Quantum bit device and method for operating a quantum bit device

Abstract

According to an aspect of the inventive concept, there is provided a qubit device (100) comprising: a semiconductor substrate layer (110); a set of control gates (112, 114, 116) configured to define a row of electrostatically confined quantum dots (122) along the substrate layer (110), each quantum dot (122) being adapted to hold a qubit; and a set of nanomagnets (124) arranged in a row on the substrate layer (110) such that a nanomagnet (124) is arranged above every second quantum dot (122a) in the row of quantum dots (122), wherein each nanomagnet (124) has an out-of-plane magnetization with respect to the substrate layer (110), and wherein every second quantum dot (122a) is subject to an out-of-plane magnetic field generated by a respective nanomagnet (124) such that a qubit spin resonance frequency of every second quantum dot (124a) is shifted with respect to adjacent quantum dots (122b) in the row of quantum dots.

Description

Technical Field

[0001] The present invention relates to a quantum bit device and a method for operating the quantum bit device. Background Technology

[0002] In recent years, significant progress has been made in the development of semiconductor quantum dot qubits. Semiconductor quantum dots enable the definition of high-fidelity qubits (i.e., "spin qubits") by confining the spin states of electrons at the quantum dot. Semiconductor quantum dots can be formed from 2DEGs in, for example, silicon-based platforms using electrostatic gates. The use of conventional fabrication techniques derived from CMOS technology allows for the compact realization of spin qubits. For these reasons in particular, semiconductor quantum dot qubit technology represents a promising candidate for scalable qubit systems.

[0003] Electron spin resonance (ESR) can be used to control spin qubits in quantum dots, where the spin state is manipulated by a radio frequency AC magnetic field. In electric dipole spin resonance (EDSR), the spin state is instead manipulated by a radio frequency AC electric field. Compared to ESR, EDSR enables a more efficient and simpler pulsed scheme for qubit control. However, EDSR relies on the coupling between the electric field and the spin of the qubit, and the spin-orbit coupling of electrons in, for example, silicon is typically too weak to support EDSR. This has been addressed in the prior art by conceptual proof-of-concept devices with on-chip micromagnets to generate spatially variable in-plane spin-electric field coupling fields at the quantum dot (e.g., "Multiphysics Simulation & Design of Silicon Quantum Dot Qubit Devices" by Mohiyaddin FA et al., IEDM).

[0004] Despite recent progress, further efforts are still needed to promote the design of scalable qubit devices. Summary of the Invention

[0005] The object of this invention is to provide an improved qubit device that facilitates scaling to a larger number of qubits. Other and alternative objectives may be understood from the following description.

[0006] According to one aspect of the present invention, a quantum bit device is provided, comprising:

[0007] Semiconductor substrate layer;

[0008] A set of control gates configured to define a row of electrostatically confined quantum dots along the substrate, each quantum dot being adapted to hold a qubit; and

[0009] A group of nanomagnets is arranged in a row above the substrate, such that the nanomagnets are positioned above every other quantum dot in the row of quantum dots.

[0010] Each nanomagnet has out-of-plane magnetization relative to the substrate, and every other quantum dot is subjected to an out-of-plane magnetic field generated by the corresponding nanomagnet, such that the spin resonant frequency of the qubit at every other quantum dot is offset relative to the neighboring quantum dots in that row.

[0011] The quantum bit device of the present invention provides a scalable design for realizing a multi-qubit system.

[0012] This device supports defining quantum dots that are highly confined and have an area suitable for maintaining electronic qubits (e.g., single-electron qubits). Using control gates to define electrostatically confined quantum dots further enables the coupling of adjacent quantum dot qubit transfers between quantum dots by sequentially shuttling qubits / electrons between neighboring quantum dots by changing the potential at the quantum dot.

[0013] The small size offered by nanomagnets and their arrangement above the substrate contribute to the area efficiency of device design.

[0014] Furthermore, providing nanomagnets with out-of-plane magnetization relative to the substrate allows the induction of magnetic fields (with out-of-plane orientation) in the corresponding quantum dots beneath each nanomagnet. Defining (only defining) every other quantum dot in that row of quantum dots under (and thus aligned with) the corresponding quantum dot causes a shift in the spin resonant frequency of the qubit at every other quantum dot relative to neighboring quantum dots. This, in turn, allows qubits in quantum dots located beneath the nanomagnets to be selectively addressed to qubits in quantum dots not located beneath the nanomagnets.

[0015] The out-of-plane orientation of the magnetic field further mitigates undesirable spin-orbit coupling and variations in the Landé g-factor caused by substrate-interface inhomogeneities. In-plane magnetic fields at the quantum dot may induce residual spin-orbit coupling, potentially introducing a degree of unpredictability into the qubit's resonant frequency.

[0016] The quantum dots in this row can be correspondingly defined as a first subgroup and a second subgroup, with the quantum dots in the first subgroup alternating with those in the second subgroup. Each quantum dot in the first subgroup is defined under its corresponding counterpart in the nanomagnet and has a qubit spin resonant frequency offset from the neighboring qubits of the second subgroup of qubits. For simplicity, any quantum dot defined under its corresponding counterpart in the nanomagnet may be referred to hereinafter as the first quantum dot. Correspondingly, any quantum dot adjacent to the first quantum dot may be referred to as the second quantum dot.

