on a second side of the flux source, opposite to the first side of the flux source. In some embodiments, the length of the shunt along the magnetic circuit is greater than the length of the air gap along the magnetic circuit. In some embodiments, the switchable shunt comprises a third shunt path having an adjustable air gap. In some embodiments, the third shunt path is formed of a soft ferromagnetic material. In some embodiments, the flux source is one of a permanent magnet, a current source or a current in a superconductor. In some embodiments, the flux source is an AlNiCo magnet.

[0017] In another aspect, the present disclosure provides a method of generating a magnetic field gradient in a quantum processor, the method comprising: providing a quantum processor comprising a ion trap configured to generate an ion trap at an ion trap position, the ion trap comprising magnetic circuit, the magnetic circuit comprising: (i) a flux source; (ii) a first parallel circuit path comprising an air gap; and (iii) a second parallel circuit path comprising a second path and a switchable shunt, the shunt forming a loop forming a first shunt path and a second, parallel, shunt path along the second parallel circuit path and a winding around the first shunt path and around the second shunt path; the method comprising switching between a first state in which the current through the winding is below a predetermined threshold and a second state in which the current through the winding is above a predetermined threshold.

[0018] In some embodiments, the current in the second state saturates the first shunt path and the second shunt path. In some embodiments, the current, in the second state, is configured togenerate a magnetic field in a first direction along the first shunt path and a magnetic field in a second direction, opposite the first direction, along the second shunt path. In some embodiments, the current in the first state is zero. In some embodiments, the current, in the first state, is configured to generate a magnetic field in a first direction along the first shunt path and a magnetic field in a first direction along the second shunt path.

[0019] Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in this art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.INCORPORATION BY REFERENCE

[0020] All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent publications and patents or patent applications incorporated by reference contradict the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such contradictory material.BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings (also “Figure” and “FIG.” herein), of which:

[0022] FIG. 1A shows an illustrative saturable electronic reluctance switch prior to application of an electrical current;

[0023] FIG. IB shows an illustrative saturable electronic reluctance switch after application of an electrical current;

[0024] FIG.2 shows an illustrative toroidal saturable electronic reluctance switch;

[0025] FIG.3A shows an illustrative current dependence of magnetic flux as described herein;

[0026] FIG.3B shows an illustrative closed magnetic flux loop formed by coil windings about a toroidal shunt;

[0027] FIG.3C shows illustrative magnetic flux through paths of least reluctance;

[0028] FIG.4 shows an illustrative magnetic circuit diagram for a saturable electronic reluctance switch;

[0029] FIG.5A shows an illustrative linear saturable electronic reluctance switch;

[0030] FIG.5B shows an illustrative current dependence of a magnetic flux as described herein;

[0031] FIG.5C shows illustrative magnetic flux through paths of least reluctance;

[0032] FIG.6 shows an illustrative reluctance modulator;

[0033] FIG. 7 shows an illustrative circuit diagram of states of a reluctance modulator;

[0034] FIG.8A shows an illustrative side and top profile of a ring quadrupole;

[0035] FIG.8B shows an illustrative ring quadrupole proximate to an ion trap;

[0036] FIG.8C shows an illustrative magnetic field strength along three dimensions for a magnetic field quadrupole generated by a ring quadrupole;

[0037] FIG.9A shows an illustrative side and top profile of a linear quadrupole;

[0038] FIG.9B shows an illustrative linear quadrupole proximate to an ion trap;

[0039] FIG.9C shows an illustrative magnetic field strength along three dimensions for a magnetic field quadrupole generated by a linear quadrupole;

[0040] FIG. 10 shows an illustrative linear quadrupole disposed on a conductive substrate;

[0041] FIG. 11 provides a non-limiting example of a method for generating a magnetic field quadrupole, in accordance with some embodiments;

[0042] FIG. 12 provides a non-limiting example of a method for switching a magnetic circuit, in accordance with some embodiments;

[0043] FIG. 13 provides a non-limiting example of a method for directing magnetic flux, in accordance with some embodiments;

[0044] FIG. 14 provides a non-limiting example of a method for suspending an ion in a magnetic field in an ion trap, in accordance with some embodiments;

[0045] FIG. 15 provides a non-limiting example of a method for generating a magnetic field gradient in a quantum processor, in accordance with some embodiments;

[0046] FIG. 16 shows an illustrative magnetic flux output versus applied current for a saturable electronic reluctance switch;

[0047] FIG. 17 shows illustrative symmetric and asymmetric activation of magnetic poles of a ring quadrupole;

[0048] FIG. 18 shows illustrative symmetric and asymmetric activation of magnetic poles of a linear quadrupole;

[0049] FIG. 19 shows an illustrative comparison of magnetic field output of a ring quadrupole versus a current carrying wire;

[0050] FIG.20 shows an illustrative comparison of magnetic field output of a ring quadrupole versus a current carrying wire;

[0051] FIG.21A shows an illustrative ring quadrupole proximate to an ion trap;

[0052] FIG.21B shows an illustrative linear quadrupole proximate to an ion trap;

[0053] FIG.22 shows an illustrative ring quadrupole proximate to an ion trap;

[0054] FIG.23 shows an illustrative ring quadrupole proximate to an ion trap;

[0055] FIG.24 shows illustrative ring quadrupole sizes versus performance;

[0056] FIG.25 shows an illustrative ring quadrupole fabricated via wire-erosion;

[0057] FIG.26 shows an illustrative schematic of quadrupoles implemented in a multimodule quantum computing system;

[0058] FIG.27 shows an illustrative pair of saturable electronic reluctance switches used to provide a plurality of linear quadrupoles;

[0059] FIG.28 shows an illustrative comparison between output magnetic field vs. current for an illustrative saturable electronic reluctance switch versus an alternative approach; and

[0060] FIG. 29 shows illustrative separations between types of ferromagnetic materials.DETAILED DESCRIPTION

[0061] Techniques for establishing magnetic fields and magnetic field gradients used in performing quantum logic operations in trapped ion quantum computers may be limited in their application to scalable computing systems. Generally, in trapped ion quantum computers, the performance of gating operations may scale with the gradients of magnetic fields to which ions are exposed. For example, as provided for herein, techniques that generate large magnetic fields proximal to a zero or near zero magnetic field may be desired for their introduction of large gradients between the maximum and minimum magnetic fields. However, existing techniques may be limited in scalability and prone to introducing postgating errors. For example, current carrying wire methods may introduce substantial resistive heating that may introduce both engineering and qubit decoherence problems. In another example, techniques based on hard ferromagnetic materials may be prone to residual magnetic flux in the path of ion transport or inconsistent magnetic field characteristics introduced by magnetic hysteresis, both phenomena being detrimental to reliable quantum computation.

[0062] Recognized herein is the need for, systems, devices, and methods that facilitate large magnetic field gradients while uniquely reducing residual magnetic flux in the path of ion transport post-gating operations. Such techniques may provide particular utility in scaling trapped ion computers by reducing errors introduced to qubits during transport between gates, transport that is valuable in creating larger, more powerful quantum computers.Overview

[0063] Disclosed herein are systems, devices, and methods for generating switchable local magnetic fields. In some cases, switchable magnetic fields may be used to generate magnetic field quadrupoles in a region of interest. For example, magnetic field quadrupoles projected above an ion trap in a trapped ion quantum computer may facilitate robust quantum logic operations. Generally, techniques herein leverage magnetic field fringing effects to generate projected magnetic field quadrupoles as magnetic flux is directed through air gaps in magnetically conductive materials. The present disclosure provides particular utility in (i) generating large magnetic field gradients with (ii) ultra-low noise field characteristics using (iii) reliable, low power, heat efficient, tunable saturable electronic reluctance switches. Such characteristics may facilitate both reliable quantum logic operations and system scalability. For example, systems and devices as disclosed herein may be accessible via existingfabrication technologies such as wire-erosion. The techniques herein may be used to generate large magnetic field gradients in quantum computing modules, chips, processors, or other quantum computing components. This may have particular utility for generating desired magnetic field topologies proximal to ions. Generally, the techniques herein facilitate spatially and temporally controllable magnetic field gradients that promote high fidelity quantum computation.

[0064] Several of the aspects disclosed herein may facilitate scalable quantum computing systems. Generally, scalability may be correlated to a number of operable qubits in a quantum computing system. Illustrated herein are systems, devices, and methods that may confer arbitrary scalability to quantum computing systems. In some cases, arbitrary scalability may indicate that the systems and devices herein may be combined an arbitrary number of times. The systems, devices, and methods herein may overcome limitations of existing techniques such that the number of qubits a quantum computing system may implement may be increased relative to the state of the art, thereby advancing the field of quantum computation as a whole.Switchable Magnetic Fields

[0065] In several aspects herein are implementations and uses of a saturable electronic reluctance switch (SERS). In some cases, a saturable electronic reluctance switch may comprise a magnetic circuit. For example, a saturable electronic reluctance switch may provide particular utility in generating a low-noise, reproducible ‘on’ and ‘off states. In some cases, a saturable electronic reluctance switch comprising this low-noise, reproducible switching may be referred to as bi-stable. In some cases, a saturable electronic reluctance switch herein may provide low-noise magnetic fields. For example, the provided magnetic field may be dependent on a permanent magnet or a magnetic flux saturation of a soft ferromagnetic material. Accordingly, this may decrease a provided magnetic field’s dependence over time on the source of the magnetic flux generating the magnetic field. In some cases, a saturable electronic reluctance switch may be power efficient. For example, techniques herein may use electricity to redirect magnetic flux through a desired path rather than to generate magnetic flux via current carrying wires or by magnetizing a demagnetized hard ferromagnetic material. In some cases, at room temperature, a saturable electronic reluctance switch may be operable with less than about 1 W, 0.9 W, 0.8 W, 0.7 W, 0.6 W, 0.5 W, 0.4 W, 0.3 W, 0.2 W or 0.1 W of power.

[0066] In some cases, a saturable electronic reluctance switch herein may provide reproducible magnetic fields. For example, a saturable electronic reluctance switch herein may not depend on demagnetizing / magnetizing materials to switch magnetic fields on and off - a process that may be prone to hysteresis. In some cases, a saturable electronic reluctance switch herein may be tunable via both electronic or mechanical techniques. As such, a magnetic field output may be configured according to the needs of a particular quantum computing system or component.

[0067] The saturable electronic reluctance switches herein may provide particular advantage over other techniques by virtue of the low power dependence used for generating bistable magnetic fields. For example, magnetic flux passing through an operating point or air gap as provided by a saturable electronic reluctance switch may have no or marginal dependence on external power supplies while simultaneously providing stable magnetic fields. As such, the techniques herein mitigate dependence on ultra-high stability power supplies that may otherwise be used to generate magnetic fields. Generally, ultra-high stability power supplies may be expensive, water-cooled, impractically large, power intensive, or any combination thereof. Alternatively, herein, a saturable electronic reluctance switch may use constant sources of magnetic flux such as permanent or semi-permanent magnets that provide a consistent magnetic field. Further, currents applied to a saturable electronic reluctance switch may have limited impact on a magnetic field supplied to an operating point or air gap at least because of the current dependent saturation of soft ferromagnetic materials used to conduct magnetic flux in saturable electronic reluctance switches.Operation of Switchable Magnetic Fields

[0068] A saturable electronic reluctance switch as disclosed herein generates a switchable magnetic field by electronically altering the path of a magnetic flux provided by a magnetic flux source. In some cases, the magnetic flux source may be a permanent magnet or a semipermanent magnet. For example, the magnet may comprise Fe, Co, Ni, Sm, Nd, or an alloy thereof. In another example the permanent magnet may comprise a solenoid. In a saturable electronic reluctance switch, a magnetic flux may be electronically switched between an operating point and a shunt. In some cases, the operating point may comprise an air gap. For example, for use in a ferromagnetic fringe quadrupole herein, the air gap may generate of a magnetic field quadrupole via fringing effects of magnetic flux crossing the air gap. In some cases, the shunt may comprise a physical connector between two poles of a magnetic flux source.

[0069] A saturable electronic reluctance switch may facilitate devices, systems, and methods that leverage switching of a path taken by a magnetic flux. For example, a permanent magnet may be embodied in a saturable electronic reluctance switch to provide a field that can be turned ‘on’ and ‘off in a bi-stable step-like fashion by application of a current to an electromagnet operatively coupled to the shunt. In some cases, the term “bi-stable” may indicate a two-state magnetic flux output that can be reliably attained via repeated operations of a saturable electronic reluctance switch. In some cases, saturable electronic reluctance switches herein may be operable with current sources with stabilities of 1 A or lower.

[0070] Generally, ‘reluctance’ herein refers to the resistance presented by a given path to the ‘flow’ of magnetic flux. Magnetic flux follows the path of least reluctance while ‘flowing’ from the magnetic ‘North’ pole to magnetic ‘South’ pole. In some cases, a magnetic pole may be referred to as a first or second pole of a magnetic flux source herein. Reluctance may be inversely proportional to a material’s relative permeability. For instance, soft ferromagnetic materials such as MuMetal® or Hiperco®50 may have large relative permeabilities. In some cases, a relative permeability comprises a ratio of the permeability of a material versus the permeability of free space. In some cases, a large relative permeability may be associated with one or both of a low reluctance or a high propensity to conduct magnetic flux. In some cases, the relative permeability of a soft ferromagnetic material herein may be about 10 to about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be about 10 to about 100, about 10 to about 1,000, about 10 to about 10,000, about 10 to about 100,000, about 10 to about 1,000,000, about 10 to about 10,000,000, about 100 to about 1,000, about 100 to about 10,000, about 100 to about 100,000, about 100 to about 1,000,000, about 100 to about 10,000,000, about 1,000 to about 10,000, about 1,000 to about 100,000, about 1,000 to about 1,000,000, about 1,000 to about 10,000,000, about 10,000 to about 100,000, about 10,000 to about 1,000,000, about 10,000 to about 10,000,000, about 100,000 to about 1,000,000, about 100,000 to about 10,000,000, or about 1,000,000 to about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be about 10, about 100, about 1,000, about 10,000, about 100,000, about 1,000,000, or about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be at least about 10, about 100, about 1,000, about 10,000, about 100,000, or about 1,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be at most about 100, about 1,000, about 10,000, about 100,000, about 1,000,000, or about 10,000,000. In some cases, a soft ferromagnetic materialmay comprise an alloy. In some cases, the alloy may comprise Fe, Co, V, Ni, Si, C, Cu, Cr, Mo, Nb, or other metal or metalloids. In some cases, the soft ferromagnetic material may be a binary alloy, a ternary alloy, a quaternary alloy, or an alloy comprising five or more metal or metalloid components. For example, a soft ferromagnetic material may comprise a binary alloy of Fe and Ni. For example, a soft ferromagnetic material may comprise a ternary alloy of Fe, Ni, and Mo or a ternary alloy of Fe, Cr and V.

