Method for Operating Charged Particles

Abstract

A method is presented that includes trapping a charged particle at a first location using an electromagnetic trap, providing a static magnetic field at the first location such that a quantum bit transition of the charged particle is defined, and providing an oscillating magnetic field using entanglement electrodes. The oscillating magnetic field present at the first location does not include a polarization component that directly couples to the quantum bit transition. The oscillating magnetic field has a spatial gradient at the first location of a polarization component of the oscillating magnetic field that couples the quantum bit transition to the motion of the charged particle.

Description

Technical Field

[0001] This specification relates to quantum sensing and quantum computing using charged particles.

Background Art

[0002] Trapped charged particles are a promising platform for quantum sensing and quantum computing. As with other candidate technologies, the challenges are to achieve a high level of fidelity in elementary logical operations and to scale the system to more qubits.

Prior Art Documents

Non-Patent Documents

[0003]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

Summary of the Invention

Means for Solving the Problems

[0004] According to one aspect of the present invention, there is provided a method including the steps of trapping charged particles at a first position using an electromagnetic trap, providing a static magnetic field at the first position such that a qubit transition of the charged particles is defined, and providing an oscillating magnetic field using entangling electrodes. The oscillating magnetic field present at the first position does not include a polarization component that directly couples to the qubit transition. The oscillating magnetic field has a spatial gradient of the polarization component of the oscillating magnetic field that couples the qubit transition to the motion of the charged particles at the first position.

[0005] In some implementations, the entangling electrodes extend in a first direction perpendicular to the direction of the static magnetic field. The qubit transition is a sigma transition between states in which each magnetic quantum number differs by only one, and the oscillating magnetic field at the first position is linearly polarized parallel to the direction of the static magnetic field such that the oscillating magnetic field does not directly couple to the qubit transition.

[0006] In some implementations, the entangling electrodes comprise a coplanar waveguide.

[0007] In some implementations, the coplanar waveguide comprises a central track, a first return track, and a second return track. The central track extends in the first direction between the first return track and the second return track, and the first return track and the second return track are electrically connected to a ground terminal shared with the electromagnetic trap.

[0008] In some implementations, the coplanar waveguide further comprises a short - circuit connection. The first return track, the second return track, and the central track are electrically connected to the short - circuit connection at one end. The distance in the first direction between the first position and the short - circuit connection is less than λ / 4, where λ is the wavelength of the oscillating magnetic field in the coplanar waveguide.

[0009] In some implementations, the coplanar waveguide is formed symmetrically with respect to the central track.

[0010] In some implementations, the method further includes trapping a second charged particle at a second position using an electromagnetic trap, providing a static magnetic field such that the magnitude and direction of the static magnetic field are the same at a first position and the second position, and providing an oscillating magnetic field for the second charged particle using a fringing electrode. The fringing electrode extends in a direction parallel to the direction of the line connecting the first position and the second position such that the oscillating magnetic field present at the second position does not include a polarization component that couples to the qubit transition of the second charged particle.

[0011] In some implementations, the method further includes generating a spin-dependent force on the charged particle and the second charged particle by exciting one or more motional sidebands of the qubit transition using the oscillating magnetic field.

[0012] According to another aspect of the present invention, there is provided a device for generating quantum entanglement between charged particles, comprising: a substrate having a first surface and a second surface facing each other; a trap electrode disposed on the first surface of the planar substrate and configured to form an electromagnetic trap for trapping a charged particle at a first position in response to a voltage such that the first surface is sandwiched between the first position and the second surface; and a fringing electrode disposed on the first surface of the planar substrate, extending in a first direction along the substrate, and configured to generate an oscillating magnetic field parallel to the substrate and perpendicular to the first direction at the first position in response to an oscillating current.

[0013] In some implementations, the fringing electrode comprises a coplanar waveguide.

[0014] In some implementations, the coplanar waveguide comprises a central track, a first return track, and a second return track. The central track extends in the first direction between the first return track and the second return track, and the first return track and the second return track are electrically connected to terminals held at a fixed potential with respect to the ground terminal of the trap electrode.

[0015] In some embodiments, the first return track, the second return track, and the central track are electrically connected to a short-circuit connection portion at one end.

[0016] In some embodiments, the widths of the first return track and the second return track are wider than the penetration depth of the material for the first return track and the second return track at the frequency of the oscillating magnetic field.

[0017] In some embodiments, the electromagnetic trap is a surface electrode pole trap.

[0018] In some embodiments, the surface electrode pole trap is configured such that the symmetry axis of the electromagnetic trap lies along a first direction.

[0019] In some embodiments, the surface electrode pole trap includes a first RF electrode and a second RF electrode extending in a first direction, and a first DC electrode and a second DC electrode extending in the first direction. The first RF electrode and the second RF electrode are disposed between the first DC electrode and the second DC electrode, and the entanglement electrode is disposed between the first RF electrode and the second RF electrode.

[0020] In some embodiments, a system for quantum information processing is provided, comprising a plurality of charged particles, the aforementioned device for entangling two or more of the plurality of charged particles, a device for generating a static magnetic field, and a signal generator for generating electrical signals for the electromagnetic trap and the entanglement electrode.

[0021] Here, specific embodiments of the present invention will be described by way of example with reference to the accompanying drawings.

Brief Description of the Drawings

[0022]

Figure 1

Figure 2

Figure 3a

Figure 3b

Figure 4

Figure 5

[0023] For the implementation of a general-purpose quantum computer using charged particles, qubits can be implemented from transitions between the states of charged particles having resonance frequencies in the RF / microwave region. For example, in the case of atomic ions, hyperfine transitions can be used as qubits.

[0024] These microwave transitions are usually manipulated via optical transitions due to the convenience of addressing each charged particle using a focused laser beam and the strong coupling between the spin and the degrees of freedom of motion generated by short-wavelength optical radiation. This specification relates to a laser-free method for generating quantum entanglement between trapped charged particles. A corresponding apparatus for generating quantum entanglement between trapped charged particles is presented.

[0025] FIG. 1 is a schematic diagram of a system for quantum information processing using trapped charged particles.

[0026] The charged particle 10 can be trapped within the vacuum chamber 20. The vacuum chamber 20 provides an ultra-high vacuum environment that allows individual charged particles to be separated. Using a radio frequency or microwave electric field, the charged particle 10 can be confined within a predetermined volume of space, and the motion of the charged particle 10 can be cooled near its motional ground state.

[0027] As used herein, the term "charged particle" is used to mean an atom, molecule, or ion having a net charge. In particular, the charged particle 10 also includes elementary charged particles such as electrons or positrons.

[0028] Surface electrode trap One or more charged particles 10 can be trapped near the surface of the surface electrode trap 100. The surface electrode trap 100 can be configured to generate an electromagnetic trap in response to a voltage provided to the surface electrode trap 100. For example, the surface electrode trap 100 can be a radio frequency Paul trap. For the sake of convenience, in this specification, as an example of the surface electrode trap 100, the radio frequency Paul trap will be discussed.

[0029] The surface electrode trap 100 includes a substrate 101 and a plurality of electrodes 110, 120, 130 microfabricated on the first surface of the substrate 101.

[0030] In some implementations, the electrodes 110, 120, 130 can form one or more elements for trapping, manipulating, and entangling the charged particle 10. The two-dimensional layout of the electrodes 110, 120, 130 on the first surface of the substrate 101 can be scalable to a large-scale array of multiplexed traps for scalable quantum information processing or quantum computing using the trapped charged particle 10, known as a quantum CCD (Nature 417, 710 - 711 (2002)). For the sake of brevity, FIG. 1 shows only a single unit of a possible large-scale array of multiplexed traps.

