Quantum devices and methods for operating quantum devices

Abstract

Various embodiments of quantum devices and methods of operating quantum devices are described. In one embodiment, the quantum device comprises a substrate, a superconducting circuit element supported on a substrate surface of the substrate and exhibiting superconductivity during operation of the quantum device, and a passive magnetic element, the passive magnetic element generating a magnetic field, the superconducting circuit element being directly or indirectly exposed to at least a portion of the magnetic field during operation of the quantum device. In some embodiments, the superconducting circuit element is indirectly exposed to a portion of the magnetic field, and the portion of the magnetic field is induced, at least in part, by one or more magnetic field inducers from a first location proximate the passive magnetic element to a second location proximate the superconducting circuit element.

Description

[Technical field]

[0001] The present disclosure relates to quantum computing, and in particular to quantum devices and methods of operating quantum devices. [Background technology]

[0002] Since its discovery decades ago, scientists and engineers have developed devices and systems that exploit the properties of quantum physics in various ways. More recently, the field of quantum computing has become a particularly active area of ​​research, particularly due to its potential to disrupt modern computing, communication, and encryption. Various architectures have been explored, either practically or theoretically, to exploit quantum properties, and in particular superconducting circuits are one form of architectural framework that has emerged as particularly promising.

[0003] In contrast to classical computers, where information is physically stored in memory, read out, transmitted and processed in binary form (bits), in quantum computers, information, called quantum information in this context, is physically stored in memory, processed with quantum algorithms and measured (read out) based on the von Neumann entropy by encoding quantum information in the state of quantum subsystems (qubits).

[0004] One of the main challenges faced in encoding quantum information in real physical devices is balancing two opposing requirements. First, quantum information is inherently fragile and subject to loss due to factors of decoherence. Unfortunately, virtually all interactions with the environment, including desired ("control") interactions, are potential sources of decoherence. Thus, systems designed to store and process quantum information should be isolated as far as possible from interactions with the environment. Second, for quantum information to be useful, it must be able to be processed and ultimately accessed, which means it must be controllable through interactions with an external control system, and to achieve high fidelity control, control of such interactions typically means being performed at high speed.

[0005] Thus, it will be appreciated that superconducting circuits, and circuits designed in a circuit quantum electrodynamic framework (CQED), have emerged as promising architectures for various quantum devices, such as quantum computers, but there remains considerable room for improvement. In particular, some superconducting circuit elements, called transmons, are useful because they can achieve desired nonlinearities while maintaining a certain level of noise immunity. Other superconducting circuit elements, such as superconducting quantum interference devices (SQUIDs), superconducting flux qubits, superconducting nonlinear asymmetric inductive elements (SNAILs), or capacitively shunted SNAILs (SNAILMONs), are "flux tunable" in the sense that they can benefit from or even require a constant magnetic flux during operation. SQUIDs and SNAILs, for example, comprise a superconducting loop with multiple Josephson junctions, providing a frequency response that depends on the magnetic induction flux traversing the loop. Other parameters such as third and fourth order nonlinearities, or interactions between qubits, to name a few, can be tuned by the magnetic flux. Flux-tunable superconducting circuit elements are designed to operate in the presence of magnetic fields, and generating suitable magnetic fields has proven to pose various challenges in practice.

[0006] This background information is presented to identify information believed by the applicant to be potentially relevant. No admission is necessarily intended, and should not be construed, that any of the preceding information constitutes prior art or forms part of the common general knowledge in the relevant art. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] Grimm, A. et al., "Stabilization and operation of a Kerr-cat qubit," Nature 584, 2020. Summary of the Invention [Means for solving the problem]

[0008] One approach to generate a magnetic field so as to provide a suitable operating environment for the superconducting circuit loop is to generate it actively, i.e. by circulating a current along a conductor separate from the superconducting circuit loop. The current can be circulated in a magnetic field coil located near the sample chip, or along a magnetic flux bias line located on the same chip and passing, for example, near the superconducting circuit loop. Such an approach can cause certain problems. Indeed, the superconducting circuit loop usually operates at very low temperatures (e.g. in the mK range), which are typically realized in dilution refrigerators. The magnetic field emission conductors are therefore located inside the dilution refrigerator, close to the superconducting circuit loop, while the driving elements are located outside the dilution refrigerator, which in practice poses challenges. In quantum computing architectures, actively biased conductors are a possible source of undesired interactions and crosstalk. Moreover, such biased conductors usually have a rather large footprint and require additional ports to be integrated in the same substrate as the superconducting loop, which can impose potential limitations on scalability. Furthermore, when considering the use of on-chip flux bias lines in the vicinity of superconducting circuit loops in 3D architectures such as 3D qubits, unique challenges arise in that the galvanic connections that typically connect the leads to the superconducting elements on the substrate may not be available. Finally, additional hardware may be required to address the dissipation that may be caused by DC current flowing into the dilution refrigerator, contributing to higher costs. It has been found that, in at least some embodiments, an alternative approach of using permanent magnets to generate fixed magnetic field components in the superconducting circuit environment, although counterintuitive, may have advantages over flux biasing by current circulation.

[0009] Various parameters can affect the effectiveness of the magnetic field on a superconducting circuit loop. For example, in a SQUID, one may wish to achieve a finely tuned constant value of magnetic induction flux (Φ) in the superconducting flux loop, which may be expressed as a magnetic induction flux quantum (Φ0=2.068×10 -15 In many practical implementations, it may not be practical to incorporate the magnetic field source in the same plane (e.g., on the same wafer surface) as the superconducting loop. This may result, for example, from losses caused by the presence of material forming a permanent magnet in the vicinity of the superconducting loop. It may therefore be preferable to locate the magnetic field source on the opposite side of the substrate supporting the superconducting loop, in which case it may be difficult to obtain the desired value of Φ, in particular due to the geometrical effects of the magnetic field. In practice, many magnetic field geometries will give the superconducting loop a value Φ / Φ0, which is approximately 1 / r n will decrease as a function of the power of the distance r from the source, such as Φ / Φ0, where n may vary between 3 and 5, depending on the details of the geometry, for example. It has been found that, in at least some embodiments, a relationship closer to 1 for n may be achieved by using superconducting through silicon vias to induce the magnetic field across the substrate, which may be preferred in at least some embodiments.

[0010] According to one aspect, a quantum device is provided comprising: a superconducting circuit comprising at least one wafer and circuit elements supported by the at least one wafer, the superconducting circuit exhibiting superconductivity during operation of the quantum device; and a passive magnetic element supported by the at least one wafer that generates a magnetic induction flux across the circuit elements at a given position relative to the superconducting circuit during operation of the quantum device.

[0011] According to another aspect, a method is provided for operating a quantum device comprising a passive magnetic element that generates a permanent magnetic induction flux across a circuit element of the quantum device, the circuit element being supported by a wafer.

[0012] According to another aspect, a quantum device is provided comprising a substrate, a superconducting circuit element supported on a substrate surface of the substrate, the superconducting circuit element exhibiting superconductivity during operation of the quantum device, and a passive magnetic element, the passive magnetic element generating a magnetic field, the superconducting circuit element being exposed directly or indirectly to at least a portion of the magnetic field during operation of the quantum device.

[0013] According to one embodiment, a superconducting circuit element comprises a superconducting loop with two branches that split and recombine at corresponding points, each branch comprising at least one Josephson junction, and wherein the portion of the magnetic field provides a magnetic induction flux that crosses the superconducting loop.

[0014] In one embodiment, both the passive magnetic elements and the superconducting circuit elements are supported on the substrate surface.

[0015] In one embodiment, the passive magnetic element is disposed adjacent to the superconducting circuit element.