[0071] In some cases, a soft ferromagnetic material may be distinguished from other types of ferromagnetic materials based on coercivity. In some cases, a soft ferromagnetic material may have a coercivity of less than about 1000 A / m. In some cases, a soft ferromagnetic material may have a coercivity of about 0 to about 1000 A / m. In some cases, a coercivity of a material may be correlated to a hysteresis of the material. For example, a material with relatively low coercivity (e.g., soft ferromagnets) may de-magnetize upon removal of an applied magnetizing field. Conversely, a material with relatively high coercivity (e.g., semi-hard and hard ferromagnets) may remain magnetized after removal of an applied magnetizing field. Further, high coercivity materials may be difficult to demagnetize and may not be readily returned to a state outputting near zero or zero magnetic flux. In some cases, these high coercivity materials may remain magnetized on a permanent or near-permanent basis and may require strong demagnetizing fields to return to a de-magnetized state. In some cases, the magnetized state of a material may be associated with a relative permeability of about 1. Accordingly, the systems and methods herein may leverage the small hysteresis of soft ferromagnetic materials that renders them easily magnetized and de-magnetized. For example, a magnetic flux may be routed between multiple paths of a magnetic circuit while residual flux in a path through which magnetic flux is not desired is low. The low residual flux, in this example, is resultant from the de-magnetization of the flux guide forming the path with the relatively higher reluctance. To illustrate with a saturable electronic reluctance switch example, a magnetic flux from a permanent magnet may be directed through the shunt in the absence of an applied current due to a lower relative reluctance as compared to the path comprising the air gap. In this example, the air gap path has near zero to zero magnetic flux passing through the air gap due to its high relative reluctance and the lack of permanent magnetization of the flux guide material abutting the air gap. In some cases, this phenomenon may facilitate the bi-stable, on or off, states of magnetic switches as described herein.

[0072] Herein, ‘reluctance switching’ may comprise switching from one value of reluctance to another value. This may be from high reluctance to low reluctance. In a saturableelectronic reluctance switch herein, a magnetic circuit may be formed whenever a magnetomotive force (mmf) is applied (e.g., through a current or permanent magnet) and the generated flux is conducted through sections of air or magnetic-materials. Techniques to switch from one reluctance to another in a magnetic circuit may facilitate routing of magnetic flux through different paths of a saturable electronic reluctance switch. For example, a soft ferromagnetic material may be used to ‘guide’ flux from a permanent magnet through a path of least reluctance. In some cases, a path of least reluctance may comprise a path of otherwise high reluctance, but of relatively low reluctance for a given operating condition. Continuing the example, an air gap in a saturable electronic reluctance switch may provide a large reluctance relative to a shunt portion as described herein. However, a saturable electronic reluctance switch may be configured to increase the reluctance of the shunt portion, thereby routing magnetic flux through the otherwise relatively high reluctance air gap.

[0073] In some cases, reluctance switching herein may exploit the non-linear behavior of magnetic materials. For example, soft ferromagnetic materials as disclosed herein may be configured to saturate with magnetic flux. In some cases, this phenomenon may be combined with closed-loop magnetization schemes to provide methods, systems, and devices operating or configured to switch a path taken by a magnetic flux. In some cases, a shunt may be disposed along at least one path and may comprise a soft ferromagnetic material. In some cases, a shunt may be permanently attached to a magnetic circuit of the saturable electronic reluctance switch. In some cases, an arrangement of solenoids may be used to ‘saturate’ the shunt-pieces by application of a current, increasing their reluctance to that of vacuum. The design of shunts and solenoids used to saturate the shunts disclosed herein may prevent the current applied to the solenoid from interfering with the output magnetic field when above the saturation threshold of the material guiding the magnetic flux to the output. In some cases, the output refers to an air gap of a saturable electronic reluctance switch. Therefore, the ‘switching current’ may be isolated from the magnetic-field output. For example, a saturable electronic reluctance switch may implement a source of magnetic flux configured to provide a constant or near constant magnetic flux to the saturable electronic reluctance switch.Accordingly, a saturable electronic reluctance switch as disclosed herein may confer advantages of reproducible magnetic fields from a constant or near constant magnetic flux source while also providing an ability to remove magnetic flux from a path of ion transport (e.g., above an ion trap) when a magnetic field is not needed or is deleterious to quantum computation.

[0074] Generally, a saturable electronic reluctance switch as described herein may comprise a magnetic flux source, a soft ferromagnetic flux guide, a shunt, a current-carrying coil (e.g., a solenoid) wrapped around the shunt, or any combination thereof. In some cases, a saturable electronic reluctance switch may comprise an air gap along the soft ferromagnetic flux guide. In some cases, the air gap may he along a first path, while the shunt may he along a second path.Illustrative Saturable Magnetic Switches

[0075] In some aspects, herein are systems or devices configured to switch magnetic flux between two more paths. An illustrative saturable magnetic switch is shown in FIG. 1A. A saturable magnetic switch may comprise a source of magnetic flux 101 configured to provide a magnetic flux, a flux guide comprising a first portion 102, a second portion 103, an air gap 104 between the first portion 102 and the second portion 103, and an electromagnet 105. In some cases, the flux guide may direct magnetic flux from a first pole of the source of magnetic flux 101 to a second pole of the magnetic flux. In some cases, directing flux from the first pole may comprise passing magnetic flux through the air gap 104. For example, flux may be directed from the first portion 102 of the flux guide to the second portion 103 of the flux guide. This may result in fringing magnetic fields as the magnetic flux passes from the first portion 102 to the second portion 103 of the flux guide through the air gap 104. The electromagnet 105 may be disposed about a shunt 106. In some cases, the shunt provides a path of least reluctance to magnetic flux. As such, when no electrical current is applied to electromagnet 105, magnetic flux flows along a first path 107. Upon application of the electrical current to the electromagnet, the magnetic flux may be directed through the air gap 104 and may follow a second path 108 as shown in FIG. IB.

[0076] In some cases, the electromagnet 105 may be operable by an electrical current. In some cases, the flux guide may pass magnetic flux to a second pole of the source of magnetic flux 101. In some cases, the electromagnet is disposed about the shunt 106. In some cases, the shunt 106 may be disposed between the first portion 102 and the first portion 103. In some cases, the shunt 106 may be configured to direct the magnetic flux through the air gap 104 upon an application of electrical current to the electromagnet 105. In some cases, prior to the application of the electrical current, the magnetic flux may be configured to flow along the shunt 106 portion. In some cases, prior to the application of the electrical current, a density of the magnetic flux along the air gap 104 is less than about 1 mT, 0.1 mT, 0.01 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some cases, magnetic flux through the air gap prior toapplication of the electrical current may be referred to as the residual magnetic flux. In some cases, prior to the application of the electrical current, a reluctance of the air gap 104 portion may be greater than a reluctance of the shunt 106. In some cases, after the application of the electrical current, relative a magnetic permeability of the shunt 106 may be about 1. In some cases, after the application of the electrical current, a density of the magnetic flux along the air gap 104 comprises a magnitude of at least about 0.1 T to about 2.5 T. In some cases, after the application of the electrical current, the shunt 106 may be saturated with magnetic flux. In some cases, a reluctance of the shunt 106 may be increased upon application of the electrical current. In some cases, after the application of the electrical current the reluctance of the shunt 106 may be greater than the reluctance of the air gap 104.

[0077] In some cases, the source of magnetic flux 101 is configured to provide a magnetic flux density along the flux guide of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, or 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some cases, the source of magnetic flux provides a magnetic flux density of about 0.1 T to about 2.5 T.

[0078] In some cases, the shunt 106 comprises a toroid shape. In some cases, the electromagnet 105 comprises at least one wire coiled around the shunt 106. In some cases, the electromagnet 105 comprises at least two wires coiled around the shunt 106. In some cases, a first wire and a second wire are configured to generate opposing magnetic fields. In some cases, magnetizing in the opposite direction may cause a flux to flow in a closed loop within the shunt 106. In some cases, the first and second wire may be magnetized in a same direction. In some cases, magnetization in the same direction may be used to modulate magnetic flux in a magnetic switch (e.g., as shown in FIG.7 bottom right). Similarly, magnetizing only a first or second of at least two wires coiled around the shunt 106 may be used to module magnetic flux in a magnetic switch (e.g., as shown in the left two panels of FIG. 3B)

[0079] In some cases, the shunt 106 comprises a reluctance modulator. In some cases, the reluctance modulator may be a screw. In some cases, the reluctance modulator may be configured to adjust one or both of a reluctance of the shunt 106 or a magnetic flux along the air gap 104.

[0080] In some cases, the shunt 106 comprises at least two shunt pieces. In some cases, a wire may be coiled around a shunt piece of the at least two shunt pieces. In some cases, eachshunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces. In some cases, the electromagnet 105 comprises the coiled wire. In some cases, the coiled wire may be a solenoid. In some cases, a first shunt piece and a second shunt piece may be configured to generate opposing magnetic fields.Illustrative Toroidal Configuration

[0081] An illustrative toroidal saturable electronic reluctance switch is shown in FIG.2. The saturable electronic reluctance switch configuration shown in FIG.2 comprises a source of magnetic flux 201. The source of magnetic flux 201 may be in physical contact with a flux guide comprising a first path 202 and second path 203. In some cases, the flux guide may comprise a soft ferromagnetic material. In some cases, the soft ferromagnetic material may comprise MuMetal® or Hiperco®50. In some cases, the soft ferromagnetic material may comprise a material with a relative permeability of about 10,000 to about 10 million as disclosed herein. In some cases, the soft ferromagnetic material may comprise a material with a coercivity of less than about 1000 A / m. In some cases, the first path 202 may provide a route for magnetic flux to pass from a first pole of a source of magnetic flux source 201 to a second pole of a source of magnetic flux 201 through a shunt 204. In some cases, a shunt 204 may comprise a toroidal morphology. In some cases, an electromagnet 205 comprising coil windings may be wrapped about the shunt 204. In some cases, the coil windings may be in one, two, or more portions. For example, a first and second portion of a coil winding may be used to modulate a flow of magnetic flux through asymmetric activation of the coil windings portions. In some cases, the second path 203 may comprise an air gap 206. In some cases, a reluctance of the first path 202 may be greater than a reluctance of the second path 203 after the application of a current to the electromagnet 205.

[0082] In some cases, a path of magnetic flux through a saturable electronic reluctance switch comprising a toroidal shunt may be operable by an applied current as demonstrated in FIG. 3A. In the “oft” state, the magnetic flux may flow through a shunt portion. In some cases, an off state may indicate a lack of electrical current flowing through coil windings configured to increase a reluctance of the shunt. In some cases, a small or modulating current may flow through the coil windings to decrease or modulate a residual magnetic flux flowing through an air gap. For example, a residual magnetic flux may flow through an air gap and create a non-zero magnetic field across the air gap when no current is applied to the coil windings. Accordingly, a small amount of current may be applied to the coil windings in the off state to further mitigate residual magnetic fields along the air gap.

[0083] Still referring the FIG.3A., current may be applied to coil windings to saturate a magnetic flux of the shunt. In some cases, this may cause a reluctance of the shunt to increase. In some cases, this may route the magnetic flux from the source of magnetic flux through the air gap. In some cases, a first portion of the coil windings may be magnetized in an opposite direction of a second portion. This may result in a closed flow of magnetic flux within the shunt.

[0084] As shown in FIG.3B., a net flux leaving a shunt subject to magnetic fields generated by electrified coil windings (e.g., a solenoid) may be zero. In some cases, an asymmetric electrification of the coil windings (e.g., on the left and right side of the shunt) may be used to modulate magnetic flux within the circuit or at an air gap.

[0085] As shown in FIG.3C, a magnetic flux will typically flow through a path of least reluctance. A path of least reluctance may be provided by a shunt or by a path with a relatively smaller air gap. Generally, a path of least reluctance through a saturable electronic reluctance switch may be through a shunt. In some cases, by increasing a reluctance of the shunt as described herein, the magnetic flux may be routed through the air gap in a switchable, bi-stable manner.

[0086] In some cases, a saturable electronic reluctance switch may be represented by an equivalent magnetic circuit diagram as shown in FIG.4. For example, when no current is applied (7=0), the reluctance of the magnetic flux path comprising the shunt may be a first value (7?T-off). In some cases, this value may be less than a reluctance of the magnetic flux path comprising the air gap ( / ga). Accordingly, when no current is applied or when a residual flux modulating current is applied, a magnetic flux may flow through the magnetic flux path comprising the shunt. Conversely, when a current equal to or above a saturating current (7sat) is applied to the coil windings about the shunt, a reluctance of the magnetic flux path comprising the shunt may increase to second value (7?T-on). In some cases, the coil windings may be configured to generate a closed loop of magnetic flux within the shunt as shown in the toroidal path where I > Isatin FIG.4. In some cases, the value of / T-OH may be greater in magnitude than / ga. indicating that a path of least reluctance has shifted to the magnetic flux path comprising the air gap. In some cases, magnetic flux through the magnetic flux path comprising the air gap may be near zero prior to applying the saturating current. In some cases, a reluctance in the off state for the magnetic flux path comprising the shunt may be modulated via configuration of a cross-sectional area of the shunt. In some cases, areluctance of an air gap path / gamay be modulated via modulation of the distance between poles (e.g., as formed by a break in the flux guide) on either side of the air gap.

[0087] In some cases, as current is applied to a winding coil about a shunt, a permeability of the shunt may decrease as the material tends toward saturation. In some cases, a reluctance of the shunt may be inversely proportional to a permeability of the shunt. In some cases, as the reluctance of the shunt increases, a greater proportion of magnetic flux from the source of magnetic flux may pass through the air gap. In some cases, a current applied to a winding coil about the shunt may decrease the permeability of the shunt until it reaches a similar permeability as vacuum. In some cases, the shunt may form a closed magnetic circuit such that circular magnetization precludes a contribution of magnetic flux to other portions of the circuit (e.g., the air gap). Generally, techniques herein may leverage magnetic flux saturation of soft ferromagnetic materials such that a magnetic field passed through an air gap of a saturable electronic reluctance switch may be stable upon saturation of a shunt. For example, in some cases, saturation of the shunt may result in the flux of a source of magnetic flux passing through the air gap. In some cases, the source of magnetic flux may be a permanent magnet, which provides a constant source of magnetic flux. Accordingly, a saturable electronic reluctance switch may be configured to generate on and off states which may depend on application of a current to winding coils (e.g., an electromagnet) about a shunt.

[0088] In some cases, application of electrical current to a shunt herein may direct stable magnetic fields to be generated about an air gap (e.g., the air gap 206 of FIG.2). Herein, application of an electrical current may saturate a shunt with magnetic flux, thereby directing magnetic flux from a source of magnetic flux through a path not comprising the shunt. As described, the source of magnetic flux herein may be a permanent or semi-permanent magnet that can generate magnetic flux on a permanent or near permanent basis. The permanent or near permanent output of magnetic flux may be as opposed to the transient generation of magnetic flux as a function of applied current, for example as with an electromagnet, solenoid, or current carrying wire. As the source of magnetic flux may provide an effectively constant magnetic flux, the magnetic fields resultant from the magnetic flux may have exceptional stability.

[0089] In some cases, exceptional stability may be compared versus magnetic fields generated transiently by electromagnets, solenoids, or current carrying wires (CCW). For example, a magnetic field generated transiently by an electromagnet, solenoid, or CCW may have instabilities (e.g., magnetic field fluctuations) in proportion to noise of the currentsource on which generation of the magnetic field depends. As saturable electronic reluctance switches herein may provide magnetic fields from a permanent or near permanent source of magnetic flux, the noise of the magnetic field output by a saturable electronic reluctance switch may have a current source noise dependence on the order of about 106of that of a comparable electromagnet, solenoid, or CCW magnetic field generator. For example, a current source used to generate a magnetic field with a given Tesla (T) would be expected to have noise of approximately one million (106) times greater magnitude than that of a saturable electronic reluctance switch herein. This provides particular advantage by decreasing complexity of power sources used to operate saturable electronic reluctance switches and devices implementing the same. For example, to achieve the same strength of magnetic field with equivalent noise in a saturable electronic reluctance switch as compared to an electromagnet, solenoid, or CCW, the saturable electronic reluctance switch may use a current source with a million times greater noise. Generally, the greater the noise of the power source, the lower the complexity and cost. As such, tolerance of greater power source (electrical current) noise provides particular advantage by decreasing complexity of devices such as quantum computers implementing the saturable electronic reluctance switches herein. In some cases, for an equivalent power source, the noise in a magnetic field generated by a magnetic switch herein may about IO1. 102. IO3. 1CH, 10s. 106or less of the magnitude of noise in a magnetic field generated by a transient magnetic field source such as an electromagnet, solenoid, or current carrying wire.