[0031] To achieve several objectives, voltages and currents can be applied to the surface electrodes 110, 120, 130. In this specification, these voltages and currents are referred to by the typical frequency ranges in which they exist, namely, the "RF" voltage for generating the ponderomotive confinement potential, the lower frequency "DC" voltage for generating the static confinement potential and transporting ions around the chip, and the "microwave" current for driving quantum logic operations and generating entanglement.

[0032] The distance between the trapped charged particles 10 and the electrodes 110, 120, 130 can be smaller than the wavelength of the RF or microwave, and thus is within the so-called near-field region.

[0033] The quantum information stored in the plurality of charged particles 10 can be processed using the magnetic fields generated by the electrodes 110, 120, 130. In particular, the magnetic fields generated by the electrodes 110, 120, 130 can be used to generate entanglement between the charged particles 10.

[0034] In some implementations, the surface electrode trap 100 can include a first DC electrode 110-1, a second DC electrode 110-2, a first RF electrode 120-1, a second RF electrode 120-2, and a central electrode 130.

[0035] The electrodes 110, 120, 130 can be conductors extending in one direction. For example, in FIG. 1, the RF electrode 120 and the central electrode 130 extend in the x direction.

[0036] In some implementations, one or more of the electrodes 110, 120, 130 can be formed from a flat strip or wire.

[0037] The first RF electrode 120-1, the second RF electrode 120-2, and the central electrode 130 can be disposed between the first DC electrode 110-1 and the second DC electrode 110-2.

[0038] In some implementations, the central electrode 130 can be disposed between the first RF electrode 120-1 and the second RF electrode 120-2.

[0039] In FIG. 1, the central electrode 130 is depicted as a single strip, but the geometric shape of the central electrode 130 can include additional structural and functional features and is thus not limited to being a flat strip or a single wire. In particular, the central electrode 130 can include additional features suitable for high-fidelity entanglement manipulation of the interacting charged particles 10. In some implementations, microwaves are applied to the DC electrodes 110-1, 110-2.

[0040] In some implementations, the central electrode 130 can include a central DC electrode 131 and an entanglement electrode 132. The central DC electrode 131 can be used to trap the charged particles 10 as part of a surface Paul trap discussed below, and the entanglement electrode 132 can be used to generate a microwave field for entangling two or more trapped charged particles 10. However, both the central DC electrode 131 and the entanglement electrode 132 contribute to entanglement and trapping in that both are held at RF ground and, for any radio frequency signal, return current flows through the central DC electrode 131.

[0041] In some implementations, the entanglement electrode 132 can be configured to generate an electromagnetic field gradient such that the magnitude of the field near the charged particles 10 includes a spatial variation. This can be used to provide a state-dependent force on the charged particles 10 that is used to generate entanglement between the charged particles 10.

[0042] In some implementations, if the surface electrode trap 100 includes several internal layers for routing signals, the entanglement electrode 132 can be disposed in one of the internal layers rather than on the surface of the substrate 101.

[0043] In some implementations, the central electrode 130 may include a separate structure for each of the central DC electrode 131 and the entangled electrode 132. Alternatively, in some implementations, the central electrode 130 may form one integrated conductor, a single wire, or a single strip that can function as both the central DC electrode 131 and the entangled electrode 132. Alternatively, in some implementations, the central electrode 130 may form one integrated conductor, a single wire, or a single strip that functions only as the entangled electrode 132. In some implementations, the central DC electrode 131 may comprise a strip of two or more electrodes.

[0044] The electrodes 110, 120, 130 may be electrically connected to the electronic control unit 30.

[0045] The electronic control unit 30 may include at least one DC source and at least one RF source or microwave source. In some implementations, the electronic control unit 30 may include a DC source, an RF source, and a microwave source. Examples of RF sources or microwave sources include direct digital synthesizers.

[0046] In response to signals received from the electronic control unit 30, the electrodes 110, 120, 130 may be designed and configured to generate an electromagnetic potential for trapping the charged particles 10. For example, the electrodes 110, 120, 130 may form a surface electrode Paul trap for trapping the charged particles 10.

[0047] Implementations of the surface electrode Paul trap using the electrodes 110, 120, 130 are described below. However, the method of trapping the charged particles 10 is not limited to these examples. Any method of trapping the charged particles 10 may be used in the surface electrode trap 100 as long as it is compatible with the design of the entangled electrode 132 detailed herein. For example, there may be various ways to implement a Paul trap or a Penning trap that can be used for the purpose of trapping the charged particles 10.

[0048] To trap the charged particle 10, the first DC electrode 110-1, the first RF electrode 120-1, the central DC electrode 131, the second RF electrode 120-2, and the second DC electrode 110-2 can form a so-called "five-wire surface trap", "five-wire Paul trap", or "five-wire design" (Quantum Information and Computation, Vol. 5, No. 6 (2005) 419-439). These five electrodes, 110-1, 110-2, 120-1, 120-2, and 131, facilitate the formation of a trap for the charged particle 10 at a fixed distance d from the surface of the substrate 101 in response to the voltages provided to these electrodes by the electronic control unit 30. The trapped charged particle 10 oscillates about the center of the trap. The charged particle 10 can be cooled so that the amplitude of this motion decreases.

[0049] In some implementations, the first DC electrode 110-1, the first RF electrode 120-1, the central DC electrode 131, the second RF electrode 120-2, and the second DC electrode 110-2 can be in the form of conductor strips or wires.

[0050] In some implementations, the first RF electrode 120-1, the central DC electrode 131, and the second RF electrode 120-2 can be parallel to each other. For example, as shown in FIG. 1, these electrodes can extend in the x direction.

[0051] In some implementations, the first DC electrode 110-1, the first RF electrode 120-1, the central DC electrode 131, the second RF electrode 120-2, and the second DC electrode 110-2 can be arranged such that the RF electrodes 120-1 and 120-2 are sandwiched between two of the DC electrodes 110-1 and 110-2. For example, in FIG. 1, the electrodes 110, 120, and 130 extending in the x direction can be arranged along the y direction in the following order, i.e., the first DC electrode 110-1, the first RF electrode 120-1, the central DC electrode 131, the second RF electrode 120-2, and the second DC electrode 110-2.

[0052] In some embodiments, the first DC electrode 110-1, the first RF electrode 120-1, the central DC electrode 131, the second RF electrode 120-2, and the second DC electrode 110-2 can be parallel to each other and symmetrically arranged with respect to an axis defined in the direction of the extension of the electrodes. For example, as shown in FIG. 1, the first DC electrode 110-1 and the second DC electrode 110-2 can be arranged at an equal distance from the central DC electrode 131 in the y direction. Similarly, the first RF electrode 120-1 and the second RF electrode 120-2 can be arranged at an equal distance from the central DC electrode in the y direction such that the five electrodes 110-1, 110-2, 120-1, 120-2, and 131 are symmetrically arranged with respect to the x axis. In some embodiments, in addition to being symmetrically arranged, the widths of the electrodes 110-1, 110-2, 120-1, and 120-2, which are symmetric partners with respect to the x axis, can be the same. For example, the first RF electrode 120-1 and the second RF electrode 120-2 can have the same width in the y direction. In this case, the x axis forms a complete symmetry axis with respect to the trap formed by the five electrodes 110-1, 110-2, 120-1, 120-2, and 131.

