Quantum bit control device, quantum computer system, and quantum bit control method

Abstract

A quantum bit control device according to the present invention comprises: an insulating layer that is disposed on a semiconductor layer; a plurality of quantum dots that are formed on the semiconductor layer and that trap quantum bits comprising electrons or holes in a predetermined spin state as a result of the application of a voltage; a plurality of electrodes that are disposed on the insulating layer and that form electromagnetic fields that act on the quantum bits through the application of a voltage; a voltage applying unit that applies a voltage for forming an electromagnetic field that acts on the quantum bits to at least one of the electrodes; a microwave generation source that radiates microwaves having a fixed frequency onto the quantum bits; and a control unit that, while the microwaves are being radiated, independently controls the spin states of a first quantum bit and a second quantum bit by modulating a first electromagnetic field applied to the first quantum bit at a first timing, modulating a second electromagnetic field applied to the second quantum bit at a second timing, and controlling the first timing and the second timing so as to be mutually different.

Description

Quantum bit control device, quantum computer system, and quantum bit control method

[0001] The present invention relates to a method for controlling quantum bits.

[0002] Quantum computers are believed to be capable of faster information processing for certain problems than existing computers. While existing computers handle only the binary values ​​of 0 and 1, quantum computers are characterized by their ability to handle superpositions of these two values.

[0003] To handle superposition states, quantum computers require elements that realize qubits. Qubits can be realized using superconducting elements, cooled atoms, photons, and quantum dots made from semiconductor elements. The basic operations of a quantum computer include initialization, calculation, and readout, and further basic operations include single-qubit gates and two-qubit gates, and it is known that universal quantum computing can be realized by combining these.

[0004] In quantum computers that use electrons (or holes; hereafter, we will use electrons as an example) as quantum bits, parallel operations that manipulate quantum bits in parallel are important. This is because, in a quantum bit array with many quantum bits, when manipulating each quantum bit sequentially, the number of quantum operations that can be performed within the coherence time is limited, limiting quantum computing to small-scale computation.

[0005] Therefore, if multiple qubits could be manipulated simultaneously (parallel computation), the effects of qubit arrays with many qubits could be utilized, enabling large-scale quantum computing. The challenge in performing such parallel computations is the qubit addressing method for selecting each qubit.

[0006] In the following, the term "semiconductor quantum dot" refers to a container that confines and stores a quantum bit, and the term "qubit" refers to a basic unit of quantum information realized by, for example, the spin of an electron, etc. Furthermore, by shuttling, a quantum bit can be moved to a different quantum dot within a quantum dot array.

[0007] A silicon quantum computer has been disclosed in which quantum dots having multiple quantum bits share wiring for applying current to control the quantum bits (Patent Document 1). However, parallel operation is important to realize the benefits of large-scale operation, but this known example does not take this into consideration. Furthermore, Patent Document 2 discloses a quantum bit control method that applies a continuous wave RF signal and locally modulates the quantum bit frequency using an electric field. However, because an electric field is used, it is difficult to perform parallel operation without disturbing the potential for confining the quantum bits.

[0008] Japanese Patent Application Publication No. 2022-130893

[0009] The object of the present invention is to perform parallel operations on multiple quantum bits.

[0010] One aspect of the present invention is a quantum bit control device comprising: a semiconductor layer; an insulating layer disposed on the semiconductor layer; a plurality of quantum dots formed in the semiconductor layer, each capturing a quantum bit consisting of an electron or hole in a predetermined spin state by applying a voltage; a plurality of electrodes disposed on the insulating layer, each forming an electromagnetic field acting on the quantum bit; a voltage application unit for applying a voltage to at least one of the electrodes to form the electromagnetic field acting on the quantum bit; a microwave generation source for irradiating the quantum bit with microwaves of a fixed frequency; and a control unit for independently controlling the spin states of the first quantum bit and the second quantum bit by modulating a first magnetic field applied to a first quantum bit at a first timing and modulating a second magnetic field applied to a second quantum bit at a second timing during the microwave irradiation, and controlling the first timing and the second timing to be different from each other.

[0011] Another aspect of the present invention is a quantum computer system including the above-described quantum bit control device.

[0012] Another aspect of the present invention is a method for controlling quantum bits constituted by electrons or holes trapped in a semiconductor layer in a quantum dot array including a semiconductor layer, an insulating layer disposed on the semiconductor layer, and a plurality of electrodes disposed on the insulating layer, the method comprising: a microwave irradiation step of irradiating microwaves of a predetermined frequency onto at least a portion of the quantum dot array; and an electromagnetic field application step of applying a voltage to the electrodes to form an electromagnetic field acting on at least one of the quantum bits, wherein in the electromagnetic field application step, during microwave irradiation, a first electromagnetic field applied to a first quantum bit is modulated at a first timing, and a second electromagnetic field applied to a second quantum bit is modulated at a second timing, and the first timing and the second timing are controlled to be different from each other, thereby independently controlling the states of the first quantum bit and the second quantum bit.