[0090] Generally, a saturable electronic reluctance switch comprising a toroid or other shape configured to generate a closed magnetic path may comprise one or more soft ferromagnetic materials. For example, the saturable electronic reluctance switch may use a first material for guiding flux and a second material to form the shunt. In some cases, the first and second material may be the same material. In some cases, the flux path comprises the shunt and forms a single piece. For example, a saturable electronic reluctance switch may comprise a source of magnetic flux disposed between a path comprising an air gap and a path comprising the shunt. In some cases, the first and second paths may be physically connected but differentiated via the relative reluctances between two paths (e.g., as shown in FIG.4).Illustrative Linear Configuration

[0091] In some cases, a shunt may comprise a linear configuration as shown in FIG.5A. In some cases, the shunt may comprise a different material that a remainder for a flux guide. For example, the shunt may comprise a material with a lower saturation flux density than the fluxguide. Continuing the example, in some cases, the flux guide may comprise Hiperco®50, and the shunt may comprise MuMetal®. In some cases, both the shunt and the flux guide may comprise large magnetic permeabilities. In some cases, the shunt may comprise two or more shunt pieces. In some cases, the shunt pieces may comprise coil windings similar to the coil windings serving a similar purpose as those shown in FIGs. 1-4.

[0092] In some cases, the linear saturable electronic reluctance switch configuration may be configured to route a magnetic flux from a first path to a second path. For example, a current applied to coil windings about the shunt may be magnetized to increase a reluctance of a first path relative to a second path, thereby diverting the magnetic flux through the second path comprising the lower relative reluctance. For example, as shown in FIG.5B, application of a saturating current ( / Sat) may generate a closed magnetic flux within the shunt of a first path and direct magnetic flux from the source of magnetic flux through an air gap of the second path. In some cases, the shunt may be magnetized in opposite directions with an equal magnitude of magnetization. This may increase the reluctance of the path comprising the shunt while confining magnetic flux generated by the coil windings to be contained in the shunt. FIG.5C shows a path of least reluctance for a magnetic flux as dependent on a shunt or relative air gap size as described for FIG.3C.

[0093] In some cases, a linear saturable electronic reluctance switch may implement a soft ferromagnetic material in the shunt with a lower saturation flux density that a saturation flux density of a material used in the rest of a flux guide. In some cases, the shunt may be driven far into saturation without saturating the guide. As such, the guide may continue to shunt magnetic flux between both saturating coils. In some cases, this may provide particular utility by decreasing the generation of stray -fields of the coils above shunt-piece saturation without a particular geometry of the shunt.Illustrative Adjustable Configurations

[0094] In some cases, configurable magnetic flux sources may be used to as a source of magnetic flux. For example, semi-permanent magnetic materials may be used as a flux source. The techniques herein may provide particular utility in facilitating the use of such materials by isolating them from demagnetizing fields. As such, a degree of magnetization of semi-permanent materials may be configured without risk of uncontrolled alteration of the magnetic flux provided by the semi-permanent magnetic material during operation of saturable electronic reluctance switch. In some cases, the degree of magnetic flux provided by the semi-permanent magnetic material may be configured in-situ to confer a configurablesource of magnetic flux. In some cases, the coil windings of the shunt, a coil winding about the source of magnetic flux, or both may be used to alter a degree of magnetization of a semipermanent magnetic material acting as a flux source. This process may be controlled so as to occur upon demand rather than as a deleterious side-effect of normal operations of the saturable electronic reluctance switch. In some cases, a semi-permanent magnetic material may comprise Alnico or other alloys of iron, Co, Ni, Sm, or Nd.

[0095] In some cases, as shown in FIG.6, a degree of magnetic flux delivered to an air gap may be in part dependent on a geometry of a saturable electronic reluctance switch. In some cases, an amount of flux delivered to an air gap may be configurable based on a reluctance of a shunt. In some cases, a reluctance of the shunt may be adjustable based on a physical component used to change the geometry of the shunt. For example, as shown in FIG.6, a screw may be controlled either physically or via electrical control of a degree of insertion or other placement of the physical component. In some cases, the adjustment of the physical component may comprise adjusting a reluctance of a path comprising a shunt portion such that more or less flux is pass through an air gap.

[0096] In some cases, a coil winding may be implemented in as shown in FIG. 7. The coil winding may facilitate directional biasing to mitigate residual flux across an air gap in an off state of a saturable electronic reluctance switch. In some cases, the coil winding may be wound about a source of magnetic flux, a shunt, or both. In some cases, biasing a coil winding may be used to fine-tune the residual magnetic flux by introducing an additional magnetic flux into a saturable electronic reluctance switch. For example, a diode may be used to control a directionality of an applied current as shown in the magnetic circuit diagrams of FIG. 7. In some cases, a current is applied unidirectionally through a coil winding about a shunt to facilitate routing of magnetic flux as disclosed herein. Alternatively, a current may be applied bidirectionally through coil windings about a shunt. In this alternative cases, two portions of coil windings of a shunt may be configured to output fields in the same direction, which can be used to augment the output flux. Generally, the configurability of the biasing of the winding coils may render a saturable electronic reluctance switch configured to mitigate or fine tune a magnetic field in an air gap in an off state.

[0097] In some cases, modulating residual flux may be performed with low complexity current sources. For example, modulating residual flux may be performed to mitigate magnetic fields to which an ion is exposed during transport. Accordingly, the magnetic field stability in an off state may be of lower importance than mitigating the magnitude of residualmagnetic flux. Further, the current supplied to modulate residual flux may be small and may not necessitate highly complex or expensive current sources that may be required to generate stable magnetic fields of a greater magnitude.Illustrative Application of a Saturable Electronic Reluctance Switch

[0098] A saturable electronic reluctance switch as described herein may be applied in a system or device configured to generate a magnetic field quadrupole. In some cases, the device or system may comprise (a) a source of magnetic flux, (b) a flux guide comprising a first path and a second path; and (c) an electromagnet. In some cases, the electromagnet may be configured to switch a flow of the magnetic flux from the first path to the second path. In some cases, the second path may be configured to generate a magnetic field quadrupole. In some cases, the first path and the second path may be as described for FIG. 1A-1B. In some cases, (a)-(c) may form a portion of a magnetic circuit. In some cases, the magnetic field quadrupole may be formed by the magnetic circuit and a second magnetic circuit. In some cases, one or both of the magnetic circuit and the second magnetic circuit may comprise a saturable electronic reluctance switch as disclosed herein.

[0099] In some cases, the system may further comprise an ion trap, wherein the source of magnetic flux, the flux guide, and the electromagnet are proximate to a first side of the ion trap, and the magnetic field quadrupole is proximate to a second side of the ion trap. For example, the magnetic field quadrupole may be projected to a region above the second ion trap. Continuing the example, the magnetic field quadrupole may be configured to provide a particular magnetic field gradient at a particular height above the second ion trap. In some cases, ion trap may be configured to trap an ion on the second side of the ion trap. In some cases, the ion trap may be configured trap the ion proximate to a nil line of the magnetic field quadrupole.

[0100] In some cases, prior to application of an electrical current to the electromagnet, the first path comprises a first reluctance lesser than a second reluctance of the second path. In some cases, after an application of an electrical current to the electromagnet, the first path comprises a first reluctance greater than a second reluctance of the second path. In some cases, the electromagnet comprises a solenoid coiled around a shunt.

[0101] In some cases, the flux guide comprises an air gap along the second path. In some cases, fringing magnetic fields passed through the air gap may be configured to generate amagnetic field quadrupole when paired with a second magnetic circuit providing a fringing magnetic field.

[0102] In some cases, the system or device further comprises a current source configured to apply a biasing current to the electromagnet. In some cases, the biasing current may be configured to decrease a remnant flux along the air gap. In some cases, a density of the remnant flux along the air gap upon application of the biasing current may be at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

[0103] In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some cases, a particular magnitude of a magnetic field gradient may be generated at a particular height as described herein.

[0104] In some cases, the flux guide comprises a material with a saturation of flux density of at least about 0 T, 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some cases, the electromagnet comprises a shunt. In some cases, the shunt comprises a material with a saturation flux density of at least about 0 T, 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some cases, the saturation flux density of the flux guide may be greater than a saturation flux density of the shunt.

[0105] In some cases, the source of magnetic flux may be configured to provide a magnetic flux density along the flux guide of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, or 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some cases, the source of magnetic flux may be configured to provide a magnetic flux density along the flux guide of about 0.1 T to about 2.5 T. In some cases, the source of magnetic flux may provide a configurable magnetic flux. In some cases, the source of magnetic flux may comprise a semi-hard ferromagnetic material. For example, an Alnico flux source may be magnetized or demagnetized to provide a particular magnetic flux. In some cases, the source of magnetic flux may be configured by a coil winding about the source of magnetic flux. For example, a solenoid or second electromagnet about the source of magnetic flux may be used to configure a magnetization of the magnetic flux. Insome cases, the source of magnetic flux is a permanent magnet. In some cases, the permanent magnet comprises Fe, Ni, Sm, Co, Nd, or any combination thereof.

[0106] In some cases, the flux guide comprises a soft ferromagnetic material. In some cases, the flux guide comprises MuMetal® or Hiperco®50. In some cases, the shunt and the flux guide comprise the same material. In some cases, the shunt and the flux guide comprise a different material. In some cases, the electromagnet is a solenoid. In some cases, the electromagnet comprises a first electromagnet portion and a second electromagnet portion. In some cases, each of the first electromagnet portion and the second electromagnet portion are configured to receive an electrical current in both forward and reverse directions. In some cases, the permanent magnet is disposed between the shunt and the air gap portion. In some cases, a saturation flux density of the shunt is lower than a saturation flux density of the flux guide. In some cases, the saturation flux density of the shunt, the saturation flux density of the flux guide, or both, is at least about 0 T, 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T .

[0107] In some cases, the electromagnet is configured to modulate residual magnetic flux through the air gap portion. In some cases, upon modulation of the residual flux through the air gap a magnetic flux density along the air gap is of less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some cases, the electromagnet is in electrical communication with a diode. In some cases, the diode may be able to apply a forward or reverse current to the electromagnet as needed. For example, a current in a forward direction may contribute magnetic flux through an air gap of the circuit, while a current in the reverse direction may remove magnetic flux through an air gap of the circuit.Ferromagnetic Fringe Quadrupole

[0108] In several aspects herein are implementations and uses of ferromagnetic fringe quadrupoles (FFQ). In some cases, a ferromagnetic fringe quadrupole may implement a saturable electronic reluctance switch as disclosed herein. Techniques for generating magnetic field quadrupole using a ferromagnetic fringe quadrupole herein may exploit the fringe-effect to project quadrupolar magnetic field topologies to a region of interest. In some cases, the region of interest may be located above an ion trap. In some cases, a magnetic field quadrupole may align at least in part spatially with a pseudopotential well used to trap an ion. For example, an ion may be transported to a region of a quantum computing system or module for execution of a quantum logic operation. In some cases, execution of a quantumlogic operation may benefit from large magnetic field gradients to induce Zeeman splitting for an ion subject to the quantum logic or gating operation. Accordingly, the fringe-effect may be used to generate a quadrupolar magnetic field, comprising a large magnetic field gradient, to a region above the ion trap to which an ion may be proximal.

[0109] The implementations and uses of ferromagnetic fringe quadrupoles herein may be used to provide magnetic field gradients on the order 10s to 1000s of T / m with millimetersized devices. Further, the devices disclosed herein may be readily machinable to tailor a desired magnetic field topology in the vicinity of trapped ions. For example, magnetic field strength, magnetic field topology, or both may be readily adjusted. Continuing the example, magnetic field strength may be tuned via varying an extent of magnetization of a ferromagnetic fringe quadrupole. In another continuation of the example, the topology of the magnetic field may be adjusted via asymmetric magnetization of elements used to generate a magnetic field, in some cases shifting a nil line of a magnetic field quadrupole.

[0110] Additionally, the implementations and uses of ferromagnetic fringe quadrupole herein may be configurable to mitigate risks of motional heating of ions. In some cases, motional heating of ions may result in phase accumulation that may require expensive or complicated correcting during operation of a quantum computing system. Herein, techniques may provide minimal resistive heating while incurring such heating effects away from points of operation, facilitating higher fidelity quantum computation while relaxing cooling demands and cooling difficulty. More specifically, the ferromagnetic fringe quadrupoles disclosed herein may provide particular utility in mitigating thermal management requirements of quantum computers. The systems and devices herein generating or providing ferromagnetic fringe quadrupoles may isolate a point of operation from the magnetic flux source of the ferromagnetic fringe quadrupoles. For example, ferromagnetic fringe quadrupoles may project magnetic field quadrupoles above a surface of an ion trap. In some cases, the output of a ferromagnetic fringe quadrupole device may be thermally isolated from the magnetic flux source used to generate the magnetic field. Further, components such as heat sinks or other cooling system may be disposed away from an operating zone of a quantum computer. For example, a saturable electronic reluctance switch used in formation of a ferromagnetic fringe quadrupole that may build some heat may be disposed below an ion trap. As such, cooling components may similarly be implemented below the ion trap without interfering with scalability or function of the quantum computing system. For example, a copper or other heat dissipating material base may be disposed beneath a saturable electronic reluctanceswitch or ferromagnetic fringe quadrupole and be used to dissipate heat away from an operating point.[oni] In some cases, a solenoid may be used to apply electric currents in a saturable electronic reluctance switch or ferromagnetic fringe quadrupoles generating or providing magnetic field quadrupoles. For example, a shunt may be driven to a higher reluctance by a solenoid (e.g., coil windings). As such, a magnetic flux may be directed to another path or operating point (e.g., an air gap). Application of electric current via a solenoid may provide particular advantages in thermal management by decreasing the current used to generate a desired magnetic flux. For example, coil windings (e.g., of a solenoid) may use a lower current than a comparable uncoiled wire when generating magnetic fields.Operation of Ferromagnetic Fringe Quadrupoles

[0112] A ferromagnetic fringe quadrupole, or a method, system, or device implementing or magnetic field quadrupole herein, may comprise a soft ferromagnet structure that facilitates ‘projection’ of a magnetic field quadrupole into a vicinity of trapped ions when magnetic flux flows through an air gap. In some cases, a system or device implementing or providing a ferromagnetic fringe quadrupole may comprise a set of ferromagnetic poles that ‘guide’ the magnetic field from a magnetic flux source to an operating point or air gap. At the operating point, the magnetic field may traverse an air gap between poles of a material used to guide the magnetic flux. The ‘fringe-effect’ may describe edge-behavior of magnetic fields when they traverse an air gap between two magnetic poles. In some cases, at the edge of an air gap a magnetic field may ‘fringe’ or ‘extend’ beyond the extent of the air gap. The shape of the poles at the operation point may be selected to promote the magnetic ‘fringe-field’ generated about the air gap. In some cases, the orientation of the poles may facilitate the generation of fringe fields specifically in the configuration of a magnetic field quadrupole. In some cases, the magnetic field quadrupole may be of particular utility in a trapped ion quantum computer. Through the effect of fringing, the magnetic field quadrupole may be effectively projected away from the device itself. Hence, the device may be used to project a quadrupolar magnetic field through other components of a device incorporating a ferromagnetic fringe quadrupole. For example, a magnetic field quadrupole may be provided above an ion-trap layer of a quantum computer module to facilitate a logic operation performed with the ion.