[0053] By using the electronic control unit 30 to apply voltages to the first RF electrode 120-1, the second RF electrode 120-2, the first DC electrode 110-1, the second DC electrode 110-2, and the central DC electrode, a Paul trap can be formed near the surface of the substrate.

[0054] Typically, together with the DC voltage, an RF voltage in the range of 10 to 100 MHz is applied to the first RF electrode 120-1 and the second RF electrode 120-2 by the electronic control unit 30.

[0055] The distance d in the z - direction between the equilibrium position of the charged particles 10, known as the "trap center", and the substrate 101 is typically in the range of 10 to 100 microns. The local minimum in the RF pseudo - potential field forms the trap axis along the axial (x) direction, only at the distance d on the central electrode 130. Thus, when a plurality of charged particles 10 are trapped, they can be aligned along the direction of the extension of the central electrode 130.

[0056] In some implementations, the first DC electrode 110 - 1 and the second DC electrode 110 - 2 can be segmented longitudinally, as shown in FIG. 1. Each segment can be maintained at a different DC voltage that can be controlled as needed. This enables the shuttling of the charged particles 10 in the longitudinal direction, or the x - direction in FIG. 1.

[0057] When the charged particles 10 are trapped in space as described above, the charged particles 10 can be cooled, addressed, or manipulated as described below.

[0058] Cooling and Detection of Charged Particles The charged particles 10 can include internal energy levels 11, 12, 13 which are electron levels. These internal energy levels 11, 12, 13 can include states such as Zeeman states and hyperfine states. These energy levels 11, 12, 13 can be affected by external biases such as an electric field or a magnetic field. For example, by applying an external bias such as a static magnetic field, some of the degeneracies of the internal energy levels 11, 12, 13 can be lifted. Due to the motion of the charged particles 10 in the trap, the state space is the product of the electron levels 11, 12, 13 and the motion states.

[0059] A qubit, which is a unit of quantum information, can be stored in two states within the energy levels 11, 12, 13 of the charged particles 10. The state of the qubit is sometimes called the "0" and "1" states, or the "up" and "down" states.

[0060] The charged particle 10 may include a ground state 11 and an excited state 12. There may be a first transition 14 between the ground state 11 and the excited state 12, which is at least one electric dipole allowed transition.

[0061] The first transition 14 may exist in the optical region ranging from UV to near IR, where conventional light sources and detectors are available for excitation and detection.

[0062] The natural decay of the state from the excited state 12 results in the emission of optical photons from the charged particle 10, which can be used for the detection of the charged particle 10.

[0063] For this purpose, the shelving level 13 may be an electronic level of the charged particle 10 having a long lifetime.

[0064] For example, the ground state 11 may be the 4S 40 Ca + level, and the shelving level 13 may be the 3D 1 / 2 level. When the charged particle 10 is in the ground state 11, the application of a laser resonant with the transition 14 results in the emitted fluorescence. As a result, the qubit state can be inferred from the fluorescence by first using a narrow linewidth laser resonant with the transition 15 to transfer one qubit state to the shelving level. 5 / 2 When the charged particle 10 is an exemplary elementary charged particle such as an electron or a positron, for example, its motion can be detected by observing the current induced in the trap structure.

[0065] In addition to the electromagnetic trap provided by the five-wire pole trap discussed above, the spatial movement of the charged particle 10 can be further confined and decelerated by laser cooling methods such as Doppler cooling.

[0066] In some implementations, allowed optical transitions such as the first transition 14 of the charged particle 10 can be used for Doppler cooling.

[0067]

[0068] As a basic unit for storing or processing quantum information, a "ground state qubit" can be implemented as the "0" and "1" states, or the lower qubit state and the upper qubit state, using qubit transitions 16 between states in the ground state 11, that is, the first qubit state 11-1 and the second qubit state 11-2. For example, the qubit states 11-1, 11-2 of the ground state qubit can be two of the Zeeman states or hyperfine states.

[0069] These qubit states 11-1, 11-2 can be mapped to the states of the first transition 14 for reading.

[0070] Zeeman levels and hyperfine levels related to qubit transitions The ground state 11 can include a hyperfine structure. Also, under the static magnetic field 40, the states within the ground state 11 can be split by the Zeeman effect.

[0071] In some implementations where there is no hyperfine structure, the first qubit state 11-1 and the second qubit state 11-2 can be two Zeeman states within the ground state 11.

[0072] To reliably read the qubit states 11-1, 11-2, each of the qubit states 11-1, 11-2 can be mapped to an "optical qubit". For example, if the first qubit state 11-1 is mapped to the shelving state 13 and the second qubit state 11-2 remains coupled to the circulating transition around the first transition 14, high-fidelity state detection of the qubit states 11-1, 11-2 can be performed by measuring the number of photons emitted from the charged particle 10 within a certain time interval during the lifetime of the shelving state 13.

[0073] In some implementations, the first qubit state 11-1 and the second qubit state 11-2 can be two hyperfine states of the ground state 11.

[0074] The ultra-fine structure allows for a transition that becomes independent of the magnetic field up to the first order at a specific location. Typically, the resonance frequency of the qubit transition 16 is in the GHz range, or microwave. For example, 43 Ca + The S of the ground state 11 1 / 2 levels are split into two different values of F, F = 3, 4, which are split by 3.226 GHz in zero field.

[0075] In some implementations, the first qubit state 11-1 and the second qubit state 11-2 can be two extended states of the ultra-fine level with the maximum M F quantum number for a given F value. These states can enable convenient state preparation and detection. For example, S 3,+3 1 / 2 and S 4,+4 1 / 2 states can be prepared by optical pumping and read out by exciting the first transition 14 using σ+ polarization.

[0076] When the extended states of the ultra-fine levels are used as qubit states 11-1, 11-2, one of the qubit states 11-1, 11-2 can be mapped to the shelving state 13 by a narrow quadrupole transition that excites the second transition 15, as discussed above.

[0077] When providing a magnetic field to excite the qubit transition 16, it can also be considered whether any component of the near-field of the microwave that does not couple to the qubit transition 16 can excite other transitions. This can affect the fidelity of quantum information processing.

[0078] Qubit entanglement When providing an electromagnetic field to excite the qubit transition 16 of the charged particle 10, the polarization of the electromagnetic field should be provided considering the direction of the static magnetic field 40, or equivalently, the direction of the quantization axis of the charged particle 10. The static magnetic field 40 defines the quantization axis of the charged particle 10 and thus defines the polarization of the microwave field that can couple to the qubit transition 16.

[0079] A sigma transition or σ-transition refers to a transition 16 of a charged particle 10 between states that differ only by one in magnetic quantum number. Only the electromagnetic field component perpendicular to the direction of the static magnetic field 40 couples to the sigma transition.

[0080] A pi transition or π-transition refers to a transition 16 of a charged particle 10 between states having the same value of magnetic quantum number. Only the electromagnetic field component parallel to the direction of the static magnetic field 40 couples to the pi transition.

[0081] To excite the microwave pi transition, the quantum bit transition 16 in FIG. 1, for example, the magnetic field that couples to the transition and is generated by the entangled electrode 132 should include a non-zero component parallel to the direction of the static magnetic field 40.

[0082] Therefore, the surface trap 100, particularly the entangled electrode 132, can be designed assuming a specific spatial alignment of the surface electrode trap 100 with respect to the direction of the static magnetic field 40.