[0017] As will become apparent from the following text, each first quantum dot can be used to control a qubit, while each second quantum dot can be used to hold an idle qubit. Therefore, the first and second quantum dots can be referred to as the "active" quantum dot and the "idle" quantum dot, respectively.

[0018] As used herein, the term “out-of-plane” (e.g., in relation to magnetization or magnetic field) refers to an orientation or direction having at least a principal component transverse to the substrate (e.g., transverse to the main extension plane of the substrate).

[0019] As used herein, the term "nanomagnet" refers to a permanent magnet having a submicron dimension, for example, a permanent magnet having at least a submicron length dimension (i.e., along the longitudinal direction of the row) and preferably also a submicron width dimension (i.e., along the transverse direction of the row, in-plane relative to the substrate). The height or thickness dimension of the nanomagnet (i.e., along the out-of-plane direction relative to the substrate) can also be submicron. According to embodiments, the length and width dimensions of the nanomagnet can be 200 nm or less, advantageously 150 nm or less. In any case, the length dimension of the nanomagnet can be such that each nanomagnet extends only above a single corresponding quantum dot (i.e., "covers"). The height dimension of the nanomagnet can be greater than the length and / or width dimensions, for example, 200 nm or more.

[0020] The substrate can be a silicon substrate. Silicon supports high-fidelity electrostatically confined quantum dot qubits. Furthermore, given the almost ubiquitous use of silicon in integrated circuit technology, it represents a favorable platform for qubit devices.

[0021] In addition to nanomagnets, qubit devices may also include a magnetic arrangement configured to contribute a uniform out-of-plane magnetic field to each quantum dot. It should be understood that this magnetic field contribution complements the out-of-plane magnetic field generated by the nanomagnets.

[0022] According to an embodiment, each quantum dot in every other quantum dot may have the same first qubit spin resonant frequency, and each quantum dot in a neighboring quantum dot may have the same second spin resonant frequency.

[0023] Every other quantum dot beneath the nanomagnet (i.e., the first quantum dot) can therefore exhibit a common "first" spin resonant frequency. Correspondingly, each quantum dot adjacent to one of the every other quantum dots (i.e., the second quantum dot) can exhibit a common "second" spin resonant frequency. In this context, the "common" first / second spin resonant frequency truly means that each qubit in the corresponding quantum dot of the first / second subgroup can be excited by an oscillating field (magnetic or electric field) with the same spectral content. That is, the common first / second spin resonant frequency means that the spin resonant frequencies of all first quantum dots overlap, and the spin resonant frequencies of all second quantum dots overlap. Therefore, the first quantum dots can be addressed in parallel, selectively addressing qubits in any of the quantum dots in the second subgroup. The interval between the first and second qubit spin resonant frequencies can be larger than the (corresponding) linewidth of the first and second qubit spin resonant frequencies, advantageously two orders of magnitude or more. The difference in out-of-plane magnetic field strength between the first quantum dot and the adjacent second quantum dot can advantageously be 5 mT or greater.

[0024] According to an embodiment, the set of control gates may include barrier gates and plunger gates arranged alternately along the longitudinal direction of the row of quantum dots.

[0025] This configuration allows for the use of a limited number of control gates to define height-restricted quantum dots.

[0026] As used herein, the term "barrier gate" refers to a gate configured to confine the quantum dots in the longitudinal direction of the row of quantum dots. Each barrier gate can define a tunneling barrier between each pair of adjacent quantum dots.

[0027] As used herein, the term "plunger gate" refers to a gate configured to control the (electrochemical) potential of a corresponding quantum dot. Therefore, each plunger gate is associated with a corresponding quantum dot. Each plunger gate can control the charge accumulated at the associated quantum dot.

[0028] The set of control gates may further include a pair of longitudinal confinement gates arranged on opposite sides of the row of quantum dots.

[0029] As used herein, the term "longitudinal confinement gate" (for brevity, "confinement gate") refers to a gate configured to confine the quantum dots in the lateral direction (in-plane relative to the substrate) relative to the row of quantum dots. This pair of confinement gates can be shared by all the quantum dots in the row, thus limiting the number of control gates required.

[0030] Barrier gates can all have the same gate length and be arranged at regular intervals (i.e., center-to-center distance). Plunger gates can all have the same gate length and each plunger gate can be centered between a corresponding pair of barrier gates.

[0031] The regular arrangement of barrier gates and plunger gates defines the electrostatic potential of the qubit, which varies periodically along the longitudinal direction of the row of quantum dots (i.e., the "qubit row direction"). In addition to contributing to the uniform electrical properties of the quantum dots, it has been recognized that the periodic and regular potential of the qubits makes the operation of qubit devices less sensitive to potential alignment errors of the nanomagnets. It is understood that the spacing between the nanomagnets can be twice the spacing of the barrier gates.

[0032] The spacing between the barrier gates can range from 50 nm to 150 nm. The center-to-center distance between the barrier gate and the adjacent plunger gate can be half the barrier gate spacing. The gate length of the barrier gate and / or plunger gate can range from 20 nm to 70 nm.

[0033] A qubit device can be configured to apply the same barrier gate potential to each barrier gate. This, when combined with a regular arrangement of barrier gates and plunger gates, can further contribute to the periodicity of the potential along the row of quantum dots.

[0034] This group of nanomagnets can be arranged in a common hierarchy above this group of control gates.