[0113] In some cases, a magnetic field quadrupole herein may comprise a magnetic field nil line in close proximity to trapped ions. In some cases, the magnetic field nil line may be projected along or normal to a direction of ion transport of a quantum computing module. Insome cases, the magnetic field quadrupole may comprise a large magnetic gradient. For example, a saturable electronic reluctance switch or ferromagnetic fringe quadrupole system as disclosed herein may be configured to provide large maximum magnetic fields while also providing a zero or near zero magnetic flux proximal to the maximum of the provided magnetic field gradient.

[0114] In some cases, the generation of a magnetic field of a specific topology may be of particular utility in performing quantum logic operations in a quantum computer. For example, large magnetic field gradients may facilitate splitting of degenerate states in ions used in trapped ion quantum computing. In some cases, this splitting may facilitate gating or logic operations. In some cases, saturable electronic reluctance switch devices or systems as disclosed herein may be paired to form magnetic field quadrupoles via interaction of the fringe fields of two proximal saturable electronic reluctance switch. For example, two appropriately aligned air gaps of two saturable electronic reluctance switches may generate or provide magnetic field quadrupoles. In some cases, these magnetic field quadrupoles may provide regions of zero or near-zero magnetic flux (e.g., along a nil line) proximal to large magnetic fields fluxes, thereby establishing a steep gradient.Illustrative Ferromagnetic Fringe Quadrupole

[0115] In some aspects herein is a ferromagnetic fringe quadrupole. A ferromagnetic fringe quadrupole may flow magnetic flux through a magnetic circuit comprising soft ferromagnetic flux guides. In some cases, the system or device comprises at least one magnetic circuit comprising a soft ferromagnetic material and an ion trap proximate to the at least one magnetic circuit. In some cases, the at least one magnetic circuit comprises a first magnetic circuit and a second magnetic circuit. In some cases, the magnetic circuit may be configured to provide a magnetic field quadrupole proximate to the ion trap and on an opposite side of the ion trap from the at least one magnetic circuit. In some cases, the ion trap is configured to trap an ion in a pseudopotential well. In some cases, the magnetic circuit comprises at least one saturable electronic reluctance switch as described herein. In some cases, the magnetic field quadrupole may be formed by fringing magnetic fields. For example, magnetic flux passing through an air gap may fringe and project magnetic fields away from the air gap. As such, a magnetic field quadrupole on the opposite side of the ion trap from the at least one magnetic circuit may be formed by fringing magnetic fields generated by the at least one magnetic circuit. In some cases, the magnetic circuit comprises a source of magnetic flux. Insome cases, the magnetic circuit comprises a flux guide configured to guide magnetic flux through the flux guide.

[0116] In some cases, the magnetic field quadrupole comprises a magnetic field nil line along an axis extending away from a surface of the ion trap. In some cases, the magnetic field quadrupole comprises a magnetic field nil line along a surface of the ion trap. In some cases, a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

[0117] In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some cases, the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some cases, the magnetic field quadrupole may be configured to provide a particular magnetic field gradient at a particular height above an ion trap or a quadrupole.

[0118] In some cases, the first magnetic circuit and the second magnetic circuit form a quadrupole. In some cases, the first magnetic circuit is configured to provide a first magnetic field and the second magnetic circuit is configured to provide a second magnetic field. In some cases, the first magnetic field comprises a different magnetic field strength than second magnetic field. In some cases, the system is configured to shift a position of the magnetic field nil line.

[0119] In some cases, the ferromagnetic fringe quadrupole comprises a ring quadrupole. In some cases, the ring quadrupole comprises four quadrants, the four quadrants comprising: (i) a first quadrant comprising a first magnetic pole of the first magnetic circuit, (ii) a second quadrant comprising a second magnetic pole of the first magnetic circuit, (iii) a third quadrant comprising a first magnetic pole of the second magnetic circuit, and (iv) a fourth quadrant comprising a second magnetic pole of the second magnetic circuit.

[0120] In some cases, a height of an ion above a ferromagnetic fringe quadrupole herein may be about 10 pm to about 3,000 pm. In some cases, a height of an ion above a ferromagnetic fringe quadrupole herein may be about 10 pm to about 40 pm, about 10 pm to about 50 pm, about 10 pm to about 100 pm, about 10 pm to about 250 pm, about 10 pm to about 500 pm, about 10 pm to about 750 pm, about 10 pm to about 1,000 pm, about 10 pm to about 1,500 pm, about 10 pm to about 2,000 pm, about 10 pm to about 2,500 pm, about 10 pm to about 3,000 pm, about 40 pm to about 50 pm, about 40 pm to about 100 pm, about 40 pm to about 250 pm, about 40 pm to about 500 pm, about 40 pm to about 750 pm, about 40 pm to about1,000 pm, about 40 pm to about 1,500 pm, about 40 pm to about 2,000 pm, about 40 pm to about 2,500 pm, about 40 pm to about 3,000 pm, about 50 pm to about 100 pm, about 50 pm to about 250 pm, about 50 pm to about 500 pm, about 50 pm to about 750 pm, about 50 pm to about 1,000 pm, about 50 pm to about 1,500 pm, about 50 pm to about 2,000 pm, about 50 pm to about 2,500 pm, about 50 pm to about 3,000 pm, about 100 pm to about 250 pm, about 100 pm to about 500 pm, about 100 pm to about 750 pm, about 100 pm to about 1,000 pm, about 100 pm to about 1,500 pm, about 100 pm to about 2,000 pm, about 100 pm to about 2,500 pm, about 100 pm to about 3,000 pm, about 250 pm to about 500 pm, about 250 pm to about 750 pm, about 250 pm to about 1,000 pm, about 250 pm to about 1,500 pm, about 250 pm to about 2,000 pm, about 250 pm to about 2,500 pm, about 250 pm to about 3,000 pm, about 500 pm to about 750 pm, about 500 pm to about 1,000 pm, about 500 pm to about 1,500 pm, about 500 pm to about 2,000 pm, about 500 pm to about 2,500 pm, about 500 pm to about 3,000 pm, about 750 pm to about 1,000 pm, about 750 pm to about 1,500 pm, about 750 pm to about 2,000 pm, about 750 pm to about 2,500 pm, about 750 pm to about 3,000 pm, about 1,000 pm to about 1,500 pm, about 1,000 pm to about 2,000 pm, about 1,000 pm to about 2,500 pm, about 1,000 pm to about 3,000 pm, about 1,500 pm to about 2,000 pm, about 1,500 pm to about 2,500 pm, about 1,500 pm to about 3,000 pm, about 2,000 pm to about 2,500 pm, about 2,000 pm to about 3,000 pm, or about 2,500 pm to about 3,000 pm. In some cases, a height of an ion above a ferromagnetic fringe quadrupole herein may be about 10 pm, about 40 pm, about 50 pm, about 100 pm, about 250 pm, about 500 pm, about 750 pm, about 1,000 pm, about 1,500 pm, about 2,000 pm, about 2,500 pm, or about 3,000 pm. In some cases, a height of an ion above a ferromagnetic fringe quadrupole herein may be at least about 10 pm, about 40 pm, about 50 pm, about 100 pm, about 250 pm, about 500 pm, about 750 pm, about 1,000 pm, about 1,500 pm, about 2,000 pm, or about 2,500 pm. In some cases, the height of the ion above the ferromagnetic fringe quadrupole may higher if an ion trap is disposed between the ferromagnetic fringe quadrupole. In some cases, the height of the ion above the ferromagnetic fringe quadrupole may be lower if the ferromagnetic fringe quadrupole protrudes through the ion trap.

[0121] In some cases, a height of an ion within a magnetic field quadrupole is about 50 pm to about 600 pm. In some cases, a height of an ion within a magnetic field quadrupole is about 50 pm to about 100 pm, about 50 pm to about 150 pm, about 50 pm to about 200 pm, about 50 pm to about 250 pm, about 50 pm to about 300 pm, about 50 pm to about 350 pm, about 50 pm to about 400 pm, about 50 pm to about 450 pm, about 50 pm to about 500 pm, about50 pm to about 550 pm, about 50 pm to about 600 pm, about 100 pm to about 150 pm, about 100 pm to about 200 pm, about 100 pm to about 250 pm, about 100 pm to about 300 pm, about 100 pm to about 350 pm, about 100 pm to about 400 pm, about 100 pm to about 450 pm, about 100 pm to about 500 pm, about 100 pm to about 550 pm, about 100 pm to about 600 pm, about 150 pm to about 200 pm, about 150 pm to about 250 pm, about 150 pm to about 300 pm, about 150 pm to about 350 pm, about 150 pm to about 400 pm, about 150 pm to about 450 pm, about 150 pm to about 500 pm, about 150 pm to about 550 pm, about 150 pm to about 600 pm, about 200 pm to about 250 pm, about 200 pm to about 300 pm, about 200 pm to about 350 pm, about 200 pm to about 400 pm, about 200 pm to about 450 pm, about 200 pm to about 500 pm, about 200 pm to about 550 pm, about 200 pm to about 600 pm, about 250 pm to about 300 pm, about 250 pm to about 350 pm, about 250 pm to about 400 pm, about 250 pm to about 450 pm, about 250 pm to about 500 pm, about 250 pm to about 550 pm, about 250 pm to about 600 pm, about 300 pm to about 350 pm, about 300 pm to about 400 pm, about 300 pm to about 450 pm, about 300 pm to about 500 pm, about 300 pm to about 550 pm, about 300 pm to about 600 pm, about 350 pm to about 400 pm, about 350 pm to about 450 pm, about 350 pm to about 500 pm, about 350 pm to about 550 pm, about 350 pm to about 600 pm, about 400 pm to about 450 pm, about 400 pm to about 500 pm, about 400 pm to about 550 pm, about 400 pm to about 600 pm, about 450 pm to about 500 pm, about 450 pm to about 550 pm, about 450 pm to about 600 pm, about 500 pm to about 550 pm, about 500 pm to about 600 pm, or about 550 pm to about 600 pm. In some cases, a height of an ion within a magnetic field quadrupole is about 50 pm, about 100 pm, about 150 pm, about 200 pm, about 250 pm, about 300 pm, about 350 pm, about 400 pm, about 450 pm, about 500 pm, about 550 pm, or about 600 pm. In some cases, a height of an ion within a magnetic field quadrupole is at least about 50 pm, about 100 pm, about 150 pm, about 200 pm, about 250 pm, about 300 pm, about 350 pm, about 400 pm, about 450 pm, about 500 pm, or about 550 pm.

[0122] In some cases, a system or device implementing a saturable electronic reluctance switch or providing a magnetic field quadrupole as disclosed herein may configured to generate a particular magnetic field gradient at a particular height. In some cases, the height may be relative to a surface of an ion trap. In some cases, the surface may be relative to the poles of a saturable electronic reluctance switch or magnetic circuit used to form the magnetic field quadrupole. In some cases, the height may be about 50 pm, about 100 pm, about 150 pm, about 200 pm, about 250 pm, about 300 pm, about 350 pm, about 400 pm,about 450 pm, about 500 pm, about 550 pm, or about 600 pm. In some cases, a magnetic field gradient at any of the preceding heights may be configured to be about 10 T / m to about 2,000 T / m. In some cases, a magnetic field gradient at any of the preceding heights may be configured to be about 10 T / m to about 100 T / m, about 10 T / m to about 200 T / m, about 10 T / m to about 300 T / m, about 10 T / m to about 400 T / m, about 10 T / m to about 500 T / m, about 10 T / m to about 600 T / m, about 10 T / m to about 700 T / m, about 10 T / m to about 800 T / m, about 10 T / m to about 900 T / m, about 10 T / m to about 1,000 T / m, about 10 T / m to about 2,000 T / m, about 100 T / m to about 200 T / m, about 100 T / m to about 300 T / m, about 100 T / m to about 400 T / m, about 100 T / m to about 500 T / m, about 100 T / m to about 600 T / m, about 100 T / m to about 700 T / m, about 100 T / m to about 800 T / m, about 100 T / m to about 900 T / m, about 100 T / m to about 1,000 T / m, about 100 T / m to about 2,000 T / m, about 200 T / m to about 300 T / m, about 200 T / m to about 400 T / m, about 200 T / m to about 500 T / m, about 200 T / m to about 600 T / m, about 200 T / m to about 700 T / m, about 200 T / m to about 800 T / m, about 200 T / m to about 900 T / m, about 200 T / m to about 1,000 T / m, about 200 T / m to about 2,000 T / m, about 300 T / m to about 400 T / m, about 300 T / m to about 500 T / m, about 300 T / m to about 600 T / m, about 300 T / m to about 700 T / m, about 300 T / m to about 800 T / m, about 300 T / m to about 900 T / m, about 300 T / m to about 1,000 T / m, about 300 T / m to about 2,000 T / m, about 400 T / m to about 500 T / m, about 400 T / m to about 600 T / m, about 400 T / m to about 700 T / m, about 400 T / m to about 800 T / m, about 400 T / m to about 900 T / m, about 400 T / m to about 1,000 T / m, about 400 T / m to about 2,000 T / m, about 500 T / m to about 600 T / m, about 500 T / m to about 700 T / m, about 500 T / m to about 800 T / m, about 500 T / m to about 900 T / m, about 500 T / m to about 1,000 T / m, about 500 T / m to about 2,000 T / m, about 600 T / m to about 700 T / m, about 600 T / m to about 800 T / m, about 600 T / m to about 900 T / m, about 600 T / m to about 1,000 T / m, about 600 T / m to about 2,000 T / m, about 700 T / m to about 800 T / m, about 700 T / m to about 900 T / m, about 700 T / m to about 1,000 T / m, about 700 T / m to about 2,000 T / m, about 800 T / m to about 900 T / m, about 800 T / m to about 1,000 T / m, about 800 T / m to about 2,000 T / m, about 900 T / m to about 1,000 T / m, about 900 T / m to about 2,000 T / m, or about 1,000 T / m to about 2,000 T / m. In some cases, a magnetic field gradient at any of the preceding heights may be configured to be about 10 T / m, about 100 T / m, about 200 T / m, about 300 T / m, about 400 T / m, about 500 T / m, about 600 T / m, about 700 T / m, about 800 T / m, about 900 T / m, about 1,000 T / m, or about 2,000 T / m. In some cases, a magnetic field gradient at any of the preceding heights may be configured to be at least about 10 T / m, about 100 T / m, about 200 T / m, about 300 T / m, about400 T / m, about 500 T / m, about 600 T / m, about 700 T / m, about 800 T / m, about 900 T / m, or about 1,000 T / m.

[0123] In some cases, a ferromagnetic fringe quadrupole may comprise a linear quadrupole. In some cases, the linear quadrupole may comprise four sections. In some cases, the linear quadrupole comprises: (i) a first magnetic pole of the first magnetic circuit, (ii) a second magnetic pole of the first magnetic circuit, (iii) a first magnetic pole of the second magnetic circuit, and (iv) a second magnetic pole of the second magnetic circuit. In some cases, the first and second magnetic poles of the first magnetic circuit are arranged between the first and second magnetic poles of the second magnetic circuit. In some cases, the linear quadrupole is configured to generate the magnetic field nil line along a surface of the ion trap.