[0016] In one embodiment, the superconducting loop has at least one axis of insensitivity and the passive magnetic element is disposed on the axis of insensitivity.

[0017] In one embodiment, the axis of insensitivity extends laterally across two branches of the superconducting loop.

[0018] In one embodiment, the passive magnetic elements have a magnetization direction perpendicular to the substrate surface.

[0019] In one embodiment, the passive magnetic element is a first passive magnetic element and further comprises a second passive magnetic element supported by the substrate surface, the second passive magnetic element being centrally disposed with respect to the superconducting loop.

[0020] In one embodiment, the device further comprises a third passive magnetic element supported by the substrate surface, the third passive magnetic element being positioned adjacent to the superconducting loop and on an opposite side from the first passive magnetic element.

[0021] In one embodiment, the passive magnetic element has a magnetization direction parallel to the substrate surface, with the magnetization direction oriented along the insensitive axis of the superconducting loop.

[0022] In one embodiment, the passive magnetic element is positioned above or below the plane defined by the superconducting loop.

[0023] In one embodiment, the substrate is a first substrate and further comprises a second substrate held in spaced relation from the first substrate, the passive magnetic element being supported by the second substrate.

[0024] In one embodiment, the passive magnetic element is disposed within a recess formed in the surface of the substrate.

[0025] In one embodiment, the superconducting circuit element is selected from the group consisting of a flux qubit, a superconducting quantum interference device (SQUID), a superconducting nonlinear asymmetric inductive element (SNAIL), and a capacitively shunted SNAIL (SNAILMON).

[0026] In one embodiment, the superconducting element is one of a plurality of superconducting elements, the plurality of superconducting elements being disposed in an array configuration on a substrate surface.

[0027] In one embodiment, the magnetic induction flux is on the order of a magnetic induction flux quantum Φ 0 .

[0028] In one embodiment, the passive magnetic elements are dot micromagnets or bar micromagnets.

[0029] In one embodiment, the maximum magnetic field amplitude on the flux loop of the passive magnetic element during operation is

number

[0030] In one embodiment, the passive magnetic element is a magnetic tunnel junction.

[0031] In one embodiment, the superconducting circuit element is indirectly exposed to a portion of the magnetic field, the portion of the magnetic field being at least partially induced by one or more magnetic field inducing units from a first location proximate the passive magnetic element to a second location proximate the superconducting circuit element, each of the one or more magnetic field inducing units operable to at least partially induce a portion of the magnetic field, the tubular passage extending across at least one substrate layer of a substrate, the tubular passage having a first end and a second end and defining an inner surface inside the at least one substrate layer, and an inductive layer of a material that exhibits superconductivity during operation of the quantum device, the inductive layer at least partially covering the inner surface of the tubular passage and extending from the first end to the second end.

[0032] In one embodiment, the device comprises one magnetic field inducing portion, the substrate surface being a first substrate surface, the substrate further comprising a second substrate surface opposite the first substrate surface, the passive magnetic element being supported by the second substrate surface, a first end of the tubular passage being positioned on the first substrate surface adjacent to the superconducting circuit element, and the second end of the tubular passage being positioned on the second substrate surface adjacent to the passive magnetic element.

[0033] In one embodiment, the substrate comprises a first substrate layer and a second substrate layer, the first substrate layer comprising a substrate surface, the substrate further comprising an internal magnetic field inducing portion, the internal magnetic field inducing portion comprising a cavity formed between the first substrate layer and the second substrate layer, the internal magnetic field inducing portion defining an internal cavity surface, and a cavity inducing layer of the material exhibiting superconductivity during operation of the quantum device, the cavity inducing layer at least partially covering the internal cavity surface, the quantum device comprising two magnetic field inducing portions, a first of the two magnetic field inducing portions being a first end of the first magnetic field induction section is coupled to the internal magnetic field induction section and a second end of the second magnetic field induction section is positioned on the substrate surface adjacent to the superconducting circuit element, the second of the two magnetic field induction sections acts as a source induction section, a first end of the second magnetic field induction section is positioned on the substrate surface adjacent to the passive magnetic element and a second end of the second magnetic field induction section is coupled to the internal magnetic field induction section, and a portion of the magnetic field is at least partially induced from the first end of the source induction section through the internal magnetic field induction section to the second end of the sink induction section.

[0034] In one embodiment, the superconducting circuit element is configured to operate as a quantum subsystem of a quantum computer, the superconducting circuit element being operable to provide at least one quantum bit within the quantum subsystem during operation of the quantum computer.

[0035] According to another aspect, a quantum device is provided comprising a substrate; a magnetic field inducing portion; the magnetic field inducing portion comprising a tubular passage extending across at least one substrate layer of the substrate, the tubular passage having a first end and a second end and defining an inner surface inside the at least one substrate layer; and an inducing layer of a material that exhibits superconductivity during operation of the quantum device, at least partially covering the inner surface of the tubular passage, extending from the first end to the second end, and operable to induce a portion of a magnetic field along the magnetic field inducing portion.

[0036] In one embodiment, the device further comprises at least one magnetic field source configured to at least partially generate the magnetic field.

[0037] In one embodiment, the device further comprises at least one superconducting circuit element, the superconducting element being exposed to the portion of the magnetic field induced by the magnetic field inducing portion.

[0038] In one embodiment, each of the at least one superconducting circuit elements comprises a superconducting loop having a plurality of Josephson junctions, and a portion of the magnetic field induced by the magnetic field inducing portion provides a magnetic induction flux across the superconducting loop during operation of the quantum device.

[0039] In one embodiment, the first end of the tubular passage and the at least one superconducting circuit element are located on the same exterior surface of the substrate, with the superconducting circuit element proximate the first end.

[0040] In one embodiment, the first end of the tubular passage is centrally located relative to the superconducting loop.

[0041] In one embodiment, the first end of the tubular passage is positioned adjacent to the superconducting loop.

[0042] In one embodiment, the device further comprises a first superconducting circuit element and a second superconducting circuit element, both of which are supported on the outer surface, and a first end of the tubular passage is disposed between a superconducting loop of the first superconducting circuit element and a superconducting loop of the second superconducting circuit element to simultaneously expose both to a portion of the magnetic field.

[0043] In one embodiment, the outer surface is a first outer surface, the substrate further comprises a second outer surface opposite the first outer surface, the second end of the tubular passage is located on the second outer surface, and the magnetic field source is disposed proximate to the second end.

[0044] In one embodiment, the passive magnetic field source is supported by the second exterior surface and adjacent the second end of the tubular passageway.

[0045] In one embodiment, the substrate is a first substrate, and the device further comprises a second substrate held at a distance from the second outer surface of the first substrate, the second substrate having a third outer surface adjacent to the second outer surface of the first substrate, and the magnetic field source is supported by the third outer surface.

[0046] In one embodiment, the substrate comprises a first substrate layer and a second substrate layer, the first substrate layer having an outer surface, the tubular passage extends across only the first layer, the second end of the tubular passage is located between the first layer and the second layer, and the magnetic field source is disposed proximate to the second end of the tubular passage within the substrate.

[0047] In one embodiment, the at least one magnetic field source includes a passive magnetic element.

[0048] In one embodiment, the at least one magnetic field source includes an active magnetic element, which comprises an electrical conductor element connected to an electrical drive.

[0049] In one embodiment, the interior volume defined by the tubular passage is at least partially filled with a non-conductive material.