[0083] In the following examples, unless otherwise specified, the surface electrode trap 100 is aligned such that the direction of the static magnetic field 40 is parallel to the surface of the substrate 101 and perpendicular to the extension direction of the electrodes 110, 120, 130. For example, in FIG. 1, the static magnetic field 40 is in the x direction. However, the inventive concept described herein is not limited to this configuration. Any possible design of the surface electrode trap 100 and the configuration of the electrodes 110, 120, 130 with respect to the direction of the static magnetic field 40 can be used as long as it is compatible with the design of the entangled electrode 132 described below.

[0084] The qubit states 11-1, 11-2 considered herein can be any two stable states of the charged particle 10 as long as the qubit transition can be excited using RF or microwave radiation.

[0085] In this specification, an experimental configuration in which entanglement is generated by the oscillating RF / microwave magnetic field generated by the entangled electrode 132 is considered.

[0086] The entanglement between charged particles 10 can be generated by using spin-dependent forces or state-dependent forces to generate an effective spin-spin interaction or an effective interaction between charged particles 10 that depends on the qubit states 11-1, 11-2. These spin-dependent forces have conventionally been generated using radiation at optical frequencies, for example, by driving an induced Raman transition using two lasers detuned from each other by a frequency close to the resonance of the qubit transition 16.

[0087] Recently, a laser-free approach or a purely electronic approach has been introduced in which near-field microwaves with a high spatial gradient are used to generate spin-dependent forces.

[0088] The laser-free or electrical techniques have several advantages compared to laser-based schemes. Lasers pose fundamental limitations on the fidelity of the entanglement that can be generated by photon scattering from the excited level 12. Such limitations do not exist for electronic techniques. Also, electronic techniques can significantly reduce the sensitivity to the initialization of the motional state such that Doppler cooling alone is sufficient instead of relying on coupling near the ground state.

[0089] Furthermore, laser-based schemes typically require high optical intensities. Integrating and scaling RF / microwave electronics can be easier than optics, especially for the UV frequencies often required for laser-based entanglement. Additionally, sources, modulators, and other components can generally be smaller, less expensive, and require lower power consumption at RF / microwave frequencies than at optical frequencies. In particular, phase control can be more maintainable at RF / microwave frequencies than at optical frequencies.

[0090] One laser-free method uses an oscillating (RF / microwave) magnetic field gradient generated in the near field of a current-carrying wire to generate spin-dependent forces. In this case, the wire corresponds to the entanglement electrode 132 discussed above.

[0091] Creation of Nodes in Near-Field Radiation The spin-dependent force used to generate entanglement is generated by the spatial gradient of the oscillating magnetic field at the position of charged particle 10. A particular problem with near-field entanglement is that this gradient generally results from the fact that it is accompanied by the amplitude of a strong field that couples to both the qubit transition 16 and any other ground state transition (not shown) connecting to the qubit state.

[0092] This unwanted coupling can potentially reduce the fidelity of the entanglement that can be generated. To minimize the effects of this unwanted coupling, various techniques have been considered, such as using microwave cavity filters to suppress noise, actively stabilizing the amplitude of the field, and using dynamic decoupling to suppress the frequency shifts introduced by the field.

[0093] Another approach is to eliminate this coupling by operating in a "nulling" configuration. In this configuration, the fields generated by different parts of the entanglement electrode 132 interfere to produce an oscillating magnetic field with zero amplitude at the location of the charged particle 10, while still maintaining a strong spatial gradient at that location. An example of an entanglement electrode for generating a nulled field is shown in FIG. 2. However, these configurations may be limited as discussed below. The design of the entanglement electrode 132 to address these issues is presented in FIGS. 3a and 3b.

[0094] FIG. 2 is a schematic diagram of a surface electrode trap for generating a nulled magnetic field distribution.

[0095] FIG. 2 shows a surface electrode trap 200 for implementing an "active nulling geometry" on the left side and a surface electrode trap 250 for implementing a "passive nulling geometry" on the right side.

[0096] The surface electrode trap 200 for active nulling includes a substrate 201 and a plurality of electrodes 210, 220, 230 disposed on a first surface of the substrate 201.

[0097] The surface electrode trap 200 includes a first DC electrode 210-1, a second DC electrode 210-2, a first RF electrode 220-1, a second RF electrode 220-2, and a central electrode 230. Similar to the example of FIG. 1, the central electrode 230 may include a central DC electrode 231 and a first entangled electrode 232-1.

[0098] When voltages are applied to the DC electrodes 210-1, 210-2 and the RF electrodes 220-1, 220-2 using the electronic control unit 30 while holding the central DC electrode 231 and the first entangled electrode 232-1 at RF / DC ground, these electrodes can function as a surface electrode pole trap as discussed in FIG. 1. To entangle the charged particles 10, an RF / microwave current can be applied to the first entangled electrode 232-1.

[0099] For the operation of the surface electrode trap 200 for active nulling, the amplitude and phase are precisely controlled so that the microwave current is simultaneously applied to three collinear conductors, namely, the first entangled electrode 232-1, the second entangled electrode 232-2, and the third entangled electrode 232-3, to actively suppress the amplitude of the field, generate a node or nulling point at the position of the charged particles 10, and still maintain a strong field gradient at that point. This technique is proposed, for example, in C. Ospelkaus et al., Phys. Rev. Lett. 101, 090502 (2008).

[0100] This active nulling technique may have several issues and may be susceptible to drift in the amplitude or phase of these microwave currents, as well as any noise that is not common to all of these three electrodes 232-1, 232-2, 232-3. At RF / microwave frequencies, the microwave qubit control current can induce current in the electrodes for the five-wire surface Paul traps 210-1, 210-2, 220-1, 220-2, 130. Since the RF electrodes 220-1, 220-2 are common to all zones within the multi-zone trap, this can lead to crosstalk across the trap 200.

[0101] The surface electrode trap 250 for the passive nulling geometry includes a substrate 251 and a plurality of electrodes 260, 270, 280, 282 disposed on a first surface of the substrate 251. The surface electrode trap 250 comprises a first DC electrode 260-1, a second DC electrode 260-2, a first RF electrode 270-1, a second RF electrode 270-2, and a central electrode 280. When voltages are applied to these collinear electrodes 260-1, 260-2, 270-1, 270-2, 280 using the electronic control unit 30, these electrodes act as a surface electrode Paul trap as discussed above.

[0102] As described in M. Carsjens et al., Appl. Phys. B 114, 243 (2014), the surface electrode trap 250 for the passive nulling geometry includes a meandering structure 282 that is a wire folded back on itself. The meandering structure 282 includes a portion corresponding to the first entangled electrode 282-1 and portions corresponding to the second entangled electrode 282-2 and the third entangled electrode 282-3, respectively. These portions are integrally formed as one meandering strip of the conductor 282 in the plane of the substrate 251.

[0103] A single current at RF / microwave frequencies can be fed into the serpentine structure 282 in order to form nodes or nulls at the position of the charged particles 10 approaching zero in accordance with the same principle as the surface electrode trap 200 for active nulling of the vibration magnetic field amplitude. The gaps between the RF electrodes 270-1, 270-2 and the serpentine structure 282, as well as the width of each part of the serpentine structure, can be determined in advance to create null points at a predetermined position within the space above the serpentine structure 282.