[0035] In other words, each nanomagnet in this group can be positioned above the control gate at the (same) level relative to the substrate. Positioning the nanomagnets at the level above the gate facilitates fabrication. Furthermore, the height (i.e., vertical dimension) of the nanomagnets can be freely chosen without affecting the gate's level above the semiconductor substrate. This arrangement also prevents the nanomagnets from interfering with the gate.

[0036] If the set of control gates includes a barrier gate and a plunger gate as discussed above, then the barrier gate and the plunger gate can be arranged at the (same) first level above the substrate, and the set of nanomagnets can be arranged at the (same) second level above the first level.

[0037] If the control gate set further includes a pair of confinement gates as discussed above, then the confinement gates can be arranged in a third level above the substrate, below the second level. The nanomagnets, barrier gates, and plunger gates, along with the confinement gates, can thus be positioned at different corresponding levels above the substrate, achieving a stacked and therefore area-efficient design. The third level of the confinement gates can be below the first level of the barrier gates and plunger gates. However, alternative configurations are also possible.

[0038] According to an embodiment, the qubit device may further include a dielectric layer structure disposed on a substrate and embedded with the set of control gates, wherein quantum dots may be defined at the interface between the substrate and the dielectric layer structure. This realizes a monolithic qubit device that can be fabricated in a reasonable manner relying on processing techniques from conventional CMOS device fabrication (e.g., dielectric layer deposition, gate layer deposition, and patterning).

[0039] According to an embodiment, a qubit device can be configured to: transfer qubits from neighboring quantum dots to selected quantum dots in every other quantum dot, by changing the potential of the plunger gate associated with the selected quantum dot and the potential of the plunger gate associated with the neighboring quantum dots; and supply a radio frequency electric or magnetic control field to the selected qubit at the selected quantum dot to control the spin state of the selected qubit.

[0040] Therefore, selective qubit control is achieved by transferring / shuttling qubits (e.g., electrons) from a second / idle quantum dot to a first / active quantum dot.

[0041] According to ESR-based qubit control, an AC magnetic control field resonating with a selected qubit can be applied to cause the qubit's spin to rotate.

[0042] The nanomagnets also enable qubit control based on EDSR: the magnetic field generated by each nanomagnet can induce a spatial magnetic gradient field with non-zero in-plane components at the quantum dot below.

[0043] Therefore, every other quantum dot (i.e., each first quantum dot) can be confined within a spatially varying magnetic field, thus allowing qubit control via EDSR. This component can advantageously be an in-plane component transverse to the row direction (relative to the substrate), as this facilitates a faster response for qubit spin rotation and oscillation control.

[0044] In other words, a qubit device can be configured to control the spin state of the qubits held at the quantum dot by using a pair of control gates arranged on opposite sides of the row of quantum dots, causing the qubits to oscillate in space within a magnetic gradient field along a direction transverse to the longitudinal direction of the row of qubits.

[0045] The control gates can generate a varying electric field so that the qubit is subjected to a varying out-of-plane magnetic field that resonates with the qubit's spin resonant frequency due to its oscillation.

[0046] The pair of control gates can advantageously be the pair of longitudinal confinement gates discussed above. Thus, the confinement gates can generate a varying electric field so that each qubit in the row of quantum dots oscillates at a certain frequency, such that spin resonance (i.e., spin rotation) is induced only in the qubits of the first quantum dot (i.e., under the nanomagnet).

[0047] The gradient amplitude at each quantum dot can, for example, be at least 0.1 mT / nm along the transverse direction, advantageously at least 0.4 mT / nm.

[0048] According to an embodiment, the qubit device may further include one or more radio frequency resonators connected to the set of control gates. This enables qubit readout by detecting the spin-dependent resonant frequency.

[0049] A qubit device may include a set of radio frequency resonators, each of which may be connected to a corresponding plunger gate of the set of control gates. This enables the readout of the qubit held by the quantum dot associated with the plunger gate connected to the resonator.

[0050] Each resonator can, for example, be connected to a corresponding plunger gate at a quantum dot (i.e., the corresponding first quantum dot) defined under a nanomagnet.

[0051] A qubit device can be configured to transfer a qubit to be read from a neighboring quantum dot to a selected quantum dot associated with a plunger gate connected to a resonator, by changing the potential of the plunger gate associated with the selected quantum dot and the potential of the plunger gate associated with the neighboring quantum dot; and subsequently detect the resonant frequency of the resonator connected to the plunger gate associated with the selected quantum dot.

[0052] Therefore, selective qubit readout is achieved by transferring / shuttling qubits (e.g., electrons) to a quantum dot associated with a plunger gate and sensing the resulting resonant frequency of a resonator associated with the quantum dot.

[0053] According to an embodiment, the qubit device may further include an ESR transmission line extending along the row of quantum dots. The ESR transmission line may be arranged on a layer above the nanomagnets to achieve a smaller spacing between the nanomagnets and the quantum dots.

[0054] According to an embodiment, the quantum bit device may further include a non-magnetic metal layer connected to a nanomagnet. Therefore, the nanomagnet can be maintained at the same potential. The non-magnetic metal layer can advantageously be disposed on top of the nanomagnet. The non-magnetic metal layer may further be connected to ground. Therefore, the risk of discharge during operation can be mitigated.

[0055] The qubit device may further include a pair of storage gates arranged at opposite ends of the row of qubits and configured to supply qubits to the row of qubits.