[0124] In some cases, the first magnetic circuit and the second magnetic circuit form a plurality of quadrupoles. In some cases, the system or device comprises a conductive material proximate to the at least one magnetic circuit and on an opposite side of the at least one magnetic circuit to the ion trap. In some cases, the conductive material dissipates heat generated upon use of the system or device. In some cases, the conductive material is copper.

[0125] In some cases, a relative permeability of the soft ferromagnetic material may be about 10 to about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be about 10 to about 100, about 10 to about 1,000, about 10 to about 10,000, about 10 to about 100,000, about 10 to about 1,000,000, about 10 to about 10,000,000, about 100 to about 1,000, about 100 to about 10,000, about 100 to about 100,000, about 100 to about 1,000,000, about 100 to about 10,000,000, about 1,000 to about 10,000, about 1,000 to about 100,000, about 1,000 to about 1,000,000, about 1,000 to about 10,000,000, about 10,000 to about 100,000, about 10,000 to about 1,000,000, about 10,000 to about 10,000,000, about 100,000 to about 1,000,000, about 100,000 to about 10,000,000, or about 1,000,000 to about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be about 10, about 100, about 1,000, about 10,000, about 100,000, about 1,000,000, or about 10,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be at least about 10, about 100, about 1,000, about 10,000, about 100,000, or about 1,000,000. In some cases, the relative permeability of a soft ferromagnetic material herein may be at most about 100, about 1,000, about 10,000, about 100,000, about 1,000,000, or about 10,000,000. In some cases, the soft ferromagnetic material comprises Hiperco®50 or MuMetal®.Illustrative Ring Quadrupole

[0126] As shown in FIG.8A, a ferromagnetic fringe quadrupole may comprise ring quadrupole. A ring quadrupole may be formed by four magnetic poles disposed in four quadrants. For example, two saturable electronic reluctance switches comprising air gaps as described herein may be paired to form a ring quadrupole. In some cases, a distance of an air gap for a magnetic circuit used in the ring quadrupole may be used to configure the distance between the poles of two magnetic circuits. Generally, a flux guide comprising an air gap may taper towards the air gap. In some cases, the flux guide may comprise a high permeability ferromagnetic material. In some cases, the high permeability ferromagnetic material may comprise a soft ferromagnetic material. In some cases, the air gaps of the two magnetic circuits may be different. In some cases, the distance between the air gaps of the two magnetic circuits may be less than, greater to, or equal to an air gap of one or both of the magnetic circuits. Generally, the air gap of a magnetic circuit may be formed by a break in a flux guide of the magnetic circuit. For example, a flux guide may direct magnetic flux form a first pole of a magnetic flux source through the flux guide and to the second pole of the magnetic flux source. In some cases, this flux guide may comprise the air gap. In some cases, the air gap may be configured to promote fringing effects of magnetic flux passing through the air gap. As such, the ring quadrupole formed as described may be configured to form a magnetic field quadrupole upon passing magnetic flux through the air gaps of the magnetic circuits. In some cases, the fringing effect may be leveraged to design or select for particular magnetic field quadrupole topologies. For example, a magnitude of magnetic flux flowing through the respective magnetic circuits, a physical configuration or design of the areas about the air gap (e.g., flux guide thickness, cross sectional area, air gap distance, separation between air gaps of magnetic circuits, etc.), or both may be used to customize a magnetic field quadrupole generated by a ring quadrupole.

[0127] In some cases, the magnetic field quadrupole may be formed above an ion trap as shown in FIG.8B. In some cases, an ion trap may comprise electrodes configured to trap an ion in a pseudopotential well. This may be performed to transport the ion among components, modules, or chips of a trapped ion quantum computer. In some cases, the electrodes may be configured to trap an ion in three dimensions. For example, an ion may be transported to a region above an ion trap proximal to a quadrupole as described herein. In some cases, the ion may be transported to a particular point above the magnetic field quadrupole so as to exposethe ion to a particular magnetic field condition. For example, the ion may be transported to a region of high magnetic field gradient.

[0128] In some cases, a magnetic field quadrupole generated or provided by a ring quadrupole as described may comprise a topology as illustrated in FIG.8C. In some cases, the ring quadrupole as shown in FIG.8A may be configured to provide a topology with a large magnetic field gradient. In some cases, the magnetic field quadrupole may be configured to provide a particular magnetic field gradient at a particular height above the quadrupole, an ion trap, or other device component. A magnetic field quadrupole topology of a ring quadrupole may comprise a magnetic field nil line projected away from the ring quadrupole. For example, a magnetic field nil line may be normal to a direction of ion transport and along an axis intersecting the ion trap. As shown in FIG.8C, the magnetic field nil line may be proximal to regions of high magnetic field strength. For example, as shown in FIG. 8C, regions of high magnetic field strength (“high mT”) may surround regions of low magnetic field strength (“low mT”), effectively forming a ring of high magnetic field strength about a core of low magnetic field strength (e.g., the nil line). These regions, forming the magnetic field quadrupole may be generated above the ring quadrupole described herein. In some cases, the strength of the proximal magnetic field may have a height dependence. In some cases, the height may indicate a distance above an ion trap or in the y-axis as shown in FIGS.8A-8C. Generally, an increase in the magnetization of the poles of the ring quadrupole may increase the magnetic field gradient. In some cases, increasing the magnetization increases the maximal magnetic field strength, but not the strength of the magnetic field along the magnetic field nil line. In some cases, magnetic circuits contributing to a magnetic field quadrupole may be magnetized asymmetrically. In some cases, such asymmetric magnetization may be used to shift a position of a magnetic field nil line. For example, asymmetric magnetization may shift a magnetic field line along a direction perpendicular to ion transport for a ring quadrupole. This may facilitate adjustment of nil line location along a direction over which an ion cannot move.

[0129] In some embodiments, low magnetic field strength herein comprises a field strength of no more than about 0.00001 mT. In some embodiments, low magnetic field strength therein comprises a field strength of about 0.00001 mT to about 0.0001 mT and increments therein. In some embodiments, low magnetic field strength herein comprises a field strength of no more than about 0.0001 mT. In some embodiments, low magnetic field strength therein comprises a field strength of about 0.0001 mT to about 0.001 mT and increments therein. Insome embodiments, low magnetic field strength herein comprises a field strength of no more than about 0.001 mT. In some embodiments, low magnetic field strength therein comprises a field strength of about 0.001 mT to about 0.01 mT and increments therein. In some embodiments, low magnetic field strength herein comprises a field strength of no more than about 0.01 mT. In some embodiments, low magnetic field strength therein comprises a field strength of about 0.01 mT to about 0.1 mT and increments therein. In some embodiments, low magnetic field strength herein comprises a field strength of no more than about 0.1 mT. In some embodiments, low magnetic field strength therein comprises a field strength of about 0.1 mT to about 1 mT and increments therein. In some embodiments, low magnetic field strength herein comprises a magnetic field strength of no more than about 1 mT.

[0130] In some embodiments, high magnetic field strength herein comprises a field strength of at least about 1 mT. In some embodiments, high magnetic field strength herein comprises a field strength of about 1 mT to about 10 mT and increments therein. In some embodiments, high magnetic field strength herein comprises a field strength of at least about 10 mT. In some embodiments, high magnetic field strength herein comprises a field strength of about 10 mT to about 100 mT and increments therein. In some embodiments, high magnetic field strength herein comprises a field strength of at least about 100 mT. In some embodiments, high magnetic field strength herein comprises a field strength of about 100 mT to about 1 T and increments therein. In some embodiments, high magnetic field strength herein comprises a field strength of at least about 1 T. In some embodiments, high magnetic field strength herein comprises a field strength of about 1 T to about 10 T and increments therein. In some embodiments, high magnetic field strength herein comprises a field strength of at least about 10 T. In some embodiments, high magnetic field strength herein comprises a field strength of about 10 T to about 100 T and increments therein. In some embodiments, high magnetic field strength herein comprises a field strength of about 100 T or more.

[0131] In some cases, a ring quadrupole may comprise four soft ferromagnetic poles bonded to a non-magnetic base in a two by two fashion as shown in FIG. 12. In some cases, plates of soft ferromagnetic materials may form the four soft ferromagnetic poles. In some cases, the gaps at the base of the plates or poles may be at least 1.5 times, 2.0 times, 2.5 times, 3 times, 3.5 times, 4 times, or more times further separated than an air gap formed by the plates or poles.Illustrative Linear Quadrupole

[0132] As shown in FIG.9A, a linear quadrupole may be formed by four magnetic poles arrayed along a shared axis. In some cases, a linear quadrupole may be formed by two magnetic switches. In some cases, a magnetic switch of the two magnetic switches may comprise a saturable electronic reluctance switch as disclosed herein. For example, two saturable electronic reluctance switches comprising air gaps as described herein may be paired to from a linear quadrupole. In some cases, the poles of a first magnetic switch may be disposed between poles of a second magnetic switch. In some cases, the air gap of the first magnetic switch may be smaller than a distance between a pole of the second magnetic switch and a pole of the first magnetic switch. In some cases, the four poles may be equally spaced. Generally, a flux guide comprising an air gap may taper towards the air gap as shown in FIG.9A. In some cases, the flux guide may comprise a high permeability ferromagnetic material. In some cases, the high permeability ferromagnetic material may comprise a soft ferromagnetic material. In some cases, the air gaps of the two magnetic circuits may be different. Generally, the air gap of a magnetic circuit may be formed by a break in a flux guide of the magnetic circuit. For example, a flux guide may direct magnetic flux form a first pole of a magnetic flux source through the flux guide and to the second pole of the magnetic flux source. In some cases, this flux guide may comprise the air gap. In some cases, the air gap may be configured to promote fringing effects of magnetic flux passing through the air gap. As such, the linear quadrupole formed as described may be configured to form a magnetic field quadrupole upon passing magnetic flux through the air gaps of the magnetic circuits. In some cases, the fringing effect may be leveraged to design or select for particular magnetic field quadrupole topologies. For example, a magnitude of magnetic flux flowing through the respective magnetic circuits, a physical configuration or design of the areas about the air gap, or both may be used to customize a magnetic field quadrupole generated by a ring quadrupole. In some cases, a physical configuration or design may comprise a flux guide thickness, cross sectional area of a flux guide, an air gap distance, or spacing of the poles of the magnetic circuits.

[0133] In some cases, the poles of the linear quadrupole may be magnetized with opposite polarity (North-South-North-South), as depicted FIG.9A. As such, flux will be guided through the poles and will cut across the shortest air gap. In doing so, the flux may ‘fringe’ over the space above the plates. A ‘fringing’ quadrupolar field may be created in the y — z plane. As such, the magnetic-nil line may be upwards from the plates but may he along the x-axis, parallel to the trap surface. By doing this, the device may create a large magnetic fieldquadrupole away from itself. In some cases, air gaps of the magnetic switches ( s / ). separation between poles of the two magnetic switches (so), thickness of the magnetic poles (wt), or any combination thereof may be configured to provide a desired magnetic field quadrupole topology.

[0134] In some cases, a linear quadrupole may comprise four parallel soft ferromagnetic poles bonded to a non-magnetic base in a linear fashion as shown in FIG. 10. In some cases, plates of soft ferromagnetic materials may form the four parallel soft ferromagnetic poles. In some cases, the gaps at the base of the plates or poles may be at least 1.5 times, 2.0 times, 2.5 times, 3 times, 3.5 times, 4 times, or more times further separated than an air gap formed by the plates or poles.

[0135] In some cases, the magnetic field quadrupole may be formed above an ion trap as shown in FIG.9B. In some cases, an ion trap may comprise electrodes configured to trap an ion in a pseudopotential well. This may be performed to transport the ion among components, modules, or chips of a trapped ion quantum computer. In some cases, the electrodes may be configured to trap an ion in three dimensions. For example, an ion may be transported to a region above an ion trap proximal to a quadrupole as described herein. In some cases, the ion may be transported to a particular point above the magnetic field quadrupole so as to expose the ion to a particular magnetic field condition. For example, the ion may be transported to a region of high magnetic field gradient.

[0136] In some cases, a magnetic field quadrupole generated or provided by a linear quadrupole as described may comprise a topology as illustrated in FIG.9C. In some cases, the linear quadrupole as shown in FIG.9A may be configured to provide a topology with a large magnetic field gradient. In some cases, the magnetic field quadrupole may be configured to provide a particular magnetic field gradient at a particular height above the quadrupole, an ion trap, or other device component. In some cases, a linear quadrupole may be configured to provide a magnetic field nil line parallel to an ion trap at a configurable height above the ion trap. For example, a magnetic field nil line may be normal to a direction of ion transport and disposed along an axis parallel to the ion trap. As shown in FIG.9C, the magnetic field nil line may be proximal to regions of high magnetic field strength. For example, as shown in FIG.9C, regions of high magnetic field strength (“high mT”) may surround regions of low magnetic field strength (“low mT”), effectively forming a valley of high magnetic field strength about a line of low magnetic field strength (e.g., the nil line). These regions, forming the magnetic field quadrupole may be generated above the linearquadrupole described herein. In some cases, the strength of the proximal magnetic field may have a height dependence, where the height may indicate a distance above an ion trap or in the y-axis as shown in FIGS.9A-9C. Generally, an increase in the magnetization of the poles of the linear quadrupole may increase the magnetic field gradient. In some cases, increasing the magnetization increases the maximal magnetic field strength, but not the strength of the magnetic field along the magnetic field nil line. In some cases, magnetic circuits contributing to a magnetic field quadrupole may be magnetized asymmetrically. In some cases, such asymmetric magnetization may be used to shift a position of a magnetic field nil line. For example, asymmetric magnetization may shift a height of magnetic field line above an ion trap.Illustrative Methods Implementing Saturable Electronic Switches or Fringe Quadrupoles

[0137] In some aspects, the systems and devices disclosed herein may be optionally used to implement various methods. A non-limiting example of a method for generating a magnetic field quadrupole 1100 is provided in FIG. 11. In some cases, the method 1100 may comprise providing at 1105 a magnetic flux from a magnetic flux source, wherein the magnetic flux flows through a first path, applying at 1110 a current to an electromagnet, thereby causing the magnetic flux to flow through a second path, and with the magnetic flux flowing through the second path, generating at 1115 the magnetic field quadrupole.

[0138] In some cases, the magnetic field quadrupole is formed by at least two magnetic circuits. In some cases, wherein a magnetic circuit of the at least two magnetic circuits comprises at least one saturable electronic reluctance switch as described herein. In some cases, the method may be performed by a system comprising at least one saturable electronic reluctance switch or ferromagnetic fringe quadrupole as described herein.

[0139] In some cases, the method further comprises transporting an ion to a position within the magnetic field quadrupole. In some cases, the method further comprises performing a quantum logic operation with the ion. In some cases, the method further comprises switching off the current to the electromagnet.

[0140] In some cases, the magnetic field quadrupole comprises a magnetic field nil line. In some cases, prior to 1110 the first path comprises a first reluctance lesser than a second reluctance of the second path. In some cases, 1110 causes the first reluctance to increase to a value greater than the second reluctance.

[0141] In some cases, the electromagnet comprises a solenoid coiled around a shunt. In some cases, the method further comprises applying a biasing current to the electromagnet, thereby modulating the magnetic flux. In some cases, the biasing current may be applied to mitigate a flow of magnetic flux through an air gap. In some cases, the biasing current may cause a decrease in a remnant flux along the air gap. In some cases, a density of the remnant flux along the air gap is at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

[0142] In some cases, prior to (b), the magnetic flux density flowing through the second path is less than about 0.1 T 0.01T, 0.001 T, or 0.0001 T. In some cases, after 1010, the magnetic flux density flowing through the second path is about 0.1 T to 2.5 T. In some cases, the second path comprises an air gap.