[0104] This technique may have its own challenges. 1. Due to the finite lengths of the nulling electrodes 282-1, 282-2 and the central electrode 280 in the x-direction near the charged particles 10, a phase shift occurs along the serpentine structure 282, which may prevent the formation of a complete null. 2. The surface electrode trap 250 still has the same number of conductors as the surface electrode trap 200 for active nulling. 3. Due to the close coupling between the serpentine conductor structure 282 and the other electrodes 260, 270 for the surface pole trap, there may be significant crosstalk between zones within the multi-zone ion trap or charged particle trap. Minimizing crosstalk is particularly important for quantum computing where low crosstalk across a large-scale multi-zone ion trap is a critical requirement. 4. The asymmetric structure of the serpentine conductor 282 forming the nulling electrodes 282-1, 282-2, 282-3 and the central electrode 280 may be sensitive to manufacturing and simulation tolerances. Furthermore, any current induced in other electrodes may affect the nulling.

[0105] This specification provides the geometric shapes of surface electrode traps 100, 200, 250 that facilitate partial nullification of the field amplitude or a partially nullified magnetic field distribution at the position of charged particle 10, which can address the problems discussed above. Instead of aiming for a complete null of the magnetic field at the position of charged particle 10, the entangled electrodes 132, 232, 282 can be designed for a specific selection of the qubit states 11-1, 11-2 and the direction of the static magnetic field 40. The entangled electrodes 132, 232, 282 are designed to nullify only the components of the field that couple to the selected qubit transitions 16. This can enable a significantly simpler and symmetric structure of the entangled electrodes 132, 232, 282 that can reduce the problems associated with active and passive nullification geometries.

[0106] FIG. 3a is a schematic diagram of a surface electrode trap for generating a partially nullified magnetic field distribution.

[0107] FIG. 3a shows a surface electrode trap 300 on the left side and a diagram showing the magnetic field distribution around the entangled electrode 330 of the surface electrode trap 300 on the right side.

[0108] The surface electrode trap 300 includes a first DC electrode 310-1, a second DC electrode 310-1, a first RF electrode 320-1, a second RF electrode 320-2, and a central electrode 330. When voltages are applied to these collinear electrodes 310-1, 310-2, 320-1, 320-2, 330 using the electronic control unit 30, these electrodes can function as a 5-wire surface Paul trap as discussed above.

[0109] The central electrode 330 includes an entangled electrode 332. The entangled electrode 332 includes a coplanar waveguide or transmission line 332 along the x direction.

[0110] The coplanar waveguide 332 includes a central track 332-1, a first return track 332-2, and a second return track 332-3, all of which extend in the x direction. The central track 332-1 is sandwiched between the return tracks 332-2 and 332-3.

[0111] In some implementations, the central track 332-1 and the return tracks 332-2 and 332-3 function as the RF and DC grounds of the five-wire surface pole trap.

[0112] The impedance of the coplanar waveguide 332 can be controlled by adjusting the dimensions of these tracks. The impedance of the coplanar waveguide 332 is determined by the geometric aspects of the coplanar waveguide 332 and is almost independent of the operating frequency and the other electrodes 310, 320, 330 within the surface electrode trap 300. The return tracks 332-2 and 332-3 are separated from the central track 332-1 by a predetermined gap that can have a constant width along the length of the coplanar waveguide 332 in the x direction. The gap between the central track 332-1 and the return tracks 332-2 and 332-3 can be determined according to a predetermined impedance of the coplanar waveguide 332.

[0113] The central track 332-1 can function as the signal line of the coplanar waveguide 332, and the first return track 332-2 and the second return track 332-3 can function as the ground lines of the coplanar waveguide 332.

[0114] In some implementations, the coplanar waveguide 332 can be formed to be symmetric with respect to the central track 332-1.

[0115] In some implementations, the first return track 332-2 and the second return track 332-3 can be held at the same potential as the ground plane of the surface electrode trap 300, particularly the ground for the five-wire surface pole trap.

[0116] When the return tracks 332-2 and 332-3 are arranged such that their respective widths are greater than the penetration depth, this can provide screening that reduces crosstalk between the trap electrodes 310-1, 310-2, 320-1, 320-2 and the coplanar waveguide 332.

[0117] The return current regarding the central track 332-1 mainly flows through the first return track 332-2 and the second return track 332-3. In other words, if the current across the cross-section of the coplanar waveguide 332 in the yz plane is integrated at any instance by the fundamental mode of the coplanar waveguide 332, it will approximately reach zero. The coplanar waveguide 332 also has higher-order modes, but those higher-order modes usually do not propagate. Furthermore, the input coupling can be designed to largely avoid exciting those higher-order modes, for example, by short-circuiting the first return track 332-2 and the second return track 332-3 to each other. This is in contrast to the active nulling geometry 200 and the passive nulling geometry 250 where a significant amount of current is induced in other electrodes such as the trap RF electrodes 232 and 282 that do not provide a controlled impedance return path.

[0118] The use of the coplanar waveguide 332 as the twisted electrode 332 provides a well-controlled path for the return current and prevents the microwave current from unexpectedly flowing along an undesirable path. It is also easy to control the impedance of the coplanar waveguide 332. The use of the coplanar waveguide 332 as the twisted electrode 332 can be advantageous in a multi-zone trap where any induced current flowing along an undesirable path can lead to strong crosstalk between zones because the RF rails are common to all trap zones.

[0119] In some embodiments, the trap axis of the five-wire surface pole trap formed by the collinear electrodes 310-1, 310-2, 320-1, 320-2 can produce a trap axis parallel to the central track 332-1 at a distance d above the central track 332-1. In this case, at the position of the charged particle 10, the magnetic field generated by the coplanar waveguide 332 is in the y direction. In other words, the direction of the magnetic field generated by the collinear waveguide at the position of the charged particle 10 is parallel to the substrate 301 and perpendicular to the direction of the central track 332-1 or the coplanar waveguide 332.

[0120] The magnetic field distribution shown in the right panel of FIG. 3a is achieved by the inherent characteristics of the coplanar waveguide 332 and can be robust against material properties or specific dimensions of the tracks 332-1, 332-2, 332-3 as long as the overall symmetry is not disrupted. Since only one RF / microwave signal source is used to supply the central track 332-1, there is no need to control the relative phases of the signals sent to the tracks 332-1, 332-2, 332-3 as in the case of the active nulling geometry 200 or the passive nulling geometry 250.

[0121] The partial nulling technique can have the following technical advantages. 1. Only one current source is required for the entangled electrodes or the coplanar waveguide 322. The direction of the resulting oscillating magnetic field of the coplanar waveguide 332 is less affected by drifts in the amplitude or phase of the microwave current. Therefore, precise control or calibration of the amplitude and phase of the current is not required. 2. The entangled electrode or coplanar waveguide 332 relies on a symmetric design instead of detailed simulation, manufacturing, and control of induced currents. Therefore, precise design and manufacturing of the entangled electrode 332 are not required. Since the coplanar waveguide 332 is compact, it leaves more space on the surface electrode trap 300 for other electrodes 310-1, 310-2, 320-1, 320-2. This can further reduce the induced currents on the DC electrodes 310-1, 310-2 and the RF electrodes 320-1, 320-2. This also enables the RF trap itself formed using the RF electrodes 320-1, 320-2 to be better optimized, for example, by choosing the geometric shapes of the RF electrodes 320-1, 320-2 to maximize the trap depth or harmonicity. 3. Crosstalk is reduced because the coplanar waveguide 332 has a ground that completely surrounds the signal (especially when the ground is of a width of several skin depths). 4. The quality of nulling is less affected by the phase shift along the electrode, which can be the case for the passive nulling geometry 250. 5. Since the entangled electrode 332 is a coplanar waveguide, a controlled impedance trace with a clearly defined path for the signal and return current is used. 6. Efficiency can be higher because the current is placed closer to the particles. Since all three conductors of the coplanar waveguide 332, namely the central tracks 332-1, 332-2, 332-3, are close to the position of the trapped charged particles 10, the use of the coplanar waveguide 332 as the entangled electrode 332 can be efficient in terms of the power required to generate a given gradient. 7. Nodes in the oscillating magnetic field are generated not only along a single line but also throughout the x-y plane centered on the particle position 10.