[0056] According to a second aspect of the present invention, a method for operating a quantum bit device is provided, the method comprising:

[0057] A row of electrostatically confined quantum dots is defined along a substrate using a set of control gates, each quantum dot being adapted to hold a qubit.

[0058] Every other quantum dot is confined under a corresponding nanomagnet in a row of nanomagnets arranged above the substrate, wherein each nanomagnet has out-of-plane magnetization relative to the substrate, and wherein each of every other quantum dots is subjected to an out-of-plane magnetic field generated by the corresponding nanomagnet, such that the spin resonant frequency of the qubit of every other quantum dot is offset relative to the neighboring quantum dots in the row.

[0059] In general, this aspect can present the same or corresponding advantages as the previous aspect. Therefore, refer to the above discussion. In particular, any reference to the function or operation of the quantum bit device or any element thereof described above can form the steps or actions of this method. Attached Figure Description

[0060] The above and additional objects, features, and advantages of the present invention will be better understood through the following illustrative and non-limiting detailed description with reference to the accompanying drawings. In the drawings, unless otherwise stated, the same reference numerals will be used for the same elements.

[0061] Figure 1 This is a schematic top view of a quantum bit device.

[0062] Figures 2A to 2F These are schematic perspective views and corresponding cross-sectional views of a quantum bit device.

[0063] Figures 3A to 3B It schematically illustrates the movement of qubits between neighboring quantum dots and single-qubit and two-qubit gates.

[0064] Figures 4A to 4C The control of the quantum dot potential during qubit shuttle is schematically shown.

[0065] Figures 5A to 5D Various properties of the magnetic field obtained using an example configuration of nanomagnets are shown. Detailed Implementation

[0066] Figure 1This is a schematic top view of a qubit device 100. The qubit device 100 can be used, for example, in a quantum computing device. Examples of algorithms that can be implemented include quantum chemistry algorithms and Grover's search algorithm. Figure 1 Some of the elements of the depicted qubit device 100 are shown transparently to allow simultaneous observation of the elements below. The qubit device 100 includes a semiconductor substrate 110. The substrate 110 may be, for example, a silicon layer of isotropically purified silicon. Other example materials for the substrate 110 include GaAs and SiGe. x and y represent a first in-plane direction and a second in-plane direction relative to the substrate 110 (i.e., parallel to the substrate 110), respectively. z represents, for example, an out-of-plane direction perpendicular to the substrate 110. It should be noted that the negative z-direction (i.e., -z) is also considered an out-of-plane direction relative to the substrate 110. Directions x and y may also be referred to as a first horizontal direction and a second horizontal direction, while z may be referred to as a vertical direction.

[0067] The qubit device 100 includes a set of control gates 112, 114, 116 configured to define a row of electrostatically confined quantum dots 122 along a substrate layer 110. As will be further described below, the qubit device 100 may include a dielectric layer defining a dielectric-semiconductor interface along the substrate layer 110, wherein the qubits 122 may be confined at the interface. The row (i.e., its longitudinal direction) may be defined to extend parallel to the x-direction. Therefore, a direction transverse to the row direction (i.e., the transverse direction of the row) may be parallel to the y-direction. The quantum device 100 is accordingly adapted to realize linear or 1D qubit arrays. As will be understood, a quantum computing device may include multiple such 1D qubit arrays that operate independently of each other.

[0068] Each quantum dot 122 can hold one or more electrons that define a qubit. However, for simplicity, the following disclosure will refer to single-electron qubits. It is further envisioned that the principle of the qubit device 100 is compatible with hole-based qubits, but holes may be more difficult to control due to their inherent spin-orbit coupling.

[0069] The qubit device 100 further includes a row of nanomagnets 124 arranged above a substrate layer 110. As shown, the row of nanomagnets can extend above and along the row of quantum dots 122 (i.e., during operation of the device 100 when the row of quantum dots 122 is defined). Each nanomagnet 124 has out-of-plane magnetization relative to the substrate layer 110. Every other quantum dot 122a is defined below a corresponding one of the nanomagnets 124 and thus experiences an out-of-plane magnetic field generated by the corresponding nanomagnet 124 above it. Figure 1In the subsequent figures, the unfilled circles along the row of quantum dots 122 represent quantum dots 122a (“first / active quantum dots”) located below nanomagnets 124. Filled circles represent quantum dots 122b (“second / idle quantum dots”) not located below nanomagnets 124. Therefore, it will be assumed that the magnetization of the nanomagnets 124 and the corresponding magnetic field at each first quantum dot 122 are parallel to the out-of-plane direction z.

[0070] The magnetic field generated by the corresponding nanomagnet 124 causes the spin resonant frequency of the qubit of quantum dot 122a below the corresponding nanomagnet 124 to shift relative to the neighboring quantum dot 122b, which does not have a nanomagnet 124 above it. The spin resonant frequency of the qubit in a magnetic field of strength B can be expressed as E. ZS / h=g e μ B B / h, where E ZS It is the Zeeman split between spin states, h is Planck's constant, and g is... e It is the electronic g factor, and μ B It is a Bohr magneton. The magnetic field strength experienced by the qubit at the first quantum dot 122a will be different from that experienced by the qubit at the second quantum dot 122b, and therefore the resonant frequencies of these qubits will also be different.