[0050] In one embodiment, a passive magnetic element is supported on a surface of the substrate, a first of the magnetic field inducing portions is a first magnetic field inducing portion arranged on the surface adjacent to the passive magnetic element, and the quantum device comprises a second magnetic field inducing portion having a first end of the second magnetic field inducing portion arranged on the surface adjacent to the passive magnetic source and opposite the first end of the first magnetic field inducing portion, and the passive magnetic element is arranged to act as a laterally directed magnetic field source such that portions of the magnetic fields induced by the first magnetic field inducing portion and the second magnetic field inducing portion each have opposite magnetic flux polarity.

[0051] Many additional features and feature combinations of the present improvements will become apparent to those of skill in the art upon reading this disclosure. [Brief description of the drawings]

[0052] [Figure 1A] FIG. 1 is a schematic circuit diagram of a classical harmonic oscillator. [Figure 1B] FIG. 1 is a schematic circuit diagram of a basic version of Transmon. [Figure 1C] FIG. 1 is a schematic circuit diagram of a superconducting circuit element with adjustable magnetic flux. [Figure 1D] FIG. 1 is a schematic circuit diagram of a superconducting circuit element with adjustable magnetic flux. [Figure 1E] FIG. 1 is a diagram showing a Josephson junction. [Figure 1F] FIG. 1 shows the frequency response of a Josephson junction to an external parallel magnetic field. [Figure 1G] FIG. 2 is a schematic diagram showing a magnetic field applied to a quantum dot in a spin qubit. [Figure 2A] FIG. 1 is a schematic diagram of a possible exemplary configuration for applying a magnetic field, an example of an actively driven magnetic field, on a superconducting circuit. [Figure 2B] 1A-1C are schematic diagrams of possible example configurations for applying a magnetic field, which are illustrative of the magnetic field emanating from a corresponding configuration of permanent magnets, more specifically, a central dot magnet configuration. [Figure 2C] 1A-1C are schematic diagrams of possible example configurations for applying a magnetic field, which are illustrative of the magnetic field emanating from a corresponding configuration of permanent magnets, more specifically, a horizontal bar magnet configuration. [Figure 2D] 1A-1C are schematic diagrams of possible example configurations for applying a magnetic field, which are illustrative of the magnetic field emanating from a corresponding configuration of permanent magnets, more specifically, a horizontal dot magnet configuration. [Diagram 3] Figure 1 shows the simulated sensitivity of the magnetic induction flux to the device parameter variations as a function of the position of the permanent magnet with respect to the superconducting loop for the dot magnet case. [Figure 4] FIG. 13 is a diagram of numerical results of a magnetic field simulation for the horizontal bar magnet configuration. [Diagram 5] FIG. 13 shows numerical results of magnetic field simulation for the central dot magnet configuration. [Figure 6]FIG. 13 is a diagram of numerical results of magnetic field simulation for the horizontal dot magnet configuration. [Figure 7A] FIG. 13 shows an example of a magnetic field emanating from a corresponding configuration of permanent magnets, more specifically, a compensated central dot configuration. [Figure 7B] FIG. 13 shows an example of the magnetic field emanating from a corresponding configuration of permanent magnets, more specifically, a doubly compensated central dot configuration. [Figure 8] FIG. 1 illustrates the variation in magnetic induction flux for various permanent magnet configurations. [Figure 9A] FIG. 13 is a diagram showing a simulation result regarding loss. [Figure 9B] FIG. 13 is a diagram showing a simulation result regarding loss. [Figure 10] 1 is a graph showing simulated loss versus scale factor for a SNAILMON loop; [Figure 11A] FIG. 1 is a diagram showing an example of a one-dimensional array configuration in which a permanent magnet is shared between multiple superconducting loops. [Figure 11B] FIG. 1 is a diagram showing an example of a one-dimensional array configuration in which a permanent magnet is shared between multiple superconducting loops. [Figure 11C] FIG. 1 is a diagram showing an example of a one-dimensional array configuration in which a permanent magnet is shared between multiple superconducting loops. [Figure 12] FIG. 1 is a cross-sectional view showing an example of an out-of-plane geometry. [Figure 13A] 13A-13C are schematic diagrams of additional out-of-plane geometries. [Figure 13B] 13A-13C are schematic diagrams of additional out-of-plane geometries. [Figure 14] 13A-13C are diagrams of simulation results showing induction of a magnetic field across a substrate and across a via to a superconducting circuit element. [Figure 15] 15 is a graph of magnetic induction flux versus substrate thickness / via length for a simulation such as that presented in FIG. 14. [Figure 16] 13A-13C are schematic diagrams of additional out-of-plane geometries. [Figure 17]17A-17C are diagrams of simulation results showing the magnetic field resulting from a configuration such as that presented in FIG. 16. [Figure 18] Graph of magnetic induction flux versus flip chip gap, as well as magnet volume scaling factor. [Figure 19] FIG. 4 is a schematic diagram of another possible embodiment of the magnetic field induction portion; [Figure 20] 1 presents simulation results carried out on a quantum device configuration comprising a superconducting magnetic induction section and a superconducting cavity. [Figure 21] 13A-13C are schematic diagrams of exemplary alternative configurations of tubular elements of the superconducting magnetic field induction section; [Figure 22A] 2 is a schematic diagram of the distribution of magnetic field inducing portions along the wafer surface; [Figure 22B] 1 is a schematic diagram of a magnetic signature profile that can be achieved using a distribution of magnetic field inducers and associated magnetic field sources. [Figure 22C] FIG. 1 illustrates an exemplary embodiment in which a single magnet is used in conjunction with two magnetic induction sections to generate magnetic fields of opposite polarity on opposite sides of the wafer. [Figure 23] FIG. 1 is a schematic diagram of a quantum system, which may be implemented as a quantum processor, comprising a number of quantum devices forming a quantum subsystem capable of providing qubits. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0053] Elements in some of the figures are illustrated for simplicity and clarity and are not necessarily drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to facilitate an understanding of the various embodiments disclosed herein. Moreover, common but well-understood elements that are useful or necessary in commercially feasible embodiments are often not shown in order to more easily view such various embodiments of the present disclosure.

[0054] Various embodiments and aspects of the present specification will be described with reference to the details discussed below. The following description and drawings are illustrative of the present specification and should not be construed as limiting the present specification. Numerous specific details are set forth to provide a thorough understanding of the various embodiments of the present specification. However, in some cases, well-known or conventional details are not described in order to concisely discuss the embodiments of the present specification.

[0055] Furthermore, numerous specific details are set forth in order to provide a thorough understanding of the embodiments described herein. However, one skilled in the art will understand that the embodiments described herein may be practiced without such specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the embodiments described herein.

[0056] An element may be described in this specification as being "configured to perform" or "configured for" one or more functions. Generally, an element that is configured to perform or configured for performing a function is corresponding to, suitable for, adapted to, operable to, or otherwise capable of performing that function.

[0057] The articles "a," "an," "the," and "said," when introducing aspects of the disclosure or elements of examples of the disclosure, are intended to mean that there are one or more elements. The terms "comprising," "including," and "having" are intended to be inclusive and mean that there may be additional elements other than the listed elements. The term "exemplary" is intended to mean "one example of." The phrase "one or more of A, B, and C" means "at least one of A, at least one of B, and / or at least one of C."

[0058] 1A-1D are schematic diagrams of circuit elements. More specifically, FIG. 1A shows a classical electrical circuit of a harmonic oscillator with inductance L and capacitance C, which is well known in the art. A harmonic oscillator has a linear resonant frequency response defined as ω0=1 / √(LC).

[0059] In superconducting circuits 102, where circuit elements exhibit superconductivity during operation (which typically requires very low temperatures), slightly anharmonic oscillators called transmons can be realized by introducing Josephson junctions instead of inductances. Josephson junctions 104 in such configurations can provide nonlinearities that can be used, for example, to encode and manipulate quantum information. Transmons can be formed in the form of traces of materials that exhibit superconductivity at low temperatures that are coated on substrates such as semiconductors and insulators.