[0122] By configuring the trap axis of the 5-wire pole trap, the charged particles 10 can be placed at a position where the charged particles 10 are only subject to the magnetic field in the y direction.

[0123] The static magnetic field 40 can be applied parallel to the substrate 301 and perpendicular to the central track 332-1 so that the quantization axis is in the plane of the trap and perpendicular to the axis along the central track 332-1 of the coplanar waveguide 332. When the trap center is arranged such that the charged particle 10 is placed at a position where it is subject only to a magnetic field parallel to the static magnetic field 40, the resulting oscillating magnetic field of the coplanar waveguide 332 is purely π-polarized.

[0124] In addition to the arrangement of the field directions at the position of the charged particle 10 discussed above, the qubit states 11-1, 11-2 of the charged particle 10 can be selected so as not to couple to the microwave field generated by the entanglement electrodes or the coplanar waveguide 332 with which the qubit transition 16 is entangled. The oscillating magnetic field does not cause any change in the motion of the charged particle 10 and does not contain a component that causes a significant coupling to any transition from the qubit state, when the importance of the coupling is determined by the detuning of the transition and the intensity of the polarization component or "Rabi frequency". The term "Rabi frequency" is used to refer to the degree of coupling between any two states of the particle to the oscillating magnetic field, including "carrier" transitions that do not involve any change in the motion of the particle and "sideband" transitions that change the motion state. Such an arrangement is referred to herein as a partial nulling geometry, as will be described in more detail below.

[0125] In the partial nulling geometry, the entanglement electrodes 232 can be designed to reliably produce a predetermined polarization at the position of the charged particle 10, and the static magnetic field 40 and the qubit transition 16 can be appropriately selected so that the predetermined polarization component does not couple to the qubit transition 16. However, there can be a gradient of the oscillating magnetic field that couples to the sideband of the qubit transition 16 that generates the spin-dependent force. In other words, the oscillating magnetic field component that couples to the qubit transition 16 does not exist at the position of the charged particle 10, but exists in the vicinity of the position of the charged particle 10. The gradient is formed such that the magnitude of the component increases as the distance from the trap center increases.

[0126] Partial nullification can be applied to qubits at any ground or metastable level.

[0127] For example, in FIG. 3a, the position of the charged particle 10 is directly above the central track 332-1 in the z direction, where the direction of the oscillating magnetic field generated by the coplanar waveguide is parallel to the substrate 310 in the y direction and perpendicular to the direction of the coplanar waveguide 332. Since the static magnetic field 40 is in the y direction, the charged particle 10 only receives a π-polarized oscillating magnetic field. When a "spin 1 / 2" particle (e.g., a particle without a nuclear spin) is selected as the charged particle 10, the qubit transition 16 is the only ground state transition with σ polarization.

[0128] Therefore, the qubit transition 16 at the trap center does not couple purely to the π-polarized oscillating magnetic field, thereby producing the same result as a completely nullified field regardless of the amplitude of the actual field. However, away from the trap center or the position of the charged particle 10, there is a σ polarization component whose intensity increases according to the distance from the trap center. As a result, there is a strong gradient of the σ polarization component of the oscillating magnetic field that can be used to generate entanglement.

[0129] Partial nullification only requires a single entangled electrode 332 and is not sensitive to the relative size or phase stability or differential noise between multiple electrodes. In some implementations, if the frequencies of all transitions from the qubit state coupled to the magnetic field are sufficiently far from the frequency of the qubit transition 16 to render the interaction meaningless, partial nullification can be applied to the qubit transition 16 at the level with hyperfine structure. For example, 43 Ca + of S 3,+3 1 / 2 state and S 4,+4 1 / 2 In the hyperfine qubit transition 16 between the state and the S43 Ca + Regarding the ground level transition in 43 , a static magnetic field of 150 mT can generate a 50 MHz splitting between transitions. The oscillating magnetic field can be considered to be partially nullified as long as the "Rabi frequency" in the transition from the qubit state is sufficiently small compared to this splitting.

[0130] In some implementations, the widths of the return tracks 332-2, 332-3 can be determined to be greater than the skin depth or penetration depth of the material. At RF / microwave frequencies, this depends greatly on the operating frequency and the material. The surface electrode trap 100 has a resistance, and Therefore, it can be operated at cryogenic temperatures where the penetration depth is lower than that at room temperature.

[0131] Figure 3b is a schematic diagram of a coplanar waveguide on a surface electrode trap for generating a partially nullified magnetic field distribution.

[0132] The upper panel of Figure 3b shows the electrical connection arrangement of the coplanar waveguide 332.

[0133] To generate an oscillating magnetic field at RF / microwave frequencies from the coplanar waveguide, a signal generator 31 configured to generate an RF / microwave frequency current can be connected to the central track 332-1.

[0134] A common ground terminal 32 of the circuit of the surface electrode trap 300 including a 5-wire surface pole trap is connected to the first return track 332-2 and the second return track 332-3. The RF / microwave ground of the signal generator 31 is also connected to the ground terminal 32. These provide a controlled impedance ground path as discussed above, which minimizes the unwanted coupling of the signal generated from the coplanar waveguide to other parts of the trap.

[0135] The lower panel shows a coplanar waveguide 332a including a central track 332a-1, a first return track 332a-2, and a second return track 332a-3. The electrical connection arrangement for generating an oscillating magnetic field from the coplanar waveguide 332a using the signal generator 31 and the ground terminal 32 is as in the upper panel of FIG. 3b.

[0136] In some embodiments, the coplanar waveguide 332a may further include a short-circuit connection portion 332a-4 that electrically connects the ground track 332a-1, the first return track 332a-2, and the second return track 332a-3. Accordingly, the short-circuit connection portion 332a-4 is connected to ground via the first return track 332a-2 and the second return track 332a-3. In this case, the charged particle 10 can be disposed at a first distance 332a-5 from the short-circuit connection portion. To avoid the end effect in the magnetic field distribution, the first distance 332a-5 may be, for example, greater than five times the width of the central track 332a-1. The short-circuit connection portion 332a-4 is included to dispose the charged particle 10 near the current antinode of the coplanar waveguide 332a. Accordingly, the charged particle 10 can be disposed as close as possible to the short-circuit connection portion 332a-4 without encountering the end effect. For example, the charged particle 10 can be disposed much closer than λ / 4 from the short-circuit connection portion 332a-4, where λ is the wavelength of the microwave current in the coplanar waveguide 332a.

[0137] The oscillating RF / microwave current can be supplied to the tracks 332a-1, 332a-2, 332a-3 from the end of the coplanar waveguide 332a opposite to the end where the short-circuit connection portion 332a-4 is disposed.