[0071] like Figure 1 As shown, a uniform magnetic field contribution B0 with an out-of-plane orientation (e.g., parallel to the z or -z direction) can also be provided at quantum dot 122. The magnetic field B0, which may be referred to as the external magnetic field B0 for illustrative purposes, can be generated by a magnetic arrangement of one or more permanent magnets and / or electromagnets. It is understood that the magnetic field B0 can also be generated by one or more magnets located outside the quantum bit device 100.

[0072] Therefore, the effective magnetic field experienced by the qubits in quantum dot 122 can be given by the sum of the external magnetic field B0 and the local magnetic field generated at the location of the nanomagnet 124 at quantum dot 122. As can be understood, the nanomagnet 124 can thus cause a local variation in the out-of-plane magnetic field along the row of quantum dots 122, such that the spin resonant frequency of the qubits of each first quantum dot 122a is shifted relative to each neighboring second quantum dot 122b in that row.

[0073] Turn again Figure 1Each first quantum dot 122a can have the same first qubit spin resonant frequency, and each second quantum dot 122b can have the same second spin resonant frequency. This allows the same control signal to be used to control the qubits in any of the first quantum dots 122a. This applies accordingly to the qubits in any of the second quantum dots 122b. The same resonant frequencies can be achieved, for example, using a set of identical nanomagnets 124 aligned with the quantum dots 122 such that each first quantum dot 122a and each second quantum dot 122b experiences corresponding (at least substantially) equal magnetic field strengths along the z-direction. However, it is conceivable that, for example, different subgroups of the first quantum dots 122a can have different corresponding qubit spin resonant frequencies (and correspondingly, the second quantum dots 122b), which is achieved, for example, by using nanomagnets 124 with different strengths and / or arranged at different levels above the quantum dots 122.

[0074] The set of control gates of the illustrated qubit device 100 includes barrier gates 112 and plunger gates 114 arranged alternately along the row direction (i.e., along the x-direction). Hereinafter, reference numeral 114 will be used to uniformly refer to plunger gate 114, while reference numerals 114a and 114b will refer to the plunger gates associated with the first quantum dot 122a and the second quantum dot 122b, respectively. The set of control gates further includes a pair of (longitudinal) confinement gates 116. Confinement gates 116 are arranged on opposite sides of the row of quantum dots 122 and extend along the row of quantum dots. Quantum dots 122 can be electrostatically confined by barrier gates 112 along the x-direction and by confinement gates 116 along the y-direction. Barrier gates 112 and confinement gates 116 can be biased to cause depletion of free electrons beneath gates 112 and 116. The electrochemical potential of each quantum dot 122 and the number of electrons accumulated therefrom can be controlled by the corresponding plunger gate 114a.

[0075] As shown in the figure, the barrier gates 112 can each have the same gate length and are arranged at a regular spacing. Similarly, the plunger gates 114 can each have the same gate length and are arranged at the center between the respective pairs of barrier gates 112. The quantum dots 122 can therefore be defined with a regular spacing / interval corresponding to the spacing of the barrier gates, such as... Figure 1 p in dot The spacing / interval of the nanomagnets 124 can correspond to twice the spacing of the quantum dots, p magnet =2p dot To further regularize the grid pattern, the barrier grid 122 and the plunger grid 114 can have the same grid length, but this is not necessary.

[0076] For example, the quantum dot spacing can be, for instance, approximately 50 nm to 150 nm. The barrier gate spacing can also be in the range of 50 nm to 150 nm. The center-to-center distance between the barrier gate and the adjacent plunger gate can be half the barrier gate spacing. The gate length of the barrier gate and / or plunger gate can be 20 nm to 70 nm.

[0077] Each barrier gate 112 can be configured to apply the same barrier gate potential / voltage to each barrier gate 112. The height of the tunnel barrier between adjacent quantum dots 122a, 122b can therefore be the same along the row of quantum bits 122. The tunnel barrier height can, for example, be in the range of 5 meV to 15 meV. This assumes a quantum dot spacing p. dot Within the aforementioned range, tunnel coupling of approximately 1 GHz can be generated. c Larger tunnel coupling values ​​can be achieved with lower tunnel barrier heights. For example, tunnel coupling in the 10 GHz to 100 GHz range can be achieved with tunnel barrier heights ranging from 40 μeV to 400 μeV. c The voltage of the plunger gate 114 can be selected so that one or zero electrons are confined in the associated quantum dot 122.

[0078] Electrons defining a qubit can be loaded into or unloaded from the row of qubits 112 from corresponding electron storage units, which are defined under corresponding storage gates 118 arranged at opposite ends of the row of qubits 122. The electron storage units can be, for example, 2DEGs.

[0079] The quantum bit device 100 can achieve the movement of quantum bits along the row of quantum dots 122 by controlling the potential of the quantum dots 122. Figure 3A The diagram schematically depicts an example of a qubit (“qubit 3”) shuttling / transferring between a pair of neighboring qubits 122a and 122b. Figures 4A to 4C It schematically shows the process before the transfer ( Figure 4A During tunnel crossing ( Figure 4B ) and after the transfer is completed ( Figure 4C The potential wells of the corresponding quantum dots 122a and 122b and the position of quantum bit 3 are shown. The two pairs of solid and dashed lines in the corresponding potential wells represent the Zeeman split of the energy levels. A similar approach can be applied when loading electrons from / unloading electrons from the electron storage device by lowering or increasing the potential of the quantum dot 122 adjacent to the electron storage device relative to the potential of the electron storage device.