[0060] In the basic embodiment of the superconducting circuit shown in FIG. q is not adjustable. Other superconducting circuit elements with Josephson junctions have also been developed, where a superconducting loop is introduced into the circuit. The superconducting loop may more specifically comprise two branches that split and recombine at corresponding points on either side of the superconducting loop. One (or more) Josephson junctions may be introduced at each branch of the superconducting loop, thereby allowing the frequency ω q It is possible to create configurations where the magnetic flux Φ through the superconducting loop depends on the magnetic induction flux Φ. Other parameters and interactions can be tuned by the magnetic induction flux Φ, such as setting the magnetic flux to tune the superconducting device to be flux insensitive (e.g., Φ / Φ=0.5 in a flux qubit), or by mixed functions such as, but not limited to, third order cubic interactions or fourth order Kerr interactions.

[0061] Examples of superconducting circuits with loops are presented in Figures 1C and 1D. Figure 1C presents an example of a transmon device, more specifically, commonly referred to in the art as a SQUID (Superconducting Quantum Interference Device), with one Josephson junction at each of the two branches of the superconducting loop 106. Figure 1D presents an example of a transmon device, commonly referred to in the art as a SNAIL (Superconducting Nonlinear Asymmetric Inductive Element), with one small Josephson junction at a first of the two branches of the superconducting loop and one or more large Josephson junctions in series at a second of the two branches of the superconducting loop 106. A detailed illustrative embodiment of the capacitively shunted SNAIL, SNAILMON, is described in Grimm, A. et al., "Stabilization and operation of a Kerr-cat qubit," Nature 584, 2020. The illustrative embodiment of SNAILMON from this document is used herein as a reference for demonstrating the proof of concept, and for ease of reference will be referred to as "Grimm's SNAILMON."

[0062] However, it will be understood that other types of superconducting circuit elements may benefit from or even require the application of a magnetic field in some other embodiments, including superconducting circuit elements with superconducting loops, such as other versions of superconducting circuits, and the teachings presented below may be applicable to such other embodiments as well. FIG. 1E presents one specific example, for example, of a Josephson junction 122 having a tunnel junction 116 (shown with an insulating layer 112 and a superconducting layer 114) that may exhibit a frequency response as shown in FIG. 1F to a magnetic field aligned along the width of the tunnel junction 116. Such Josephson junctions may also benefit from the presence of a permanent magnetic field, although the magnetic field required here may be significantly larger than that used in SQUID or SNAIL superconducting loops, since the active area of ​​the magnetic flux defined by the cross section 118 of the tunnel junction shown in the figure is small, potentially several orders of magnitude smaller than a typical magnetic flux loop. In this sense, this specification should not be construed as being limited to the limited subset of specific examples used for demonstration purposes.

[0063] It will be appreciated that in some other embodiments, quantum devices comprising circuit elements other than superconducting circuit elements may also benefit from or even require the application of a magnetic field. For example, FIG. 1G provides an example of a qubit. A magnetic field source 124 may be used to generate a transverse magnetic field 120 as shown for a quantum dot 110 in a spin qubit. A control gate 108 is also shown in FIG. 1G. A magnetic field gradient may contribute to the control of the spin qubit, for example.

[0064] The superconducting or non-superconducting circuit elements of the quantum device may be supported by passive components called wafers, in a manner that may be somewhat reminiscent of one of the fabrication techniques used in conventional electronic circuits, where the wafers may be made of electrical insulators or semiconductor materials, the most common wafers being silicon and sapphire. The fabrication of superconducting circuit elements may require micro- and nano-fabrication techniques, and thus in some embodiments the wafers may be required to be compatible with such micro- and nano-fabrication techniques.

[0065] FIG. 2A presents a first technique by which a magnetic field B can be generated so as to apply a magnetic induction flux Φ through the circuit elements of the superconducting circuit. In this technique, an electric driver, for example a current source, is placed outside the cooled volume of the dilution refrigerator. Leads extend across the walls of the dilution refrigerator. The superconducting circuit (typically realized in the form of a pattern of tracks or lines of a material that exhibits superconductivity during operation) can be defined in one or several wafers, each of which can comprise one or several wafer layers (for simplicity, the wafers are not shown), and the conductors responsible for generating the magnetic field based on the input of the electric driver can also be integrated in the same wafer and typically connected to the leads via galvanic connections at both ends. Hereafter, during operation of the device, an electric bias source 202, which can be located at ambient temperature (for example, around 300 K), generates a current in an electric circuit that generates a magnetic field. This circuit comprises leads 208 extending across the walls 206 of the dilution refrigerator and the galvanic connections, as well as a conductor bias line 210 on the wafer. Current circulating along conductive bias line 210 generates a magnetic field B. Conductor line 210 is placed at a carefully designed location relative to superconducting loop 204 such that magnetic field B generates a magnetic induction flux Φ that penetrates superconducting loop 204, the magnetic field's amplitude depending on bias current I. This magnetic field generation technique can be considered "active" as opposed to "passive" because it requires actively generated current circulation to generate the magnetic field.

[0066] 2B, 2C, and 2D present an illustrative example of another technique that can generate a magnetic field B to apply a magnetic induction flux Φ through a circuit element (e.g., comprising superconducting loop 214) of a superconducting circuit. In FIG. 2B and FIG. 2D, the magnetization direction of the magnet is perpendicular to the surface supporting the superconducting loop, whereas in FIG. 2C, the magnetic field is oriented parallel to the surface supporting the superconducting loop. The magnets are sized and positioned in each case to apply a suitable magnetic induction flux. In FIG. 2B, magnet 212 is centrally located with respect to loop 214, whereas in FIG. 2C and FIG. 2D, magnets 216 and 218, respectively, are located next to loop 214 (e.g., at a distance 1, as shown in FIG. 2C). In the examples of FIG. 2B, 2C, and FIG. 2D, a permanent magnet (e.g., magnets 212, 216, or 218, respectively) is used instead of a current to generate the magnetic field B. This technique can be considered "passive" in the sense that it does not actively require the circulation of current in a classical circuit to maintain a magnetic field. For those skilled in the art, it was highly counterintuitive to surmise that such a technique for generating magnetic induction flux could be a suitable solution in superconducting circuits for quantum devices. This may be counterintuitive for a series of reasons including feasibility, variability, and losses, and perhaps the paradigms that existed in the field.

[0067] First, from the viewpoint of feasibility, it should be noted that in many practical implementations where the quantum device is biased with a magnetic flux, specifically those with a magnetic flux loop, the targeted magnetic induction flux can be of the order of the magnetic flux quantum Φ, where Φ / Φ can be in the range [0,1]. Achieving a smaller magnetic induction flux, on the one hand, allows the use of magnets with smaller volumes, but on the other hand, smaller magnets can be more difficult / expensive to produce and, at smaller dimensions, the dimensional variation between magnets can be greater due to variations in the production process. It can be quite difficult to produce magnets with dimensions below, for example, 100 nm, for example in terms of width, height, length or diameter. The dimensional variation can have a direct impact on the accuracy and value of the magnetic induction flux during operation in the final assembly. Another important factor is the amplitude B of the magnetic field along the superconducting circuit, which is determined by the amplitude of the magnetic field on the superconducting loop, which is equal to the critical magnetic field H of the superconductor. c If it exceeds (B>μ0H c ), which can damage the superconductivity. Finally, the presence of the magnet itself in the electromagnetic environment of the superconducting circuit can disrupt the operation of the device in the form of losses.