[0143] In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some cases, the method provides a particular magnetic field gradient at a particular height as described herein.

[0144] In some cases, the magnetic flux source is a permanent magnet. In some cases, the magnetic flux source is a second electromagnet. In some cases, the second electromagnet is a solenoid. For example, the magnetic flux source may be a solenoid. In another example, the magnetic flux source may comprise a solenoid. Furthering the example, coil windings (e.g., a solenoid) may be disposed about a magnetic flux source. As such, application of electrical current to the coil windings may be used to increase or decrease a magnetization of the magnetic flux source.

[0145] In some cases, one or both of the first or second paths comprise a material with a saturation of flux density of at least about 0 T to about 2.5 T.

[0146] A non-limiting example of a method for switching a magnetic circuit 1200 is provided in FIG. 12, in accordance with some embodiments. In some cases, a method optionally implemented by a device or system as disclosed herein may comprise a method for switching a magnetic circuit 1200, the method comprising providing at 1205 a source of magnetic flux, directing at 1210 magnetic flux from a first pole of the source of magnetic flux through a flux guide towards an air gap, wherein the flux guide comprises a first portion, a second portion, and the air gap, and at an electromagnet, controlling at 1215 a flow of the magnetic flux from the first portion through the air gap and from the air gap to the second portion by anapplication of an electrical current to the electromagnet. In some cases, the method may be performed by a system comprising a saturable electronic reluctance switch or a quadrupole as disclosed herein. In some cases, the magnetic flux of 1215 flows to a second pole of the source of magnetic flux.

[0147] In some cases, the electromagnet comprises a shunt disposed between the first portion and the second portion. In some cases, prior to the application of the electrical current, the magnetic flux is configured to flow along the shunt. In some cases, prior to the application of the electrical current, a density of the magnetic flux along the air gap is less than about 1 mT, 0.1 mT, 0.01 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT. In some cases, prior to the application of the electrical current, a reluctance of the air gap portion is greater than a reluctance of the shunt. In some cases, after the application of the electrical current, a relative magnetic permeability of the shunt portion is about 1.

[0148] In some cases, after the application of the electrical current, a density of the magnetic flux along the air gap comprises a magnitude of at about 0.1 T to about 2.5 T. In some cases, the density of magnetic flux along the air gap comprises a magnitude of about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T. In some cases, after the application of the electrical current, the shunt may be saturated with magnetic flux. In some cases, a reluctance of the shunt may be increased upon application of the electrical current. In some cases, after the application of the electrical current the reluctance of the shunt is greater than the reluctance of the air gap.

[0149] In some cases, the shunt comprises a toroid shape. In some cases, the electromagnet comprises at least one wire coiled around the shunt. In some cases, the electromagnet comprises at least two wires coiled around the shunt. In some cases, a first wire and a second wire are configured to generate opposing magnetic fields. In some cases, the shunt comprises a reluctance modulator. In some cases, the reluctance modulator is a screw. In some cases, the reluctance modulator is configured to adjust one or both of a reluctance of the shunt or a magnetic flux along the air gap. In some cases, the shunt comprises at least two shunt pieces. In some cases, a wire is coiled around a shunt piece of the at least two shunt pieces. In some cases, each shunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces. In some cases, the electromagnet comprises the coiled wire. In some cases, the coiled wire is a solenoid. In some cases, a first shunt piece and a second shunt piece are configured to generate opposing magnetic fields.

[0150] A non-limiting example of a method for directing magnetic flux 1300 is provided in FIG. 13, in accordance with some embodiments. In some cases, the method 1300 optionally implemented by a device or system as disclosed herein may comprise directing at 1305 magnetic flux from at least one magnetic circuit comprising a soft ferromagnetic material, wherein the at least one magnetic circuit is configured to flow the magnetic flux through the soft ferromagnetic material toward an ion trap; and forming at 1310 a magnetic field quadrupole proximate to the ion trap and on an opposite side than the at least one magnetic circuit, wherein the magnetic field quadrupole is formed at least in part by directing the magnetic flux in 1305.

[0151] In some cases, the method is performed by a saturable electronic reluctance switch or ferromagnetic fringe quadrupole as described herein. In some cases, the magnetic field quadrupole comprises a magnetic field nil line. In some cases, the magnetic field nil line along an axis perpendicular to the ion trap. In some cases, the magnetic field nil line along an axis parallel to the ion trap. In some cases, a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

[0152] In some cases, a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m. In some cases, the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m. In some cases, the magnetic field quadrupole comprises a particular magnetic field gradient at a particular height as disclosed herein.

[0153] In some cases, the method further comprises performing the operations at 1205 and 1210 for a second magnetic circuit. In some cases, the magnetic circuit and the second magnetic circuit form the magnetic field quadrupole. In some cases, the method further comprises trapping an ion in a pseudopotential well.

[0154] In some cases, an ion as described herein may be a Yb ion, a Ba ion, a Mg ion, a Ca ion, Sr ion, or a Be ion.

[0155] A non-limiting example of a method for suspending an ion in a magnetic field in an ion trap 1400 is provided in FIG. 14, in accordance with some embodiments. In some cases, the method comprises providing at 1405 an ion trap. In some cases, the ion trap comprises a first plurality of electrodes and a first plurality of DACs configured to apply a DC field configured to confine an ion along a first axis in a first direction, a second plurality of electrodes and a second DAC configured to apply an RF field configured to confine an ion ina second and third perpendicular direction, each of the first, second, and third directions being perpendicular, and four soft ferromagnetic poles. In cases, the method comprises applying at 1410 an RF field, by the second DAC to the second plurality of electrodes to position the ion at an ion position a first height above the four soft ferromagnetic poles. In some cases, the method comprises applying at 1415, DC fields by the first plurality of DACs, to the first plurality of electrodes to position the ion in a position between the soft ferromagnetic poles in a first direction. In some cases, the method comprises magnetizing at 1420 each of the four soft ferromagnetic poles using magnetic flux from the at least one magnetic flux source to generate a magnetic field of less than ImT at the ion position.

[0156] A non-limiting example of a method for generating a magnetic field gradient in a quantum processor 1500 is provided in FIG. 15, in accordance with some embodiments. In some cases, the method 1500 comprises providing at 1505 a quantum processor comprising an ion trap configured to generate an ion trap at an ion trap position. In some cases, the ion trap comprises a magnetic circuit, the magnetic circuit comprising a flux source, a first parallel circuit path comprising an air gap, and a second parallel circuit path comprising a second path and a switchable shunt, the shunt forming a loop forming a first shunt path, and a second parallel shunt path along the second parallel circuit path, and a winding around the first shunt path and around the second shunt path. In some cases, the method 1500 comprises switching at 1510 between a first state in which the current through the winding is below a predetermined threshold and a second state in which the current through the winding is above a predetermined threshold.Definitions

[0157] Unless defined otherwise, all terms of art, notations and other technical and scientific terms or terminology used herein are intended to have the same meaning as is commonly understood by one of ordinary skill in the art to which the claimed subject matter pertains. In some cases, terms with commonly understood meanings are defined herein for clarity or for ready reference, and the inclusion of such definitions herein should not necessarily be construed to represent a substantial difference over what is generally understood in the art.

[0158] As used herein, the term “about” or “substantially” in reference to a value or percentage can refer to an amount that is greater or less the stated value or percentage by 10%, 5%, or 1%, including increments therein.As used herein, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Any reference to “or” herein is intended to encompass “of unless otherwise stated.EXAMPLESExample 1: Output of a SERS device

[0159] A SERs device as disclosed herein may provide a magnetic field through an air gap. The magnetic field at the air gap may rise from an off-state of near 0 T to an on-state of nonzero T. As shown in FIG. 16, the non-zero T may be dependent on a current used to saturate a shunt with magnetic flux. As shown, the magnetic field increases to a threshold value that is determined by a saturation current associated with a saturation magnetic flux of a material used to guide flux in a saturable electronic reluctance switch. This provides a bi-stable system, where no or negligible magnetic flux is passed through an air gap or operating point of a saturable electronic reluctance switch in a first (off) state, but a stable magnetic flux can be passed through the same point in a second (on) state upon application of current and saturation of a flux conducting material.Example 2: Magnetic Field Nil Line Magnetization

[0160] A device implementing a saturable electronic reluctance switch as disclosed herein comprises two saturable electronic reluctance switches coupled to form a ring quadrupole configuration of a ferromagnetic fringe quadrupole as shown in FIG. 17. As shown, symmetric magnetization of the two switches forming the ring quadrupole results in a magnetic field quadrupole with a magnetic field nil line central and projected away from the four quadrants comprising the ring quadrupole. In another case, asymmetric magnetization of components of the ring quadrupole is shown to generate a magnetic field nil line displaced from the center of the four quadrants yet still projected away from the ring quadrupole.

[0161] In another device implementing a saturable electronic reluctance switch as disclosed herein comprises two saturable electronic reluctance switches coupled to form a linear quadrupole as shown in FIG. 18. As shown, symmetric magnetization of the two switches forming the linear quadrupole results in a magnetic field quadrupole with a magnetic field line along an axis parallel and above the poles generating the magnetic field quadrupole. As shown, asymmetric magnetization of the poles may be used to change a height of the magnetic field nil line.Example 3: Magnetic Field Gradient Consistency Comparisons

[0162] A magnetic field gradient used in the context of quantum computations benefits from consistency of the magnitude of the magnetic field gradient over a spatial extent of a trapped ion chain. As shown in FIG. 19, a ring quadrupole as disclosed herein can generate a gradient with good spatial consistency as compared with a current carrying wire (CCW) design. The two cases are compared via finite element analysis of a ring quadrupole system and a CCW system. The CCWs resulting in the presented data have been optimized and simulated at their nominal distance below the trapped ions, hion= 125pm, where the CCWs are embedded within a trap substrate. The ring quadrupole is simulated at its nominal distance bellow the trapped ions, hion= 515pm, assuming the device is not embedded within the trap substrate. As shown, the comparison drawn is between the gradients of the two devices. In this case, it is shown that the ring quadrupole has a superior gradient-consistency when compared to the CCWs.

[0163] A second comparison between ring quadrupoles as disclosed herein and CCWs is shown in FIG.20. In the second comparison, the hionfor both devices is set at 515 pm. In both cases, the devices are optimized for the current ion height. In this case, CCW data is obtained theoretically using the thin-wire approximation. It is demonstrated in FIG.20 that, while the gradient-consistency of the CCWs is now more comparable to that of the ring quadrupole, the ring quadrupole remains superior. As shown, relative the CCWs, the ring quadrupole provides steep gradients for greater distances from the central nil line of the magnetic field quadrupole. Additionally, though not shown and unlike the ring quadrupole, CCW designs incur greater heat buildup and typically require expensive, complicated power sources to reliably confer magnetic field quadrupoles. The limitations both limit the fidelity of quantum computation and general scalability of CCW-based quantum computing systems. Example 4: Illustrative Devices Implementing Quadrupoles and Ion Traps

[0164] Shown in FIGs.21A and 21B are two illustrative devices implementing ferromagnetic fringe quadrupole as disclosed herein. FIG.21A depicts a ring quadrupole disposed beneath an ion trap. FIG.21B depicts a linear quadrupole disposed beneath and ion trap. Both illustrative devices implement toroidal saturable electronic reluctance switches with reluctance modulating screws. For each device, the source of magnetic flux is a SmCo magnet with a Brof 1 T. The ferromagnetic materials used in the flux guide and the shunt are MuMetal®. The device is built on a copper base. As shown, the dimensions of the completedevice are 32 x 20 x 11 mm. The device shown in FIG.21A was simulated to provide a magnetic field gradient of 60 T / m at a height of 0.52 mm above the device. The device shown in FIG.21B was simulated to provide a magnetic field gradient of 90 T / m at a height of 3.2 mm above the device.

[0165] Shown in FIG.22 is another illustrative device implementing a linear saturable electronic reluctance switch with a ring quadrupole and an ion trap. In this device, the source of magnetic flux is a SmCo magnet with a Brof 1 T. The shunt material in this device is MuMetal® and the flux guide is Hiperco®50. The device is built on a copper base. As shown, the dimensions of the complete device are 30.6 x 9 x 5.5 mm. The device shown in was simulated to provide a magnetic field gradient of 60 T / m at a height of 0.52 mm above the device.

[0166] Shown in FIG.23 is another illustrative device implementing a linear saturable electronic reluctance switch with a ring quadrupole and an ion trap. In this device, the source of magnetic flux is a SmCo magnet with a Brof 1 T. The shunt material in this device is MuMetal® and the flux guide is Hiperco®50. The device is built on a copper base. As shown, the dimensions of the complete device are 9.5 x 9 x 9 mm. The device shown in was simulated to provide a magnetic field gradient of 73 T / m at a height of 0.52 mm above the device.Example 5: Size Considerations for Ferromagnetic Fringe Quadrupole Devices

[0167] Shown in FIG.24 is a magnetic field gradient (along the z-axis, parallel to a direction of ion transport) versus ion-device distance (Z / ion) for an illustrative device implementing a ring quadrupole. These results indicate that a ferromagnetic fringe quadrupole device on the scale of just a few millimeters can provide sufficiently large magnetic field gradients for quantum computing. The magnetic field gradient versus ion height trends show, from top to bottom, the behavior of magnetized ring quadrupoles of decreasing sizes. From top trend line to bottom trend line, the “a” dimension of the device as shown in FIG.24 decreases from 9 mm to 3.8 mm and 1.6 mm. The height of the ion, hioa, is defined in this image as the height above the plane containing dimension ‘c’. In the trend line graph, the dashed lines indicate a range of magnetic field gradients useful in some trapped ion quantum computers.Example 6: Illustrative Ferromagnetic Fringe Quadrupole Device Prototype

[0168] Shown in FIG. 25, existing fabrication techniques such as wire erosion have been used to fabricate ferromagnetic fringe quadrupole as disclosed herein. Specifically, FIG. 25 shows a ring quadrupole.Example 7: Illustrative Integrations of Quadrupoles and Saturable Magnetic Switches

[0169] Shown in FIG. 26 are illustrative integrations of ferromagnetic fringe quadrupoles and saturable electronic reluctance switches in an ion-trap module. For simplicity, the ferromagnetic fringe quadrupole devices integrating the saturable electronic reluctance switches has been shown as a ‘C’ chape. As shown on the right, multiple of these ion-trap modules may be tiled together to form a larger quantum computing system.Example 8: Illustrative Device Implementing Two Saturable Magnetic Switches to Form Three Quadrupoles

[0170] Shown in FIG. 27 are two toroidal saturable electronic reluctance switches paired to form three linear quadrupoles. Linear quadrupoles configured to project magnetic field quadrupole are magnetically connected in parallel and magnetized by a single flux-source outside of the footprint of the ion trap array such that any power generating during the switching of the device can be effectively heat sunk. Note that many more projecting structures can be linearly added to this arrangement. In this mode of scaling, ion-trap modules would be aligned above the linear quadrupoles such that a magnetic field gradient is generated at a gate-zone of an ion-trapping module. To avoid magnetic field leakage as the field is guided to distant projecting structures, superconducting strips (not depicted) may be interleaved between flux guiding regions.Example 9: Output Magnetic Field Stability for Saturable Electronic Reluctance Switch Comparison to Solenoid

[0171] As shown in FIG. 28, the magnetic field stability of the saturable electronic reluctance switch (SERS) method is compared to the stability of a simple magnetizing solenoid (solenoid method). Using a solenoid to magnetize an air gap is analogous to using current carrying wires (CCWs) to generate a field in the same location, provided the material forming magnetic circuit is always far from saturation. In effect, the magnetic circuit is simply guiding the flux from the solenoid (CCW) to a desired location. To evaluate their respective stabilities, COMSOL Multiphysics was used to simulate the magnetization of an air gap within a magnetic circuit by each method. In this example, the target operational B-field output at the air gap was chosen as Boutput = 0.2 T, similar to the nominal air gap field for some implementations of a ferromagnetic fringe quadrupole and CCW schemes. In both the SERS and solenoid cases, identical magnetic circuit geometries were used (e.g., shape of flux guide, size of air gap, etc.).