[0080] A single-qubit grid can typically be implemented as follows: a selected qubit (e.g., "qubit 3") can be transferred from a neighboring quantum dot 122b to the first / active quantum dot 122a (e.g., as in combination). Figure 3A and 4A to Figure 4C (As discussed). The qubit at the selected quantum dot 122a can then be subjected to a radio frequency electrical control field (for EDSR-based qubit control) or a magnetic control field (for ESR-based qubit control) to control the spin state of the selected qubit.

[0081] like Figure 3B As demonstrated, a dual-qubit grid (e.g., CNOT / CZ) can be implemented in a corresponding manner by transferring a selected first qubit (e.g., "qubit 3") to a first / active qubit 122a adjacent to a second / idle qubit 122b that also holds a qubit (e.g., "qubit 2"). Dual-qubit operations (dependent on ESR or EDSR) can then be performed based on the tuning of the exchange coupling between the selected qubit 122a and the qubits in the neighboring qubits 122b (e.g., "qubits 2 and 3"). The exchange coupling can be tuned by changing the tunneling coupling or energy detuning between the qubits 122a and 122b.

[0082] To support ESR-based qubit control, the qubit device 100 may further include an electron spin resonant ESR transmission line 130 extending along the row of quantum dots 122. The qubit device 100 may include radio frequency generation circuitry for supplying ESR control signals to the ESR transmission line 130 to achieve ESR-based qubit control in a conventional manner.

[0083] As an alternative to or complement to ESR-based qubit control, the qubit device 100 can allow EDSR-based qubit control. Each nanomagnet 124 can induce a spatial magnetic gradient field with a non-zero in-plane component (e.g., dBy / dy) at the location of the associated quantum dot 122a. Therefore, the spin state of the qubit held at the first quantum dot 122a can be controlled via the EDSR by causing the qubit to oscillate spatially within the magnetic gradient field along the in-plane direction. An oscillation amplitude of approximately 1 nm can be readily achieved by changing the potential of a pair of control gates (e.g., confinement gates 116) arranged on opposite sides of the quantum dot.

[0084] As an alternative to the transverse magnetic gradient field component dBy / dy, the EDSR can rely on the longitudinal magnetic gradient field component dBx / dy, in which case a pair of barrier gates 112 can be used to control the longitudinal oscillation of the qubit within the magnetic gradient field.

[0085] To enable the readout of the qubit state, the qubit device 100 may further include Figure 1One or more radio frequency resonators are uniformly represented by reference numeral 132 in the figure. As shown, resonator 132 can be connected to each plunger gate 114a associated with the first quantum dot 122a. Each resonator 132 can be connected to its associated plunger gate 112 via a corresponding transmission line. The frequency of resonator 132 will depend on the state of the qubit at the associated quantum dot 122a.

[0086] refer to Figure 3B Therefore, the state of a qubit can be detected by transferring a selected first qubit (e.g., "qubit 3") to a first / active qubit 122a associated with resonator 132 and adjacent to a second / idle qubit 122b that also holds a qubit (e.g., "qubit 2"); and detecting the resulting resonant frequency, for example, by measuring the reflectivity of resonator 132. When the qubits adjacent to qubits 122a and 122b are biased in an appropriate manner, the Pauli spin repulsion principle causes spin-dependent tunneling of the qubit / electron to its neighboring qubit 122b. This spin-dependent inter-point tunneling can modify the capacitance of resonator 132 and thus its resonant frequency, thereby facilitating spin readout.

[0087] According to an alternative configuration, resonator 132 can alternatively be connected to each plunger gate 114 associated with the second quantum dot 122b, where readout can be performed in a corresponding manner by transferring the qubit to be read to the quantum dot 122b associated with the plunger gate 114b. A similar readout approach can be applied using a shared lumped element resonator connected to the plunger gates 114 (e.g., plunger gates 114a or 114b).

[0088] Figures 5A to 5D Various properties of the magnetic field that can be obtained using a cobalt (Co) nanomagnet positioned 100 nm above quantum dot 122a, having a length dimension of 100 nm, a width dimension of 100 nm, and a height of 200 nm are shown. Boxes and circles represent the positions of nanomagnet 124 and the first quantum dot 122a / second quantum dot 122b relative to the magnetic field, respectively.

[0089] Figure 5A The out-of-plane component B of the effective magnetic field in the regions of the two first quantum dots 122a and adjacent to the second quantum dot 122b is shown. Z The strength of the magnetic field. The axis represents the spatial coordinates relative to the second quantum dot 122b, in nanometers. As shown, the use of the nanomagnet 124 enables a magnetic field strength difference of, for example, about 10 mT at the first quantum dot 122a and the second quantum dot 122b. This translates to a resonant frequency difference of about 280 MHz, which is more than two orders of magnitude larger than the typical maximum qubit linewidth of an electrostatically confined quantum dot (e.g., about 1 MHz).

[0090] Figure 5B The transverse magnetic gradient field components dBy / dy are shown. As shown in the figure, the use of nanomagnet 124 achieves an in-plane magnetic gradient of approximately 0.5 mT / nm.

[0091] Figure 5C The longitudinal magnetic gradient field component dBx / dx of approximately 0.3 mT / nm is shown in quantum dots 122a and 122b.