[0068] Before moving to the case study, it should be noted that in the exemplary embodiment presented in Figures 2B, 2C, and 2D, the permanent magnets are located on the same wafer surface as the surface on which the superconducting circuit elements to be biased are supported. This configuration may be referred to herein as "in-plane," especially in situations where the wafer surface is planar. In other embodiments, such as those exemplified below, the location of the magnet elements relative to this wafer surface may vary, such as being recessed in the wafer or aligned with another wafer surface or plane. The wafer surface may be non-planar, such as curved, in some other embodiments.

[0069] Case Study - Introduction A case study was carried out to determine whether the use of a permanent magnet as a source of magnetic induction flux Φ through a superconducting loop could be a suitable means for a particular embodiment. In this particular embodiment, the frequency ω q Various geometries of permanent magnets, the magnetic induction flux sources used to impose (commonly referred to in the art as "tuning") the cubic interactions, were considered. In this particular example, to obtain the results shown in Figures 4 and 5, e.g., b = w loop = 7.94 μm and a = h loop = 8.20 μm. The magnetic induction flux quantum Φ0 is approximately 2.068 × 10 -15 Wb, and the magnetic induction flux Φ is defined as the surface integral of the normal component of the magnetic field B within the area defined by the superconducting loop. The electromagnetic simulations are R The study was based on magnets made of FeCo with a remanence of ≈1.98 T, which was considered to be favorable for testing smaller magnet dimensions. Indeed, if the remanence decreases to achieve the same ambient magnetic field, the magnet dimensions must be increased, and from this point of view, materials with a higher remanence may be favorable. In the case study, the authors set somewhat arbitrary targets that seemed to be linked to a subjective feeling suitable for this particular example. From this point of view, the case study set the target magnetic induction flux to be on the order of a flux quantum, e.g. Φ∈[0,1]Φ0, and the maximum magnetic field amplitude on the flux loop conductor to be an order of magnitude smaller than the critical magnetic field Hc of the superconductor, e.g.

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[0070] Feasibility To optimize the magnet design and geometry with respect to its intended function, it may be desirable to consider the effects of final manufacturing process variations in the final situation. The choice of magnet shape, orientation, and location with respect to the superconducting loop may affect the sensitivity to manufacturing process variations, and a scenario where sensitivity to manufacturing process variations is minimized may be desirable. In the case study, the main parameters t, w, h, x, y, z (x, y, z are the position coordinates of the magnet with respect to the center of the flux loop), h loop , and w loop For each, the partial derivative of the magnetic induction flux is evaluated.

[0071] FIG. 2C shows a first example of magnet shape, position, and orientation 20 that is the subject of a case study. The magnet is a bar magnet, in this case, located transverse to the superconducting loop, on the same wafer surface that supports the superconducting loop. In the case study, ΔV=0.05×V0 ​​(5% of the magnet volume V), Δx, Δy, Δw loop , Δh loop = 50 nm, and Δz = 10 nm,

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[0072] 4, the optimum bar magnet configuration was determined from derivative analysis to be a magnet thickness of 0.3 μm (target >0.1 μm), width of 0.65 μm (target >0.2 μm), length of 1.94 μm (target >0.2 μm), and Z offset from the wafer surface of 0.5 μm. This configuration is the feasible size of the magnet configuration.

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[0073] A similar simulation was performed with a central dot magnet configuration as diagrammed in FIG. 2B, the results of which are presented in FIG. 5, and another simulation was performed with a horizontal dot magnet configuration as diagrammed in FIG. 2D, the results of which are presented in FIG. 6. These two additional simulations also met all the requirements set out in the case study, confirming from a feasibility point of view the possibility of a permanent magnet generating magnetic induction flux in cooperation with a superconducting loop.

[0074] scattering The case study, as revealed above, targeted 2σ<0.05Φ0 and was carried out with five different permanent magnet configurations. The first permanent magnet, called the central dot, is presented in FIG. 2B (e.g., central dot 212), where w (and h) is 130 nm. The second permanent magnet, called the compensated central dot, is shown in FIG. 7A, and includes a central dot magnet 702 separated from a lateral dot magnet 704 by a spacing l of 4.62 μm. The w1 of the central dot 702 is 216 nm, and the w2 of the lateral dot 704 is 132 nm. The third permanent magnet, called the doubly compensated dot, further includes a second lateral dot 706 opposite the first lateral dot 704, as shown in FIG. 7B. In this third case, the w1 of the central dot 702 is 308 nm, the w2, w3 of the horizontal dots 704 and 706 are 247 nm, and the spacing l is 5.43 μm. The fourth permanent magnet is the horizontal dot 218 presented in FIG. 2D, with w=625 nm. The fifth permanent magnet is the horizontal bar 216 presented in FIG. 2C, with w=3.73 μm, h=11.2 μm, and l=21.9 μm. The same thickness t of 200 nm was used throughout the design. Monte Carlo simulations, with a sample scale of 100,000 units, show that the variations are ±20 nm Δw, Δh, and Δw, taking into account the positions of all magnets, ±5 nm Δt, and ±10 nm Δl, with a uniform distribution. loop, with Δx and Δy of ±30 nm. The results of the Monte Carlo simulations for five different designs are plotted in FIG. 8 (e.g., plots 802, 804, 806, 808, and 810). The flux variation target was achieved for the last four designs (e.g., 804, 806, 808, and 810). M R Since reducing reduces the variability, even the first design (e.g., 802) may be able to achieve the goal of the case study.

[0075] loss Loss simulations were performed using the Ansys High Frequency Structure Simulator (HFSS) using Grimm's SNAILMON design invoked above.

[0076] total loss

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[0077] The results are shown in Figures 9A and 9B and presented numerically in the table below. [Table 1] where V is the volume, S is the surface, cap is the capacitive loss (electric field loss), ind is the inductive loss (magnetic field loss), MA is the metal-air interface, MS is the metal-wafer interface, and m is the

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[0078] The losses were found to not meet the targets selected for the case study. However, as shown in Figure 10,

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[0079] Case Study - Conclusion Case studies have concluded that, at least in some embodiments, the use of one or more permanent magnets to apply a magnetic induction flux across a superconducting loop is a preferred approach.

[0080] It will be appreciated that while the case study addresses the use of permanent magnets as a preferred source of magnetic induction flux Φ in a somewhat specific context, the results of the case study can be extrapolated to many other similar contexts, and thus the case study more generally demonstrates that the use of permanent magnets as a source of magnetic induction flux Φ is preferred in many superconducting loop implementations. Furthermore, it is expressly noted that in the specific examples used in the case studies presented above, some of the imposed goals, limitations, and / or restrictions may not be present or may be relaxed in some alternative implementations.

[0081] Magnetic Field Type Depending on the details and type of quantum device in which passive magnet elements are used to generate the magnetic induction flux, various possible scenarios are possible. The magnetic field generating source may in some embodiments be intended to provide only a fixed magnetic field component during the entire duration of a given operation phase. For this purpose, one or more permanent magnets located at a suitable location relative to the superconducting circuit elements may allow to completely replace the active magnetic field elements comprising DC power supplies, leads, conductor traces and galvanic connections. This may be extremely beneficial in some embodiments. In other embodiments, the intended magnetic field may include a fixed component and a variable component, such as an AC component, or other variable component, for example superimposed on a DC bias. In embodiments in which such a variable component is included, it may still be appropriate to use active magnetic field elements to provide the variable component of the magnetic field. However, the use of passive magnet elements may still be beneficial, such as reducing or eliminating the need to incorporate DC components in the active magnetic field device. Thus, any permanent magnetic field components, such as part or all of the DC bias equivalent, may be applied using one or more passive magnet elements, while the variable magnetic field components can continue to be applied using the active magnetic field device. In this way, active magnetic field devices may, for example, be simplified or reduced. Thus, various implementation schemes are possible, the details of which are left to the designer of a particular implementation based on the teachings of this specification.