[0172] When considering magnetization of the circuit by a solenoid, a linear relationship was observed between the applied current and the air gap magnetic field. For a given magnetic circuit, the response of the output field (Boutput) to current (7), \BSoienoid = dBoutput / dl, was controlled through the geometry of the magnetizing solenoid (e.g., number of turns, length). A steeper response is sometimes desired since the operating point can be achieved with less current. However, a steeper response will also increase the device’s sensitivity to current noise, since a perturbation in the applied current, 81, will lead to a perturbation in the output field SB output = AB solenoid SI. The designed magnitude of ABsoie oid leads to an applied current of / applied = 2.5 A to reach the operating point (B output = 0.2 T).

[0173] When considering magnetization of an equivalent circuit by a flux source as used in a saturable electronic reluctance switch as described herein, shunt saturation occurred a lappiied = 1.3 A and the output field, B output, was shown to plateau such that further increases in current applied to the solenoid (here used to saturate the shunt) did not increase Boutput.Further, given the saturation of the shunt, further increases in applied current did not increase Boutput.

[0174] Past the point of saturation for the saturable electronic reluctance switch approach, the ABSERS is much smaller than that of the solenoid. By fitting the curves, it was found that,

[0175] Equation 1:&~ 6.2 x 10-6, therefore since^ solenoid — 2-5)[0176| Equation then

[0177] Equation 3: 6BSERS= 6.2 X 10“6■ 8Bsolenoid

[0178] These findings indicate that, for this example, the magnetic field noise generated at the output (e.g., an air gap) as a function of the noise in the current source was approximately 160,000 times less for the saturable electronic reluctance switch approach versus the solenoid approach. This can be generally attributed to the difference in source of the output magnetic fields. In the saturable electronic reluctance switch, the output magnetic field was resultant from a permanent magnet (or alternatively a semi-permanent) magnet, while the solenoid output magnetic field was resultant directly from the applied current.Example 10: Power Source Versus Noise for Saturable Electronic Reluctance Switches

[0179] Two systems provide a 0.3 T magnetic field about an air gap. The first system uses a saturable electronic reluctance switch as described herein to generate the magnetic field. The second system uses a current carrying wire (CCW) to transiently generate the magnetic field. Both systems use a power source with 1 pA of current stability to provide electrical current to their respective solenoids. The solenoid of the first system is used to saturate a shunt, thereby directing magnetic flux from a separate source of magnetic flux to the air gap. The solenoid of the second system is used directly to generate the magnetic flux delivered to the air gap. The first system generates a magnetic field with a magnitude of noise one millionth that of the second system.Example 11: Illustrative Materials Separated by Coercivity

[0180] FIG.29 shows an illustrative separation between soft and semi-hard / hard ferromagnetic materials. The division between the materials occurs at coercivities of 1 kA / m (or 1000 A / m).

[0181] While preferred embodiments of the present invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

CLAIMSWhat is claimed is:

1. A system, comprising:(a) a source of magnetic flux;(b) a flux guide comprising a first portion, a second portion, and an air gap between the first portion and the second portion, wherein the first portion is configured to direct the magnetic flux from a first pole of the source toward the air gap; and(c) an electromagnet, wherein an application of an electrical current to the electromagnet is configured to control a flow of the magnetic flux from the first portion through the air gap and from the air gap to the second portion.

2. The system of claim 1, wherein the second portion is configured to direct the magnetic flux to a second pole of the source.

3. The system of claim 1 or 2, wherein the electromagnet comprises a shunt disposed between the first portion and the second portion.

4. The system of claim 3, wherein the shunt is configured to direct the magnetic flux through the air gap upon an application of electrical current to the electromagnet.

5. The system of any one of claims 1 to 4, wherein the source of the magnetic flux is configured to provide a magnetic flux density along the flux guide of about 0.1 T to about 2.5 T.

6. The system of any one of claims 1 to 5, wherein prior to the application of the electrical current, the magnetic flux is configured to flow along the shunt portion.

7. The system of any one of claims 1 to 6, wherein prior to the application of the electrical current, a density of the magnetic flux along the air gap is less than about 1 mT, 0.1 mT, 0.01 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

8. The system of any one of claims 3 to 7, wherein prior to the application of the electrical current, a reluctance of the air gap portion is greater than a reluctance of the shunt.

9. The system of any one of claims 1 to 4, wherein after the application of the electrical current, relative a magnetic permeability of the shunt is about 1.

10. The system of any one of claims 1 to 4, or 9, wherein after the application of the electrical current, a density of the magnetic flux along the air gap comprises a magnitude of at about 0.1 T to about 2.5 T.

11. The system of any one of claims 1 to 4, 9, or 10, wherein after the application of the electrical current, the shunt is saturated with magnetic flux.

12. The system of any one of claims 1 to 4, or 9 to 11, wherein a reluctance of the shunt is increased upon application of the electrical current.

13. The system of claim 12, wherein after the application of the electrical current the reluctance of the shunt is greater than the reluctance of the air gap.

14. The system of any one of claims 3 to 13, wherein the shunt comprises a toroid shape.

15. The system of claim 14, wherein the electromagnet comprises at least one wire coiled around the shunt.

16. The system of claim 14 or 15, wherein the electromagnet comprises at least two wires coiled around the shunt.

17. The system of any one of claims 14 to 16, wherein a first wire and a second wire are configured to generate opposing magnetic fields.

18. The system of any one of claims 15 to 17, wherein the shunt comprises a reluctance modulator.

19. The system of claim 18, wherein the reluctance modulator is a screw.

20. The system of claims 18 or 19, wherein the reluctance modulator is configured to adjust one or both of a reluctance of the shunt or a magnetic flux along the air gap.

21. The system of any one of claims 3 to 20, wherein the shunt comprises at least two shunt pieces.

22. The system of claim 21, wherein a wire is coiled around a shunt piece of the at least two shunt pieces.

23. The system of claim 21, wherein each shunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces.

24. The system of claim 22 or 23, wherein the electromagnet comprises the coiled wire.

25. The system of any one of claims 22 to 24, wherein the coiled wire is a solenoid.

26. The system of any one of claims 21 to 25, wherein a first shunt piece and a second shunt piece are configured to generate opposing magnetic fields.

27. A system, comprising:(a) at least one magnetic circuit comprising a soft ferromagnetic material; and (b) an ion trap proximate to the at least one magnetic circuit, wherein the magnetic circuit is configured to provide a magnetic field quadrupole proximate to the ion trap and on an opposite side of the ion trap from the at least one magnetic circuit.

28. The system of claim 27, wherein the magnetic circuit comprises at least one system of any one of claims 1 to 26.

29. The system of claim 27 or 28, wherein the magnetic field quadrupole comprises a magnetic field nil line along an axis extending away from a surface of the ion trap.

30. The system of claims 27 or 28, wherein the magnetic field quadrupole comprises a magnetic field nil line along a surface of the ion trap.

31. The system of any one of claims 27 to 30, wherein a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

32. The system of any one of claims 27 to 31, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m.

33. The system of any one of claims 27 to 32, wherein the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m.

34. The system of any one of claims 27 to 33, further comprising a second magnetic circuit.

35. The system of claim 34, wherein the first magnetic circuit and the second magnetic circuit form a quadrupole.

36. The system of any one of claims 34 to 35, wherein the first magnetic circuit is configured to provide a first magnetic field, and wherein the second magnetic circuit is configured to provide a second magnetic field.

37. The system of claim 36, wherein the first magnetic field comprises a different magnetic field strength than second magnetic field.

38. The system of any one of claims 27 to 37, wherein the system is configured to shift a position of the magnetic field nil line.

39. The system of claim 35, wherein the quadrupole is a ring quadrupole.

40. The system of claim 39, wherein the ring quadrupole comprises four quadrants, the four quadrants comprising:(i) a first quadrant comprising a first magnetic pole of the first magnetic circuit,(ii) a second quadrant comprising a second magnetic pole of the first magnetic circuit,(iii) a third quadrant comprising a first magnetic pole of the second magnetic circuit, and(iv) a fourth quadrant comprising a second magnetic pole of the second magnetic circuit.

41. The system of claim 35, wherein the quadrupole is a linear quadrupole.

42. The system of claim 41, wherein the linear quadrupole comprises four sections.

43. The system of claim 41 or 42, wherein the linear quadrupole comprises:(i) a first magnetic pole of the first magnetic circuit,(ii) a second magnetic pole of the first magnetic circuit,(iii) a first magnetic pole of the second magnetic circuit, and (iv) a second magnetic pole of the second magnetic circuit, wherein the first and second magnetic poles of the first magnetic circuit are arranged between the first and second magnetic poles of the second magnetic circuit.

44. The system of any one of claims 41 to 43, wherein the magnetic field nil line is about 20 pm to about 2000 pm above the linear quadrupole.

45. The system of any one of claims 41 to 44, wherein the linear quadrupole is configured to generate the magnetic field nil line along a surface of the ion trap.

46. The system of any one of claims 34 to 45, wherein the first magnetic circuit and the second magnetic circuit form a plurality of quadrupoles.

47. The system of any one of claims 27 to 46, further comprises a conductive material proximate to the at least one magnetic circuit and on an opposite side of the at least one magnetic circuit to the ion trap.

48. The system of claim 47, wherein the conductive material is copper.

49. The system of any one of claims 27 to 48, wherein the soft ferromagnetic material comprises a relative permeability of about 10 to about 10 million.

50. The system of any one of claims 27 to 49, wherein the soft ferromagnetic material comprises Hiperco®50 or MuMetal®.

51. The system of any one of claims 27 to 50, wherein the ion trap is configured to trap an ion in a pseudopotential well.

52. The system of any one of claims 27 to 51, further comprising a source of magnetic flux.

53. The system of any one of claims 27 to 52, wherein the magnetic circuit comprises a flux guide.

54. A system, comprising:(a) a source of magnetic flux;(b) a flux guide comprising a first path and a second path; and(c) an electromagnet, wherein the electromagnet is configured to switch a flow of the magnetic flux from the first path to the second path, and wherein the second path is configured to generate a magnetic field quadrupole.

55. The system of claim 54, wherein (a)-(c) form a portion of a magnetic circuit.

56. The system of claim 55, wherein the magnetic field quadrupole is formed by the magnetic circuit and a second magnetic circuit.

57. The system of any one of claims 54 to 56, wherein the magnetic circuit comprises at least one system of any one of claims 1 to 26.

58. The system of any one of claims 54 to 57, further comprising an ion trap, wherein the source of magnetic flux, the flux guide, and the electromagnet are proximate to a first side of the ion trap, and the magnetic field quadrupole is proximate to a second side of the ion trap.

59. The system of claim 58, wherein the ion trap is configured to trap an ion on the second side of the ion trap.

60. The system of claim 59, wherein the ion trap is configured trap the ion proximate to a nil line of the magnetic field quadrupole.

61. The system of any one of claims 54 to 60, wherein prior to application of an electrical current to the electromagnet, the first path comprises a first reluctance lesser than a second reluctance of the second path.

62. The system of any one of claims 54 to 60, wherein after an application of an electrical current to the electromagnet, the first path comprises a first reluctance greater than a second reluctance of the second path.

63. The system of any one of claims 54 to 62, wherein the electromagnet comprises a solenoid coiled around a shunt.

64. The system of any one of claims 54 to 63, wherein the flux guide comprises an air gap along the second path.

65. The system of any one of claims 54 to 64, further comprising a current source configured to apply a biasing current to the electromagnet.

66. The system of claim 65, wherein the biasing current is configured to decrease a remnant flux along the air gap.

67. The system of claim 66, wherein a density of the remnant flux along the air gap is at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

68. The system of any one of claims 54 to 67, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m.

69. The system of any one of claims 54 to 68, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m.

70. The system of any one of claims 54 to 69, wherein the flux guide comprises a material with a saturation of flux density of at least about 0 T to about 2.5 T.

71. The system of any one of claims 54 to 70, wherein the flux guide comprises a material with a saturation flux density of at least about 0.1 T.

72. The system of any one of claims 54 to 71, wherein the electromagnet comprises a shunt.

73. The system of claim 72, wherein the shunt comprises a material with a saturation flux density of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T.

74. The system of claim 72, wherein the saturation flux density of the flux guide is greater than a saturation flux density of the shunt.

75. The system of any one of the preceding claims, wherein the source of magnetic flux is configured to provide a magnetic flux density along the flux guide of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T.

76. The system of any one of the preceding claims, wherein the source of magnetic flux is a permanent magnet.

77. The system of claim 76, wherein the permanent magnet comprises Fe, Ni, Sm, Co, or any combination thereof.

78. The system of any one of the preceding claims, wherein the source of magnetic flux comprises a second electromagnet.

79. The system of claim 78, wherein the second electromagnet is a solenoid.

80. The system of any one of the preceding claims, wherein the flux guide comprises a soft ferromagnetic material.

81. The system of any one of the preceding claims, wherein the flux guide comprises MuMetal® or Hiperco®50.

82. The system of any one of the preceding claims, wherein the flux guide comprises a coercivity of less than about 1000 A / m.

83. The system of any one of the preceding claims, wherein the shunt and the flux guide comprise the same material.

84. The system of any one of the preceding claims, wherein the shunt and the flux guide comprise a different material.

85. The system of any one of the preceding claims, wherein the electromagnet is asolenoid.

86. The system of any one of the preceding claims, wherein the electromagnet comprises a first electromagnet portion and a second electromagnet portion.

87. The system of claim 86, wherein each of the first electromagnet portion and the second electromagnet portion are configured to receive an electrical current in both forward and reverse directions.

88. The system of any one of the preceding claims, wherein the permanent magnet is disposed between the shunt and the air gap portion.

89. The system of any one of the preceding claims, wherein a saturation flux density of the shunt is lower than a saturation flux density of the flux guide.

90. The system of claim 89, wherein the saturation flux density of the shunt, the saturation flux density of the flux guide, or both, is at least about 0.5 T.

91. The system of any one of the preceding claims, wherein the electromagnet is configured to modulate residual magnetic flux through the air gap portion.

92. The system of claim 91, wherein upon modulation of the residual flux through the air gap a magnetic flux density along the air gap is of less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

93. The system of any one of the preceding claims, wherein the electromagnet is in electrical communication with a diode.

94. A method for generating a magnetic field quadrupole, comprising:(a) providing a magnetic flux from a magnetic flux source, wherein the magnetic flux flows through a first path;(b) applying a current to an electromagnet, thereby causing the magnetic flux to flow through a second path; and(c) with the magnetic flux flowing through the second path, generating the magnetic field quadrupole.

95. The method of claim 94, wherein the magnetic field quadrupole is formed by at least two magnetic circuits.

96. The method of claim 95, wherein a magnetic circuit of the at least two magnetic circuits comprises at least one system of any one of claims 1 to 26.