[0138] In some embodiments, the short-circuit connection portion 332a-4 can be electrically connected to the central track 332a-1, the first return track 332a-2, and the second return track 332a-3 toward the end in the x direction of the region defined by the 5-wire surface pole trap.

[0139] With the short - circuit connection 332a - 4, for a given power input to the coplanar waveguide 332a, the coplanar waveguide 332a can supply a larger current near the position of the charged particle 10 compared to the coplanar waveguide 332 without the short - circuit connection 332a - 4. Further, the coplanar waveguide 332a does not require a separate off - chip termination. The field gradient at the position of the charged particle 10 can be further increased by implementing impedance matching between the source and the coplanar waveguide.

[0140] The traps used in partial nullification are completely symmetric, so no exact and detailed simulation or fabrication is required to generate the necessary field gradient at the center of the trap, or at the position of the charged particle 10. In contrast to the active nullification geometry 200 and the passive nullification geometry 250, the partial nullification geometry 300 with the coplanar waveguide 332, 332a design provides a well - defined current return path. This allows for a controlled determination of the impedance of the coplanar waveguides 332, 332a, and thus enables an accurate design based on simple simulations.

[0141] The widths of the first return tracks 332 - 2, 332a - 2 and the second return tracks 332 - 3, 332a - 3 can be made larger than the typical penetration depth or skin depth of the RF / microwave current that tends to concentrate near the ends of the tracks of the coplanar waveguide 332. So both the first return tracks 332 - 2, 332a - 2 and the second return tracks 332 - 3, 332a - 3 allow the return current to flow, minimize the induced RF / microwave current in the trap RF electrodes 320 - 1, 320 - 2, and thus also provide an effective screening layer to strongly suppress crosstalk.

[0142] FIG. 4 is a schematic diagram of an exemplary embodiment of a surface - electrode trap for providing a partially nullified magnetic - field distribution.

[0143] The surface electrode trap 400 shown in FIG. 4 can be part of a larger design where many units of the surface electrode trap 400 are integrated as an array of multiple surface electrode traps 400.

[0144] In some implementations, the surface electrode trap 400 can comprise a metal film deposited on a substrate. For example, the metal film can include gold, and the thickness of the gold film can range from 100 nm to 10 μm. Starting from a uniform metal film, a pattern can be fabricated by standard lithography techniques such as photolithography. The appropriate mode of lithography can be selected depending on the material and the feature size such as the width or height of the feature. For example, the metal film can be deposited by electroplating around a patterned photoresist material deposited on the substrate.

[0145] The surface electrode trap 400 includes a first DC electrode 410-1, a second DC electrode 410-2, a first RF electrode 420-1, a second RF electrode 420-2, and a coplanar waveguide or a meandered electrode 432.

[0146] In the example of FIG. 4, the first DC electrode 410-1 and the second DC electrode 410-2 each comprise at least five sections. This provides the degrees of freedom necessary to control the position of the charged particles 10 in the x direction. Using three consecutive sections of the first DC electrode 410-1 and the second DC electrode 410-2, a potential well can be formed to confine the charged particles 10 in the x direction. When separating a pair of charged particles 10 starting in the same potential well, multiple sections of the first DC electrode 410-1 and the second DC electrode 410-2 can be used.

[0147] The first DC electrode 410-1 and the second DC electrode 410-2 cover a distance of 400 microns in the x direction. The charged particles 10 can be loaded within this region, and confinement in the x direction can be provided by the first DC electrode 410-1 and the second DC electrode 410-2.

[0148] The widths of the first RF electrode 420-1 and the second RF electrode 420-2 can range from 10 to 500 microns, and can be, for example, 28 microns.

[0149] The length of the coplanar waveguide 432 in the x direction can be between 100 microns and 100 mm.

[0150] The gap in the y direction between the first DC electrode 410-1 and the first RF electrode 420-1, or between the second DC electrode 410-2 and the second RF electrode 420-2, can be between 1 and 50 microns, for example 5 microns. The gap is independent of the operating frequency and is smaller than the height of the charged particles 10 above the surface electrode trap 400. The lower limit of the gap is set by manufacturing tolerances.

[0151] The coplanar waveguide 432 includes a central track 432-1, a first return track 432-2, and a second return track 432-3. These tracks extend in the x direction, and the central track 432-1 can be sandwiched between the first return track 432-2 and the second return track 432-3.

[0152] The length, or the range in the x direction, of the first return track 432-2 and the second return track 432-3 can range from 1 to 100 microns and can be, for example, 10 microns.

[0153] The gap in the y direction between the first RF electrode 420-1 and the first return track 432-2, or between the second RF electrode 420-2 and the second return track 432-3, can be between 1 and 50 microns, for example 5 microns.

[0154] The gap in the y direction between the central track 432-1 and the first return track 432-2, or between the central track 432-1 and the second return track 432-3, can be between 1 and 50 microns, for example 10 microns.

[0155] The coplanar waveguide 432 may include a short - circuit connection portion 432 - 4 that electrically connects a central track 432 - 1, a first return track 432 - 2, and a second return track 432 - 3.

[0156] As described above in FIG. 3b, the short - circuit connection portion 432 - 4 enables the coplanar waveguide 432 to have a larger field gradient in the charged particle 10 for the same input current compared to the coplanar waveguide 432 without the short - circuit connection portion 432 - 4. Further, the coplanar waveguide 432 does not require a separate off - chip termination.

[0157] The charged - particle position 10 can be trapped above the central track 432 - 1 in the z - direction. The distance in the z - direction between the charged particle 10 and the central track 432 - 1 can range from 20 to 100 microns.

[0158] The position of the charged particle 10 in the x - direction can be determined according to the arrangements of the first DC electrode 410 - 1 and the second DC electrode 410 - 2.

[0159] Also, the position of the charged particle 10 in the x - direction can also be determined to be sufficiently far from the short - circuit connection portion 432 - 4 in order to avoid the end - effect. The first distance 432 - 5 between the short - circuit connection portion 432 - 4 in the x - direction and the position of the charged particle 10 is much smaller than λ / 4, where λ is the wavelength of the microwave in the coplanar waveguide 432.

[0160] FIG. 5 is a flowchart of a method for entangling charged particles.

[0161] In step 510, the charged particle 10 is trapped at a first position using electromagnetic traps 110, 120, 130, 210, 220, 230, 260, 270, 280, 310, 320, 330, 410, 420, 430.

[0162] In step 520, a static magnetic field 40 is provided at the first position such that the qubit transition 16 of the charged particle 10 is defined.

[0163] In step 530, an oscillating magnetic field is provided using the entangled electrodes 332, 332a, 432. The oscillating magnetic field present at the first position does not include a polarization component that directly couples to the qubit transition. The oscillating magnetic field has a spatial gradient of the polarization component of the oscillating magnetic field that couples the qubit transition to the motion of the charged particle at the first position. In this step, at the position of the charged particle 10, a partial nulling of the field amplitude, or a partially nulled magnetic field distribution, is facilitated.

[0164] The embodiments of the invention shown in the drawings and described above are merely exemplary embodiments and are not intended to limit the scope of the invention as defined by the following claims. Any combination of non - mutually exclusive features described herein is intended to be within the scope of the invention.