[0082] Furthermore, it is understood that although permanent magnets such as ferromagnetic materials can be considered as good candidates for use as passive magnet elements, ferromagnetic materials are not the only possible candidates. For example, in one embodiment, it can be considered interesting or preferable to use magnetic tunnel junctions as passive magnet elements. In fact, the magnetic field of a magnetic tunnel junction can be switched by passing a current through it, but once switched, it will continue to generate a magnetic field without active circulation of a current. For example, if a stack of magnetic tunnel junctions interspersed with permanent magnets or magnetic field strengths is used, and the magnetic field orientation of the magnetic tunnel junctions can be selectively switched to cancel or amplify the magnetic field of the neighboring permanent magnets, a system in which the magnetic field strength can be digitally adjusted by controlling the magnetic field orientation of the magnetic tunnel junctions may be realized.

[0083] Possible Architectures 11A-11C, it will be appreciated that in some embodiments, it may be preferable to use one or more magnets positioned and configured to favorably affect multiple superconducting loops, whether or not the magnets' static magnetic field may be part of the same superconducting device (e.g., FluxQubit, SQUID, SNAIL, or SNAILMON), and such an approach may potentially lead to a reduced footprint of the device, which may be desirable in some embodiments. For example, in FIG. 11C, multiple superconducting loops 1102 are positioned next to each other, and a "horizontal dot" type magnet (e.g., dot magnet 1104) is positioned between adjacent superconducting loops to simultaneously contribute magnetic induction flux through both adjacent superconducting loops 1102. The loops may form part of different quantum bits, for example, or may form part of the same quantum bit, in such embodiments. In FIG. 11B, a transversely oriented bar magnet 1106 is used to apply magnetic induction flux to a pair of adjacent superconducting loops. In FIG. 11A, a doubly compensated central dot geometry (eg, using a central dot magnet 1112) is extended to multiple adjacent superconducting loops 1110 by sharing lateral dots 1114.

[0084] Many other alternative architectures are possible, and indeed, while the three examples presented in Figures 11A-11C present relatively simple one-dimensional arrays, the concept can be extended to two-dimensional and even three-dimensional arrays, and to curved rather than planar virtual surfaces.

[0085] Moreover, in the embodiments presented and described above, the magnet or magnets are typically located relatively "in-plane," where "in-plane" means generally aligned with the wafer surface supporting the superconducting loops, and "on-chip" means on the same wafer. For an in-plane geometry, perhaps the most likely geometry is to pattern the permanent magnets on the same wafer on which the superconducting traces forming the superconducting circuit elements are supported. However, in other embodiments, it may be somewhat preferred to embed the permanent magnets in such wafers rather than patterning them on a common, planar, flat surface. This may be accomplished, for example, by placing the permanent magnets in recesses or other depressions formed in the wafer. Many other embodiments are possible, particularly out-of-plane embodiments. In particular, FIG. 12A presents one such other possible embodiment. In the embodiment presented in FIG. 12A, two wafers (1204 and 1206) are used, separated by solder balls 1208 or other spacing elements. Each wafer has a surface that faces the other wafer. As yet another possible example, a superconducting circuit element 1210, such as a superconducting loop, may be deposited on a first of the surfaces, and a magnet 1202 may be affixed to the other of the surfaces.

[0086] Figure 12B presents yet another exemplary embodiment in which a micromagnet 1216 is supported by the same surface of the wafer that also supports SNAILMON, and is housed within a rectangular 3D cavity 1222 as an electrically suspended and insulated chip 1212. A coaxial cable 1214, connector chip / RF antenna 1218 are also shown in Figure 12B, and arrow 1220 indicates the closing of the cavity. Such an embodiment can be used, for example, to realize qubits in a 3D geometry, and passive magnetic elements can be used, for example, in the process of magnetostatic flux control.

[0087] Magnetic field induction part As alluded to above, the exact selection of the relative locations of one or more magnetic field sources, whether passive (e.g., magnets, magnetic tunnel junctions) or active (e.g., conductors driven by circulating current), and one or more circuit elements (e.g., superconducting loops, Josephson junctions, spin qubits), may be suitably left to the designer in light of the specific circumstances of a particular implementation or application, and there may be many possible configurations.

[0088] In some embodiments, it may be preferable to position a magnetic field source on a side of the wafer opposite the surface of the wafer that supports the circuit elements through which the magnetic induction flux is to be applied (e.g., the second side) and use a magnetic field inducer to transmit the magnetic field across one or more layers of the wafer. A first exemplary embodiment of this is provided in FIG. 13A.

[0089] The quantum device may comprise circuit elements supported by a wafer, similar to the examples presented above. The circuit elements, in this particular example, are superconducting loops provided in the form of traces of material that exhibit superconductivity during operation of the device and that are supported on a first surface of the wafer. The wafer may more specifically comprise a first surface supporting the circuit elements and a second surface opposite the first surface, the circuit elements being "on chip".

[0090] In the embodiment shown in Fig. 13A, a magnetic field induction section 1302 is provided. More specifically, a tubular passage 1310 extends across the wafer 1304 from a first end 1312 of the first side, which opens through a first surface 1314, to a second end 1308 of the second side, which opens through a second surface 1316. The magnetic field induction section 1302 comprises a layer of material that exhibits superconductivity during operation of the quantum device (e.g., at very low temperatures inside a dilution refrigerator), which in this embodiment completely coats the inner surface 1318 of the tubular passage 1310 inside the wafer 1304. The magnetic field induction section 1302 is now used to induce a magnetic field across the wafer 1304, i.e., from the second surface to the first surface, during operation of the quantum device, if the induction layer is superconducting.

[0091] In this first example, the magnetic field source is a bar magnet 1306 (an elongated rectangular parallelepiped with the field aligned longitudinally), which is placed next to the second end 1308 of the via 1310 on the second surface 1316, i.e., on the side of the wafer opposite the circuit element 1320, with the magnetic field of the bar magnet pointing towards the magnetic field inducer, here offset slightly from the wafer surface, coinciding with the second end of the magnetic field inducer. HFSS simulations were performed using the model presented on the left side of FIG. 14. The center and right sides of FIG. 14 present the results. The magnetic flux loops, for example, at each end 1402 and 1406 of the via 1404. The left side of FIG. 14 also shows the location of the micromagnet 1408. The wafer had finite dimensions that allowed the magnetic flux lines to close back on themselves around the wafer. It has been found that the magnetic field is interestingly confined within the magnetic field induction section and induced by the magnetic field induction section all the way to the other end of the magnetic field induction section, while the strength of the magnetic field adjacent to the magnetic field induction section drops off in an inverse polynomial manner. A portion of the magnetic field induced by the via can be expanded to provide a suitable magnetic induction flux, for example across a superconducting loop or other superconducting circuit element.

[0092] From the feasibility analysis of a bar magnet with t=0.5μm, w=1μm, l=10μm, and a via with a radius of 2μm,

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[0093] As can be seen in FIG. 15, the relative magnetic induction flux generally decreases as a multiple of r (e.g., 1 / r, as expected from the geometry and magnetic dipole equations). 4 ), but the use of vias makes it possible to change this relationship, so that the relative magnetic induction flux varies inversely with r (for example 1 / r) or else varies inversely with r by a power less than 2, or even less than 1.5. The relationship is similar for magnetic field induction sections with openings located outside the superconducting circuit loop.