[0092] Figure 5D It shows the result of The dephase gradient of an example configuration of a defined nanomagnet 124. When coupled with electric field noise, the derivative of the in-plane magnetic field with respect to the z-direction causes dephase. Therefore, in an ideal periodic lattice, DG should be zero, as... Figure 5D As can be seen, this is almost entirely achieved for the example configuration.

[0093] Figures 2A to 2F It shows a schematic perspective view and corresponding cross-sectional view of the structure and geometry of the quantum bit device 100 in more detail.

[0094] Figure 2A and Figure 2B A portion of the quantum bit device 100 is shown from two different angles. As shown, a dielectric layer structure 120 is disposed on a substrate layer 110 (e.g., which may be a silicon layer) and the set of control gates 112, 114, 116 is embedded therein. The dielectric layer structure 120 is schematically shown as a single-layer structure, but may typically comprise multiple layers of different dielectric materials, such as different oxides, for example, silicon oxide and other conventional interlayer dielectrics. As described above, quantum dots 122 may be defined at the interface between the substrate layer 100 and the dielectric layer structure 120. More specifically, quantum dots 122 may be defined at the interface between the silicon substrate layer 110 and the bottom oxide layer of the dielectric layer structure 120. For the silicon substrate 110, a silicon oxide layer of 5 nm to 20 nm thickness may be present between the substrate 110 and the control gates 112, 114, 116.

[0095] Figure 2D It shows along Figure 2CThe diagram shows a cross-section of the qubit device 100 as captured by a line cut. Barrier gate 112 and plunger gate 114 can be arranged at a common first level above substrate layer 110. Nanomagnet 124 can be arranged at a common second level above substrate layer 110, with the second level above the first level. Storage gate 118 can also be arranged at the first level. Confinement gate 116 can be arranged at a common third level above substrate layer 110, below the first and second levels. In an alternative configuration, the common third level of confinement gate 116 can be located above the first level, for example, below the second level.

[0096] The second layer of the nanomagnet 124 allows each quantum dot 122a to be confined in the far field of the associated magnetic field of the nanomagnet 124.

[0097] Figure 2E It shows along Figure 2F The line shown represents a cross-section of the qubit device 100. As illustrated, the plunger gate 114 can be arranged not to extend into the space between the nanomagnet 124 and the associated first quantum dot 122a.

[0098] The quantum bit device 100 can be fabricated using conventional CMOS processes, such as patterning of a metal-oxide-semiconductor stack of suitable gate dielectric, gate electrode material, and substrate material (e.g., Si, Si-28, SiGe). The nanomagnet 124 can be made of a suitable magnetic material at appropriate locations and embedded within the dielectric material.

[0099] The qubit device 100 may further include a nonmagnetic metal layer 126, for example, in the form of a wire, connected to the nanomagnet 124. The metal layer 126 may be disposed on top of the nanomagnet 124, for example, in direct contact with the upper surface of the nanomagnet 124. The metal layer 126 can reduce potential variations between the nanomagnets 124. The metal layer 126 may be connected to the electrical ground of the qubit device 100. Suitable nonmagnetic materials for the metal layer 126 include TiN, Al, and Au.

[0100] In the foregoing, the inventive concept has been described primarily with reference to a limited number of examples. However, as will be readily understood by those skilled in the art, other examples besides those disclosed above are equally possible within the scope of the inventive concept as defined by the appended claims.

[0101] For example, while the qubit device 100 depicted in the figure includes a vertical confinement gate 116, lateral confinement of the quantum dots can also be provided by using barrier gates 112 and plunger gates 114, which are arranged alternately along horizontal nanowires (e.g., patterned in a semiconductor substrate) with a lateral dimension of a few nanometers. In other words, the row of quantum dots 112 can be electrostatically confined by the barrier gates 112 and plunger gates 114 along the nanowires and physically confined by the nanowires in the lateral direction.

Claims

1. A quantum bit device (100), comprising: Semiconductor substrate (110); A set of control gates (112, 114, 116) configured to define a row of electrostatically confined quantum dots (122) along the substrate layer (110), each quantum dot (122) being adapted to hold a qubit; and A group of nanomagnets (124) are arranged in a row above the substrate (110) such that the nanomagnets (124) are positioned above every other quantum dot (122a) in the row of quantum dots (122). Each nanomagnet (124) has out-of-plane magnetization relative to the substrate layer (110), and every other quantum dot (122a) is subjected to an out-of-plane magnetic field generated by the corresponding nanomagnet (124), such that the spin resonant frequency of the qubit of every other quantum dot (122a) is shifted relative to the neighboring quantum dot (122b) in that row of quantum dots. The control grid includes barrier grids (112) and plunger grids (114) arranged alternately along the longitudinal direction of the row of quantum dots (122), wherein the barrier grids (112) are configured to confine the quantum dots (122) in the longitudinal direction of the row of quantum dots, the plunger grids (114) are configured to control the potential of the corresponding quantum dots, and the set of nanomagnets (124) are arranged above every other plunger grid (114).

2. The quantum bit device (100) according to claim 1, wherein, The quantum dots (122a) have the same first qubit spin resonant frequency, and each of the neighboring quantum dots (122b) has the same second spin resonant frequency.

3. The quantum bit device (100) according to claim 1, wherein, The control gates further include a pair of longitudinal confinement gates (116) arranged on opposite sides of the row of quantum dots (122) to laterally confine the quantum dots (122).