Description of Reference Numerals

[0165] 10 Charged particle, particle position, charged particle position 11 Internal energy level, ground level 11 - 1 First qubit state, qubit state 11 - 2 Second qubit state, qubit state 12 Internal energy level, excited level 13 Internal energy level, shelf level, shelf state 14 First transition 15 Transition, second transition 16 Qubit transition 20 Vacuum chamber 30 Electronic control unit 31 Signal generator 32 Ground terminal 40 Static magnetic field 100 Surface - electrode trap 101 Substrate 110 Electrode, surface electrode, electromagnetic trap 110 - 1 First DC electrode, DC electrode 110 - 2 Second DC electrode, DC electrode 120 Electrode, surface electrode, RF electrode, electromagnetic trap 120-1 First RF electrode 120-2 Second RF electrode 130 Electrode, surface electrode, central electrode, five-wire surface Paul trap, electromagnetic trap 131 Central DC electrode 132 Entangled electrode 200 Surface electrode trap, active nulling geometric shape 201 Substrate 210 Electrode, electromagnetic trap 210-1 First DC electrode, five-wire surface Paul trap 210-2 Second DC electrode, five-wire surface Paul trap 220 Electrode, electromagnetic trap 220-1 First RF electrode, five-wire surface Paul trap 220-2 Second RF electrode, five-wire surface Paul trap 230 Electrode, central electrode, electromagnetic trap 231 Central DC electrode 232 Entangled electrode, trap RF electrode 232-1 First entangled electrode 232-2 Second entangled electrode 232-3 Third entangled electrode 250 Surface electrode trap, passive nulling geometric shape 251 Substrate 260 Electrode, electromagnetic trap 260-1 First DC electrode, collinear electrode 260-2 Second DC electrode, collinear electrode 270 Electrode, electromagnetic trap 270-1 First RF electrode, collinear electrode 270-2 Second RF electrode, collinear electrode 280 Electrode, central electrode, trap RF electrode, electromagnetic trap 282 Electrode, serpentine structure, conductor, serpentine conductor, serpentine conductor structure, entangled electrode 282-1 First entangled electrode, nulling electrode 282-2 Second entangled electrode, nulling electrode 282-3 Third entangled electrode 300 Surface electrode trap, partially nullified geometric shape 310 Electrode, electromagnetic trap 310-1 First DC electrode, trap electrode, collinear electrode 310-2 Second DC electrode, trap electrode, collinear electrode 320 Electrode, electromagnetic trap 320-1 First RF electrode, trap electrode, collinear electrode 320-2 Second RF electrode, trap electrode, collinear electrode 330 Central electrode, electromagnetic trap 332 Entangled electrode, coplanar waveguide or transmission line, coplanar waveguide, entangled electrode or coplanar waveguide 332a Coplanar waveguide 332-1 Central track 332a-1 Central track, ground track 332-2 First return track, return track, central track 332a-2 First return track 332-3 Second return track, return track, central track 332a-3 Second return track 332a-4 Short circuit connection 332a-5 First distance 400 Surface electrode trap 410 Electromagnetic trap 410-1 First DC electrode 410-2 Second DC electrode 420 Electromagnetic trap 420-1 First RF electrode 420-2 Second RF electrode 430 Electromagnetic trap 432 Coplanar waveguide or entangled electrode, coplanar waveguide 432-1 Central track 432-2 First return track 432-3 Second return track 432-4 Short circuit connection 432-5 First distance

Claims

Step of trapping charged particles at a first position using an electromagnetic trap generated by applying a voltage to a surface electrode trap; Step of providing a static magnetic field at the first position using a device for generating a static magnetic field so that a qubit transition of the charged particles is defined; Step of providing an oscillating magnetic field using the entangled electrodes of the surface electrode trap comprising wherein the oscillating magnetic field present at the first position does not include a polarization component that directly couples to the qubit transition; wherein the oscillating magnetic field has, at the first position, a spatial gradient of the polarization component of the oscillating magnetic field that couples the qubit transition to the motion of the charged particles; wherein the entangled electrodes extend in a first direction perpendicular to the direction of the static magnetic field; wherein the qubit transitions are sigma transitions between states in which each magnetic quantum number differs by only 1; wherein the oscillating magnetic field at the first position is linearly polarized parallel to the direction of the static magnetic field so that the oscillating magnetic field does not directly couple to the qubit transition; wherein the entangled electrodes are coplanar waveguides Method.

2. wherein the coplanar waveguide comprises a central track, a first return track, and a second return track and wherein the central track extends in the first direction between the first return track and the second return track; wherein the first return track and the second return track are electrically connected to a ground terminal shared with the electromagnetic trap; The method according to claim 1.

3. wherein the coplanar waveguide further comprises a short-circuit connection; wherein the first return track, the second return track, and the central track are electrically connected to the short-circuit connection at one end; wherein the distance in the first direction between the first position and the short-circuit connection is less than λ / 4, where λ is the wavelength of the oscillating magnetic field in the coplanar waveguide; The method according to claim 2.

4. wherein the coplanar waveguide is formed symmetrically with respect to the central track; The method according to claim 2 or 3.

5. Step of trapping a second charged particle at a second position using the electromagnetic trap; Step of providing the static magnetic field so that the magnitude and direction of the static magnetic field are the same at the first position and the second position; providing, using the entangled electrode, the oscillating magnetic field for the second charged particle further comprising the entangled electrode extending in a direction parallel to the direction of the line connecting the first position and the second position such that the oscillating magnetic field present at the second position does not include a polarization component that couples to the qubit transition of the second charged particle The method according to any one of claims 1 to 4

6. generating a spin-dependent force on the charged particle and the second charged particle by exciting one or more motional sidebands of the qubit transition using the oscillating magnetic field The method according to claim 5, further comprising

7. A device for generating quantum entanglement between charged particles, comprising a substrate having a first surface and a second surface facing each other a trap electrode disposed on the first surface of the substrate and configured to form an electromagnetic trap for trapping charged particles at the first position in response to a voltage such that the first surface is sandwiched between the first position and the second surface an entangled electrode disposed on the first surface of the substrate, extending in a first direction along the substrate, and configured to generate an oscillating magnetic field parallel to the substrate and perpendicular to the first direction at the first position in response to an oscillating current comprising the entangled electrode being a coplanar waveguide device

8. The coplanar waveguide comprises a central track a first return track a second return track comprising the central track extending in the first direction between the first return track and the second return track the first return track and the second return track being electrically connected to terminals held at a fixed potential with respect to the ground terminal of the trap electrode The device according to claim 7

9. the first return track, the second return track, and the central track being electrically connected to a short-circuit connection at one end The device according to claim 8

10. the widths of the first return track and the second return track being wider than the penetration depth of the material for the first return track and the second return track at the frequency of the oscillating magnetic field The device according to claim 8 or 9

11. the electromagnetic trap being a surface electrode pole trap The device according to any one of claims 7 to 10.

12. The surface electrode pole trap is configured such that the symmetry axis of the electromagnetic trap exists along the first direction. The device according to claim 11.

13. The surface electrode pole trap comprises a first RF electrode and a second RF electrode extending in the first direction, and a first DC electrode and a second DC electrode extending in the first direction. The first RF electrode and the second RF electrode are disposed between the first DC electrode and the second DC electrode, and the entanglement electrode is disposed between the first RF electrode and the second RF electrode. The device according to claim 12.

14. A plurality of charged particles, a device according to any one of claims 7 to 13 for entangling two or more of the plurality of charged particles, a device for generating a static magnetic field, and a signal generator for generating electrical signals for the electromagnetic trap and the entanglement electrode. A system for quantum information processing. ​

Images