[0094] The magnetic field source is a dot magnet 1608 (axially aligned cylindrical / frustoconical geometry) in the second example diagrammed in FIG. 16. A superconducting loop 1616 is supported on a first surface 1620 of a first substrate or wafer 1602 (here a silicon wafer), and a (superconducting) magnetic induction field inducer 1614 is defined across the first wafer 1602 from a first end 1618 adjacent to the superconducting loop 1616 to a second end 1612 at an opposite surface 1622 of the first wafer 1602. A second wafer 1604, such as another silicon wafer, is positioned adjacent to the first wafer 1602, but is held at a given gap from the first wafer by spacer elements, such as solder ball bumps 1606. The dot magnet 1608 is positioned on the surface 1610 of the second wafer 1604 in a configuration that may be referred to as a "flip chip", aligned with the length of the magnetic field inducer 1614 and adjacent to the second end 1612 of the magnetic field inducer. Additionally, the gap or distance 1624 between the surfaces 1610 and 1622 is also referred to as the "flip chip gap". FIG. 17 shows details of the HFSS model (left) and the results of the HFSS simulation are shown in the middle and on the right (flip chip gap 0.01 mm and magnet volume multipliers 1 and 2, respectively). The magnetic flux loop 1702, micro magnet 1704, and vias (or magnetic field inducers) 1706 are shown on the left side of FIG. 17.

[0095] Relative magnetic induction flux, flip-chip gap, and magnet volume scaling factor (initial magnet volume 4.69 μm 3 ) is presented in FIG. 18 for comparison between scenarios with and without vias.

[0096] Various alternative embodiments are possible. For example, FIG. 19 presents yet another possible embodiment in which the wafer comprises multiple wafer layers, more specifically here two wafer layers (e.g. layers 1902 and 1912). The tubular passage of the magnetic field inducing portion 1906 is dead-ended in the sense that it extends across only the first wafer layer 1902. Furthermore, a magnetic field source, here provided in the form of a micro-magnet 1904, can be located between the two wafer layers, adjacent to the second end 1914 of the magnetic field inducing portion 1906, and the circuit element 1908 can be located adjacent to the first end 1916, and the magnetic field inducing portion 1906 can be used to induce a magnetic field in the quantum device circuit element 1908 while it is superconducting. FIG. 19 also shows another circuit element 1910.

[0097] In some embodiments, for a magnetic field inducer to be fully effective, the magnetic induction flux lines must have the ability to close back on themselves after penetrating the magnetic field inducer. Indeed, if the end of the magnetic field inducer is open to the closed superconducting cavity, the magnetic field has no way back and cannot penetrate the closed superconducting cavity across the magnetic field inducer. In some embodiments, providing a magnetic field inducer across a wafer of finite dimensions may be sufficient to allow the magnetic field to close back around the edge of the wafer. In other embodiments, one or more "return" magnetic inducers may be introduced across the wafer to encourage the magnetic field to close back across the return magnetic inducer. One particular embodiment is presented in FIG. 20. In the embodiment presented in FIG. 20, a cavity 2002 is formed between two wafer layers 2004 and 2006, and the surface of the cavity 2002 is completely coated with a layer of superconducting material. Here, one magnetic induction section, which may be called source induction section 2008, is provided to induce the magnetic field of the magnetic field source (micromagnet 2010) into the cavity, and two return magnetic induction sections, which may be called suction induction sections 2012 and 2014, are used to provide a return path from the superconducting cavity 2002. Interestingly, in such a configuration, the magnetic field can be induced by the superconducting cavity 2002 to many suction magnetic induction sections (e.g., suction induction sections 2012 and 2014) located at various distances from the source induction section 2008 without detectable or significant magnetic loss, as shown in the simulation results shown. In alternative configurations, for example, one or more than two suction magnetic induction sections, or multiple source magnetic induction sections, can be used. The magnetic field can be divided equally between the suction induction sections even if they are not at the same distance from the source induction section. Each suction induction section can receive the same maximum amplitude of the magnetic field, and the magnetic flux can differ depending on the area of ​​the tubular passage. This coupling can perhaps be visualized as the source inductor being a current source, the current being a magnetic induction flux inside the source inductor, and the sink inductor being a resistive load with an impedance proportional to the inner area of ​​the superconducting coating of the tubular passage, in which case it can be seen that Ohm's law is considered in a similar way to how it is considered in an electric circuit.

[0098] In some embodiments, it may be preferred that the magnetic field induction layer completely covers the inner surface of the tubular passage. In other embodiments, such as that shown diagrammatically in FIG. 21, it may be preferred that the magnetic induction layer 2102 covers most, but not all, of the inner surface of the tubular passage. In the illustrated example, a relatively long and narrow gap 2104, specifically less than 15% of the diameter of the tubular passage, has been left along the entire length of the induction layer, but is only shown here for ease of understanding. Indeed, in some embodiments, the presence of such a gap may aid the function of the magnetic field induction, specifically facilitating the penetration of the magnetic field as the induction layer transitions between the non-superconducting state and the superconducting state of the induction layer. This may be particularly useful in some embodiments where the circuit element subject to the magnetic field is a superconducting loop, and the superconducting loop may resist changes in magnetic flux across the superconducting loop during the transition from the non-superconducting state to the superconducting state, and the presence of the gap may help accommodate the transition. This structure can be achieved in some embodiments using, for example and non-limiting example, angle evaporation techniques where the deposition is directional, e.g., electron beam evaporation. By slowly rotating the sample less than 360° while evaporating at an angle, the inner portion of the via can be covered with superconducting material while leaving the desired gap across the length of the via. In some embodiments, a variation of the same technique may be used, using a suspended mask, by shadow evaporation (also known as the grease gun technique or angle evaporation).

[0099] Various configurations are possible. For example, in an embodiment such as that presented in FIG. 11C, a magnetic field inducer with an associated active or passive magnetic field source can be used instead of a micromagnet on the opposite side of the supporting wafer to share the magnetic field with two or more circuits of a quantum device. Furthermore, multiple magnetic field inducers 2202 can be arranged as presented in FIG. 22A and used to generate a magnetic signature profile 2204 along a given wafer surface as presented in FIG. 22B, where:

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[0100] In the examples presented in Figures 13A and 16, magnets were used as the magnetic field source, however, it is expected that replacing the permanent magnets with equivalent magnetic flux bias lines of appropriate geometry will yield similar results, and it will be appreciated that in some examples an active magnetic field source may be a suitable alternative to a passive magnetic field source.

[0101] In both the FIG. 13A and FIG. 16 embodiments, the superconducting circuit is located proximate the first end and the magnetic field source is located proximate the second end.

[0102] Interestingly, if the magnets are placed completely outside the wafer surface (e.g., flat) of the superconducting loop and transmit their magnetic field through the magnetic field guide, as is the case in the examples presented in Figures 13A and 16, the magnets may not cause any conductive losses or may cause significantly less conductive losses. Losses can therefore be expected to be significantly smaller than in the simulations presented above with the "front" magnets.

[0103] There may be embodiments in which the magnetic field inducing portion and the magnetic field source associated with the magnetic field inducing portion can be used as a magnetic field source for quantum device circuit elements other than a superconducting loop, such as a Josephson junction as shown in FIG. 1E, or a spin qubit as shown in FIG. 1G.

[0104] In one embodiment, the volume within the dielectric layer may be left empty, while in another embodiment, for example, the volume may be filled with a non-conductive material.