4. The quantum bit device (100) according to claim 1 or 3, wherein, These barrier gates (112) have the same gate length and are arranged at regular intervals, and these plunger gates (114) have the same gate length and each plunger gate (114) is centered between a corresponding pair of barrier gates (112).

5. The quantum bit device (100) according to any one of claims 1 to 3, wherein, The group of nanomagnets (124) is arranged in a common hierarchy above the group of control gates (112, 114, 116).

6. The quantum bit device (100) according to any one of claims 1 to 3 further includes a dielectric layer structure (120) disposed on the substrate (110) and embedded with the set of control gates (112, 114, 116), wherein the quantum dots (122) are defined at the interface between the substrate (110) and the dielectric layer structure (120).

7. The quantum bit device (100) according to any one of claims 1 to 3, wherein, The qubit device (100) is configured to: transfer qubits from neighboring quantum dots (122b) to selected quantum dots in every other quantum dot (122a) by changing the potential of the plunger gate (114a) associated with the selected quantum dot and the potential of the plunger gate (114b) associated with the neighboring quantum dot (122b); and supply a radio frequency electric or magnetic control field to the selected qubit at the selected quantum dot to control the spin state of the selected qubit.

8. The quantum bit device (100) according to any one of claims 1 to 3, wherein, The magnetic field generated by each nanomagnet (124) induces a spatial magnetic gradient field with a non-zero in-plane component at the quantum dot below.

9. The quantum bit device (100) according to claim 8, wherein, The qubit device (100) is configured to control the spin state of the qubit held at the quantum dot (122a) by using a pair of longitudinal confinement gates (116) arranged on opposite sides of the row of quantum dots (122) to make the qubit oscillate in the magnetic gradient field along a direction transverse to the longitudinal direction of the row of qubits.

10. The quantum bit device (100) according to any one of claims 1 to 3 further includes one or more radio frequency resonators (132) connected to the plunger gate (114a) of the set of control gates.

11. The quantum bit device (100) according to claim 10, wherein, The qubit device (100) is configured to transfer the qubit to be read from a neighboring quantum dot (122b) to a selected quantum dot associated with a plunger gate (114a) connected to a radio frequency resonator (132) by changing the potential of the plunger gate (114a) associated with the selected quantum dot and the potential of the plunger gate (114b) associated with the neighboring quantum dot (122b); and subsequently detect the resonant frequency of the radio frequency resonator (132) connected to the plunger gate (114a) associated with the selected quantum dot.

12. The quantum bit device (100) according to any one of claims 1 to 3 further includes an electron spin resonant ESR transmission line (130) extending along the row of quantum dots (122).

13. The quantum bit device (100) according to any one of claims 1 to 3 further comprises a nonmagnetic metal layer (126) connected to the nanomagnets.

14. The quantum bit device (100) according to any one of claims 1 to 3, wherein, The row of electrostatically confined quantum dots (122) is a single row.

15. A method for operating a quantum bit device (100), the method comprising: A row of electrostatically confined quantum dots (122) is defined along the substrate layer (110) using a set of control gates (112, 114, 116), each quantum dot (122) being adapted to hold a qubit. Every other quantum dot (122a) is confined under a corresponding nanomagnet (124) of a row of nanomagnets (124) arranged above the substrate (110), wherein each nanomagnet (124) has out-of-plane magnetization relative to the substrate (110), and wherein each quantum dot in every other quantum dot (122a) is subjected to an out-of-plane magnetic field generated by the corresponding nanomagnet (124), such that the qubit spin resonant frequency of every other quantum dot (122a) is shifted relative to the neighboring quantum dot (122b) in that row of quantum dots, and The control grid includes barrier grids (112) and plunger grids (114) arranged alternately along the longitudinal direction of the row of quantum dots (122), wherein the barrier grids (112) are configured to confine the quantum dots (122) in the longitudinal direction of the row of quantum dots, the plunger grids (114) are configured to control the potential of the corresponding quantum dots, and the set of nanomagnets (124) are arranged above every other plunger grid (114).

16. The method for operating a quantum bit device (100) according to claim 15, wherein, The set of control gates includes barrier gates (112) and plunger gates (114) arranged alternately along the longitudinal direction of the row of quantum dots (122), wherein the barrier gates (112) are configured to confine the quantum dots (122) in the longitudinal direction of the row of quantum dots, the plunger gates (114) are configured to control the potential of the respective quantum dots, and the set of nanomagnets (124) are arranged above every other plunger gate (114).

17. The method for operating a quantum bit device (100) according to claim 16, wherein, The control gates further include a pair of longitudinal confinement gates (116) arranged on opposite sides of the row of quantum dots (122) to laterally confine the quantum dots (122).

18. The method for operating a qubit device (100) according to any one of claims 15 to 17, further comprising transferring a qubit from a neighboring quantum dot (122b) to a selected quantum dot in every other quantum dot (122a) by changing the potential of a plunger gate (114a) associated with the selected quantum dot and the potential of a plunger gate (114b) associated with the neighboring quantum dot (122b); and supplying a radio frequency electric or magnetic control field at the selected quantum dot to the selected qubit to control the spin state of the selected qubit.

19. The method for operating a quantum bit device (100) according to any one of claims 15 to 17, wherein, The row of electrostatically confined quantum dots (122) is a single row.

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