97. The method of claim 94, wherein the method is performed by a system comprising at least one system of any one of claims 1 to 93.

98. The method of any one of claims 94 to 97, further comprising transporting an ion to a position within the magnetic field quadrupole.

99. The method of claim 98, further comprising performing a quantum logic operation with the ion.

100. The method of any one of claims 94 to 99, further comprising switching off the current to the electromagnet.

101. The method of any one of claims 94 to 100, wherein the magnetic field quadrupole comprises a magnetic field nil line.

102. The method of any one of claims 94 to 101, wherein prior to (b) the first path comprises a first reluctance lesser than a second reluctance of the second path.

103. The method of claim 94, wherein (b) causes the first reluctance to increase to a value greater than the second reluctance.

104. The method of any one of claims 94 to 103, wherein the electromagnet comprises a solenoid coiled around a shunt.

105. The method of any one of claims 94 to 104, further comprising applying a biasing current to the electromagnet, thereby modulating the magnetic flux.

106. The method of claim 105, wherein the biasing current causes a decrease in a remnant flux along the air gap.

107. The method of claim 106, wherein a density of the remnant flux along the air gap is at most about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

108. The method of any one of claims 94 to 107, wherein prior to (b), the magnetic flux density flowing through the second path is less than about 0.1 T 0.01T, 0.001 T, or 0.0001 T.

109. The method of any one of claims 94 to 108, wherein after (b), the magnetic flux density flowing through the second path is at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T110. The method of any one of claims 94 to 109, wherein the second path comprises an air gap.

111. The method of any one of claims 94 to 110, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m.

112. The method of any one of claims 94 to 111, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m.

113. The method of any one of claims 94 to 112, wherein the magnetic flux source is a permanent magnet.

114. The method of any one of claims 94 to 113, wherein the magnetic flux source is a second electromagnet.

115. The method of claim 114, wherein the second electromagnet is a solenoid.

116. The method of any one of claims 94 to 115, wherein one or both of the first or second paths comprise a material with a saturation of flux density of at least about 0.5 T.

117. A method for switching a magnetic circuit, the method comprising:(a) providing a source of magnetic flux;(b) directing magnetic flux from a first pole of the source of magnetic flux through a flux guide towards an air gap, wherein the flux guide comprises a first portion, a second portion, and the air gap; and(c) at an electromagnet, controlling a flow of the magnetic flux from the first portion through the air gap and from the air gap to the second portion by an application of an electrical current to the electromagnet.

118. The method of claim 117, wherein the method is performed by a system comprising at least one system of any one of claims 1 to 93.

119. The method of claim 117 or 118, wherein the magnetic flux of (c) flows to a second pole of the source of magnetic flux.

120. The method of any one of claims 117 to 119, wherein the electromagnet comprises a shunt disposed between the first portion and the second portion.

121. The method of claim 120, wherein prior to the application of the electrical current, the magnetic flux is configured to flow along the shunt.

122. The method of any one of claims 117 to 121, wherein prior to the application of the electrical current, a density of the magnetic flux along the air gap is less than about 1 mT, 0.1 mT, 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

123. The method of any one of claims 117 to 122, wherein prior to the application of the electrical current, a reluctance of the air gap portion is greater than a reluctance of the shunt.

124. The method of claim 117, wherein after the application of the electrical current, a relative magnetic permeability of the shunt portion is about 1.

125. The method of claim 117 or 124, wherein after the application of the electrical current, a density of the magnetic flux along the air gap comprises a magnitude of at least about 0.1 T, 0.2 T, 0.3 T, 0.4 T, 0.5 T, 0.6 T, 0.7 T, 0.8 T, 0.9 T, 1.0 T, 1.1 T, 1.2 T, 1.3 T, 1.4 T, 1.5 T, 1.6 T, 1.7 T, 1.8 T, 1.9 T, 2.0 T, 2.1 T, 2.2 T, 2.3 T, 2.4 T, or 2.5 T.

126. The method of any one of claims 117, 124, or 125, wherein after the application of the electrical current, the shunt is saturated with magnetic flux.

127. The method of any one of claims 117 or 124 to 126, wherein a reluctance of the shunt is increased upon application of the electrical current.

128. The method of any one of claims 117 or 124 to 127, wherein after the application of the electrical current the reluctance of the shunt is greater than the reluctance of the air gap.

129. The method of any one of claims 117 to 128, wherein the shunt comprises a toroid shape.

130. The method of claim 129, wherein the electromagnet comprises at least one wire coiled around the shunt.

131. The method of claim 129 or 130, wherein the electromagnet comprises at least two wires coiled around the shunt.

132. The method of any one of claims 129 to 131, wherein a first wire and a second wire are configured to generate opposing magnetic fields.

133. The method of any one of claims 129 to 132, wherein the shunt comprises a reluctance modulator.

134. The method of claim 133, wherein the reluctance modulator is a screw.

135. The method of claim 133 or 134, wherein the reluctance modulator is configured to adjust one or both of a reluctance of the shunt or a magnetic flux along the air gap.

136. The method of any one of claims 120 to 135, wherein the shunt comprises at least two shunt pieces.

137. The method of claim 136, wherein a wire is coiled around a shunt piece of the at least two shunt pieces.

138. The method of claim 136, wherein each shunt piece of the at least two shunt pieces comprises a wire coiled around a shunt piece of the at least two shunt pieces.

139. The method of claim 137 or 138, wherein the electromagnet comprises the coiled wire.

140. The method of any one of claims 137 to 139, wherein the coiled wire is a solenoid.

141. The method of any one of claims 136 to 140, wherein a first shunt piece and a second shunt piece are configured to generate opposing magnetic fields.

142. A method, comprising:(a) directing magnetic flux from at least one magnetic circuit comprising a soft ferromagnetic material, wherein the at least one magnetic circuit is configured to flow the magnetic flux through the soft ferromagnetic material toward an ion trap; and(b) forming a magnetic field quadrupole proximate to the ion trap and on an opposite side than the at least one magnetic circuit, wherein the magnetic field quadrupole is formed at least in part by directing the magnetic flux in (a).

143. The method of claim 142, wherein the method is performed by a system comprising at least one system of any one of claims 1 to 93.

144. The method of claims 142 or 143, wherein the magnetic field quadrupole comprises a magnetic field nil line.

145. The method of any one of claims 142 to 144, wherein the magnetic field nil line along an axis perpendicular to the ion trap.

146. The method of any one of claims 142 to 144, wherein the magnetic field nil line along an axis parallel to the ion trap.

147. The method of any one of claims 144 to 146, wherein a density of the magnetic flux along the magnetic field nil line is less than about 0.01 mT, 0.001 mT, 0.001 mT, 0.0001 mT, or 0.00001 mT.

148. The method of any one of claims 142 to 147, wherein a gradient of the magnetic field quadrupole comprises a magnitude of at least about 10 T / m to about 10,000 T / m.

149. The method of any one of claims 142 to 148, wherein the gradient of the magnetic field quadrupole comprises a magnitude of at least about 20 T / m to about 200 T / m.

150. The method of any one of claims 142 to 149, further comprising performing operations (a) and (b) for a second magnetic circuit.

151. The method of claim 150, wherein the magnetic circuit and the second magnetic circuit form the magnetic field quadrupole.

152. The method of any one of claims 142 to 151, further comprising trapping an ion in a pseudopotential well.

153. A method of suspending an ion in a magnetic field in an ion trap, the ion trap comprising:a first plurality of electrodes and a first plurality of DACs configured to apply a DC field configured to confine an ion along a first axis in first direction;a second plurality of electrodes and a second DAC configured to apply an RF field configured to confine an ion in second and third perpendicular directions, each of the first, second and third directions being perpendicular; andfour soft ferromagnetic poles; the method comprising:(a) applying an RF field, by the second DAC to the second plurality of electrodes to position the ion at an ion position a first height above the four soft ferromagnetic poles;(b) applying DC fields, by the first plurality of DACs, to the first plurality of electrodes to position the ion in a position between the soft ferromagnetic poles in a first direction; and(c) magnetising each of the four soft ferromagnetic poles using magnetic flux from at least one magnetic flux source to generate a magnetic field gradient in a first direction and a magnetic field of less than ImT at the ion position.

154. The method of claim 153, wherein the four soft ferromagnet poles are arranged in a line along the first axis.

155. The method of claim 154, wherein the magnetic flux applied to each soft ferromagnetic pole along the line along the first axis has alternating magnetic polarity.

156. The method of claim 154, wherein the magnitude of the magnetic flux applied to each soft ferromagnetic pole is equal and the zero magnetic field line is at a centre line of the soft ferromagnetic poles.

157. The method of claim 156, wherein the magnitude of the magnetic flux applied to each of the soft ferromagnetic poles closest to a centre line of the soft ferromagnetic poles differs from than that applied to the outer ferromagnetic poles.

158. The method of claim 153, wherein the four soft ferromagnetic poles are arranged in a quadrangle.

159. The method of claim 158, wherein the magnetic flux applied to each soft ferromagnetic pole around the quadrangle has alternating magnetic polarity.

160. The method of claim 159, wherein the magnitude of the magnetic field applied to each soft ferromagnetic pole is equal and the zero magnetic field line is at the centre line of the soft ferromagnetic poles.

161. The method of claim 159, wherein the magnitude of the magnetic flux applied to one pair of oppositely polarised soft ferromagnetic poles is greater than the magnitude of the magnetic flux applied to another pair of oppositely polarised soft ferromagnetic poles.

162. The method of any one of claims 152 to 161, wherein each of the soft ferromagnetic poles has a first end and a second end, the first end being proximate the ion position and the second end being distal the ion position and wherein the distancebetween each of the soft ferromagnetic poles at the second ends is greater than the distance between each of the soft ferromagnetic poles at the first ends.

163. The method of claim 162 wherein the distance between the soft ferromagnetic poles at the second end is at least 10 times greater than the distance at the first end.

164. The method of any one of claims 152 to 163, wherein the cross section of each soft ferromagnetic pole at the second end is at least 5 times greater than the cross section of each soft ferromagnetic pole at the first end.

165. The method of any one of claims 152 to 164, further comprising a nonmagnetic base and wherein each of the four soft ferromagnetic poles are bonded to the non-magnetic base.

166. The method of any one of claims 152 to 165, wherein the height of the ion position above the first end of the ferromagnetic poles, proximate the ion position, is lOOum-lmm.

167. The method of any one of claims 152 to 166, wherein the magnetic poles are formed of Hiperco50.

168. The method of any one of claims 152 to 167, wherein the flux source is one of a permanent magnet, a current source or a current in a superconductor.

169. The method of any one of the preceding claims further comprising a magnetic circuit, coupled to at least two of the magnetic poles, the magnetic circuit comprising:(i) a flux source;(ii) a first parallel circuit path comprising an air gap; and(iii) a second parallel circuit path comprising a second path and a switchable shunt.

170. The method of claim 169 wherein the switchable shunt comprises:(i) a loop forming a first shunt path and a second, parallel, shunt path along the second parallel circuit path;(ii) a winding around the first shunt path and around the second shunt path;and(iii) a current source coupled to the winding.

171. The method of claim 170 wherein the winding and the current source are configured to generate a magnetic field in a first direction along the first shunt path and a second direction, opposite the first direction along the second shunt path.

172. The method of either claim 170 or claim 171 further comprising switching between a first state in which the current through the winding is below a predetermined threshold and a second state in which the current through the winding is above a predetermined threshold.

173. The method of claim 172 wherein the current in the second state saturates the first shunt path and the second shunt path.

174. The method of either claim 172 or claim 173 wherein the current, in the second state, is configured to generate a magnetic field in a first direction along the first shunt path and a magnetic field in a second direction, opposite the first direction, along the second shunt path.

175. The method of any one of claims 172 to 174 wherein the current in the first state is zero.

176. The method of any one of claims 172 to 175 wherein the current, in the first state, is configured to generate a magnetic field in a first direction along the first shunt path and a magnetic field in a first direction along the second shunt path.

177. A quantum processor comprising an ion trap configured to generate an ion trap at an ion trap position, the ion trap comprising a magnetic circuit, the magnetic circuit comprising:(i) a flux source;(ii) a first parallel circuit path comprising an air gap; and(iii) a second parallel circuit path comprising a second path and a switchable shunt.

178. The quantum processor of claim 177 wherein the switchable shunt comprises:(i) a loop forming a first shunt path and a second, parallel, shunt path along the second parallel circuit path;(ii) a winding around the first shunt path and around the second shunt path; (iii) a current source coupled to the winding.

179. The quantum processor of claim 178, wherein the winding and the current source are configured to generate a magnetic field in a first direction along the first shunt path and a second direction, opposite the first direction along the second shunt path.

180. The quantum processor of either claim 178 or claim 179, wherein the first shunt path and the second shunt path form a toroid.

181. The quantum processor of claim 180, wherein the first parallel circuit path and the second parallel circuit path are formed of the same material.

182. The quantum processor of any one of claims 177 to 181, wherein the first parallel circuit path and the second parallel circuit path are formed of a highly permeable soft ferromagnetic material.

183. The quantum processor of claim 181 wherein the first parallel circuit path and at least a portion of the second parallel circuit path are formed of Hiperco®50.

184. The quantum processor of any one of claims 178 to 180, wherein the first shunt path and the second shunt path are formed of a material with a lower saturation flux density than the saturation flux density of the second path and first parallel circuit path.

185. The quantum processor of claim 184, wherein the first shunt path and the second shunt path are formed of MuMetal®.

186. The quantum processor of either claim 184 or claim 185, wherein the second path and first parallel path is formed of Hiperco®50.

187. The quantum processor of any one of claims 177 to 186, wherein the first parallel circuit path is formed on a first side of the flux source and the second parallel circuit is formed on a second side of the flux source, opposite to the first side of the flux source.

188. The quantum processor of any one of claims 177 to 187, wherein the length of the shunt along the magnetic circuit is greater than the length of the air gap along the magnetic circuit.

189. The quantum processor of any one of claims 177 to 188, wherein the switchable shunt comprises a third shunt path having an adjustable air gap.

190. The quantum processor of claim 189, wherein the third shunt path is formed of a soft ferromagnetic material.

191. The quantum processor of any one of claims 177 to 190, wherein the flux source is one of a permanent magnet, a current source or a current in a superconductor.

192. The quantum processor of claim 191 wherein the flux source is an AlNiCo magnet.

193. A method of generating a magnetic field gradient in a quantum processor, the method comprising: providing a quantum processor comprising an ion trap configured to generate an ion trap at an ion trap position, the ion trap comprising a magnetic circuit, the magnetic circuit comprising:(i) a flux source;(ii) a first parallel circuit path comprising an air gap; and(iii) a second parallel circuit path comprising a second path and a switchable shunt, the shunt forming a loop forming a first shunt path and a second, parallel, shunt path along the second parallel circuit path and a winding around the first shunt path and around the second shunt path;the method comprising: switching between a first state in which the current through the winding is below a predetermined threshold and a second state in which the current through the winding is above a predetermined threshold.

194. The method of claim 193, wherein the current in the second state saturates the first shunt path and the second shunt path.

195. The method of either claim 193 or claim 194, wherein the current, in the second state, is configured to generate a magnetic field in a first direction along the first shunt path and a magnetic field in a second direction, opposite the first direction, along the second shunt path.

196. The method of any one of claims 193 to 195 wherein the current in the first state is zero.

97. The method of any one of claims 193 to 195 wherein the current, in the first state, is configured to generate a magnetic field in a first direction along the first shunt path and a magnetic field in a first direction along the second shunt path.

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