[0105] Although some examples presented and illustrated above present magnetic field inducing sections used to induce a magnetic field emanating from a permanent magnet, it will be appreciated that equivalent magnetic fields emanating from flux bias lines and the like can be expected to be induced by vias as well, thereby allowing the magnetic field inducing sections to be used to induce the magnetic field of a passive or active magnetic field source, and thus to induce a passive or active magnetic field in various embodiments. The flux bias lines can be provided in the form of a superconducting element of a given configuration / shape connected to an electric drive. By remotely locating an electromagnet and inducing its magnetic field with a via, crosstalk between the magnetic field generating circuitry of the quantum device and the superconducting circuitry (e.g., providing the qubits) may be reduced compared to scenarios where the flux bias lines are located next to, within the actual surface of, or otherwise closer to the superconducting loop. In particular, for example, by locating the ends of the vias outside the superconducting loop, it may be possible to reduce any losses experienced by the superconducting circuit and / or to allow the magnetic field transmitted by the magnetic induction flux lines to be shared, for example, by multiple superconducting loops.

[0106] Potential Uses Quantum devices that utilize magnetic fields and may benefit from the use of one or more permanent magnets, one or more magnetic field inducers that transmit the magnetic field across the wafer, or both, can be used in a wide variety of applications. One example of such an application is quantum computing, where superconducting circuits can be useful to realize qubits or couplers. A typical quantum computer architecture is presented in FIG.

[0107] Indeed, the operations to be performed on qubits depend to some extent on the choice of architecture of the complete processor. There are several competing architectures, of which illustrative examples of two will be presented below: quantum annealers and gate-based quantum processors.

[0108] Depending on the type of architecture, and also depending on the type of quantum subsystem used as a basis for the logical states, the details of the implementation of the quantum processor may vary widely from one embodiment to another. However, many architectures and types will generally require the use of more than one quantum subsystem to facilitate quantum computation. Indeed, a typical, exemplary quantum processor will require at least two quantum subsystems (e.g., 2302a, 2302b, . . . 2302N) interconnected such that the quantum states of the quantum subsystems interact with each other, typically during interactions involving quantum entanglement, as shown in FIG. 23. The type of quantum subsystem will vary depending on the architecture. Most quantum systems embodied as boson-based quantum processors will require some form of resonator that provides the quantum state, and the quantum state will be driven within the quantum subsystem using some form of driving hardware (e.g., 2304a, 2304b, . . . 2304N) that can control some bosons of the quantum subsystem. The driving hardware is referred to herein as a controller 2306, and is typically controlled by components provided in the form of a classical computer. The quantum subsystems are typically cooled to very low temperatures and isolated from the environment. In some architectures, such as quantum annealing type architectures or measurement-based quantum computing architectures, the quantum subsystems can be operatively directly interconnected. In some architectures, such as gate-based quantum computing, the quantum subsystems are typically interconnected via couplers (e.g., 2308a-N) that are used to selectively control the interaction between the quantum subsystems. The couplers 2308a-N are also quantum subsystems that are operative to provide a state in which the quantum states of two or more connected quantum subsystems should interact, and for convenience are driven by drive hardware (e.g., coupler drivers 2310a-N) that can also be controlled by the same controller 2306.23 also illustrates a controller 2306 operably coupled to control instructions 2316, e.g., stored in a non-volatile memory of the classical computer (not shown). The controller 2306 is configured to execute the control instructions 2316, which in some embodiments include definitions 2314 of logical states to be generated in the quantum subsystems 2302a-2302N and one or more functions 1316 for operating the driver hardware 2304a, 2304b, . . . 2304N and the combiner drivers 2310a-2310N to generate the logical states.

[0109] Those skilled in the art will appreciate that materials exhibiting superconductivity, such as those used in the inductive layers discussed above, may include, but are not limited to, materials such as niobium (Nb), niobium nitride (NbN), niobium titanium nitride (NbTiN), tantalum (Ta), tantalum nitride (TaN), and aluminum (Al). Similarly, the superconducting material used in the fabrication of Josephson junctions is typically Al. However, those skilled in the art will readily appreciate that the present disclosure does not preclude the use of other superconducting materials in Josephson junctions.

[0110] The magnetic field inducers, in some embodiments, may be oriented at an angle and / or have curved portions relative to one or more of the substrate surfaces. In some embodiments, two or more magnetic field inducers or vias may be directly coupled to each other to induce a portion of the magnetic field.

[0111] While the present disclosure describes various embodiments for illustrative purposes, such description is not intended to be limited to such embodiments. On the contrary, applicant's teachings as described and illustrated herein encompass various alternatives, modifications, and equivalents without departing from the embodiments, the full scope of applicant's teachings being defined in the appended claims. The information shown and described herein is capable of fully achieving the above-described objectives of the present disclosure, the presently preferred embodiments of the present disclosure, and is therefore representative of the subject matter broadly contemplated by the present disclosure.

Claims

1. A quantum device, A substrate; a superconducting circuit element supported on a substrate surface of the substrate, the superconducting circuit element exhibiting superconductivity during operation of the quantum device; Passive magnetic elements and the passive magnetic element generates a fixed magnetic field during an entire operation phase of the quantum device, and the superconducting circuit element is exposed directly or indirectly to at least a portion of the fixed magnetic field during the operation phase of the quantum device, thereby providing a constant frequency response in the superconducting circuit element; the superconducting circuit element comprises a superconducting loop having two branches that split and recombine at corresponding points, each branch having at least one Josephson junction, and the portion of the fixed magnetic field contributes to a constant magnetic induction flux across the superconducting loop; the passive magnetic element and the superconducting circuit element are both supported on the substrate surface of the substrate; the passive magnetic element is disposed adjacent to the superconducting circuit element; A quantum device wherein the superconducting loop has at least one axis of insensitivity, and the passive magnetic element is located on the axis of insensitivity.

2. The quantum device of claim 1 , wherein the axis of insensitivity extends laterally across the two branches of the superconducting loop.

3. The quantum device of claim 1 , wherein the passive magnetic element has a magnetization direction perpendicular to the substrate surface.

4. 4. The quantum device of claim 3, wherein the passive magnetic element is a first passive magnetic element, the quantum device further comprising a second passive magnetic element supported by the substrate surface, the second passive magnetic element being centrally located with respect to the superconducting loop.

5. 5. The quantum device of claim 4, further comprising a third passive magnetic element supported by the substrate surface, the third passive magnetic element positioned adjacent the superconducting loop and on an opposite side from the first passive magnetic element.

6. The quantum device of claim 1 , wherein the passive magnetic element has a magnetization direction parallel to the substrate surface, the magnetization direction being oriented along the insensitive axis of the superconducting loop.

7. The quantum device of claim 1 , wherein the passive magnetic element is located above or below a plane defined by the superconducting loop.

8. The quantum device of claim 7 , wherein the passive magnetic element is disposed within a recess formed in the surface of the substrate.

9. 2. The quantum device of claim 1, wherein the superconducting circuit element is selected from the group consisting of a flux qubit, a superconducting quantum interference device (SQUID), a superconducting nonlinear asymmetric inductive element (SNAIL), and a capacitive shunt SNAIL (SNAILMON).

10. The quantum device of claim 1 , wherein the superconducting element is one of a plurality of superconducting elements, the plurality of superconducting elements being arranged in an array configuration on the substrate surface.

11. The constant magnetic induction flux is a magnetic induction flux quantum Φ ０ The quantum device of claim 1 , wherein the quantum device is on the order of 1000 keV.

12. 10. The quantum device of claim 1, wherein the superconducting circuit element is configured to operate as a quantum subsystem of a quantum computer, the superconducting circuit element being operable to provide at least one qubit within the quantum subsystem during operation of the quantum computer.

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