[0013] It is possible to perform parallel operations on multiple quantum bits.

[0014] 1 is a block diagram of a quantum computer system that performs quantum bit gate operations using a dynamic resonant frequency change method using a local magnetic field; an enlarged cross-sectional view of a portion of a quantum dot array; an enlarged perspective view of a portion of a quantum dot array; a conceptual diagram showing an example of serial operation; a conceptual diagram showing an example of parallel operation; a conceptual diagram showing a method of changing the resonant frequency of a quantum bit using the Stark shift; a conceptual diagram showing a method of changing the resonant frequency of a quantum bit using a local magnetic field; an explanatory diagram showing a phase control method in a dynamic resonant frequency change method using a local magnetic field; an explanatory diagram showing an operation method when considering the resonant frequency variation of a quantum bit; an explanatory diagram showing an example of a phase management method; a cross-sectional view of a portion of a quantum dot array that is irradiated with microwaves; an explanatory diagram of a method of suppressing heat generation caused by large g-factor variations; an explanatory diagram of another method of suppressing heat generation caused by large g-factor variations; a schematic diagram showing how a quantum bit is moved by shuttling; a table showing various methods of local magnetic field modulation using a magnetic field generated by applying a current; a plan view showing a first example of a quantum bit selection method; a plan view showing a second example of a quantum bit selection method. 1 is a plan view showing a third example of a quantum bit selection method; a plan view showing a fourth example of a quantum bit selection method; a graph showing applied current values ​​for generating a magnetic field used in phase-modulation CCD parallel operation; and a graph showing applied current values ​​for generating a magnetic field used in phase-modulation CCD parallel operation when there is element variation.

[0015] The following describes the embodiments in detail with reference to the drawings. However, the present invention should not be construed as being limited to the description of the embodiments shown below. Those skilled in the art will readily understand that the specific configurations of the present invention can be modified within the scope of the concept and purpose of the present invention.

[0016] In the configuration of the invention described below, the same parts or parts with similar functions are denoted by the same reference numerals in different drawings, and redundant explanations may be omitted. When there are multiple elements with the same or similar functions, they may be described with different subscripts. However, in some cases, the subscripts may be omitted.

[0017] The terms "first," "second," "third," and the like used in this specification are used to identify components and do not necessarily limit the number, order, or content thereof. Furthermore, numbers used to identify components are used in different contexts, and numbers used in one context do not necessarily indicate the same configuration in another context. Furthermore, a component identified by a certain number does not preclude consideration of the function of a component identified by another number.

[0018] In order to facilitate understanding of the invention, the position, size, shape, range, etc. of each component shown in the drawings etc. may not represent the actual position, size, shape, range, etc. Therefore, the present invention is not necessarily limited to the position, size, shape, range, etc. disclosed in the drawings etc.

[0019] An embodiment relates to a method for performing parallel computation in a quantum bit array. One embodiment is a quantum bit array including: a semiconductor layer; an insulating layer disposed on the semiconductor layer; a plurality of first electrodes disposed on the insulating layer, the first electrodes configured to capture electrons or holes of a predetermined spin state in the semiconductor layer by applying a voltage thereto; a plurality of second electrodes disposed on the insulating layer, the second electrodes configured to pass a current therethrough to form a magnetic field acting on the electrons or holes; a current application unit configured to apply a current to at least one of the second electrodes to form the magnetic field acting on the electrons or holes; a microwave generation source configured to irradiate the electrons or holes with microwaves of a fixed frequency; and an applied current control unit configured to control the spin state of the electrons or holes by controlling the timing and duration of the current applied to the second electrodes, and to apply different currents to at least two of the second electrodes.

[0020] In another example, the applied current control unit selects the second electrode to which the current is applied based on the resonant frequency of the spin of the electron or hole. Further, the microwave generation source irradiates the electrons or holes with at least two fixed frequencies, and the applied current control unit controls the spin state using the microwave with the closer fixed frequency based on the resonant frequency of the spin of the electron or hole.

[0021] In the embodiment described in detail below, for example, a microwave is irradiated onto the entire quantum dot array, and a local magnetic field is applied to a selected quantum bit, thereby matching the microwave frequency with the resonant frequency of the quantum bit and performing a gate operation on the selected quantum bit. At this time, a local magnetic field is induced in the selected quantum bit by applying a current to a plurality of electrodes arranged on the quantum dot array.

[0022] By modulating at least one of the strength, frequency, and phase of the local magnetic field, the phase difference between the microwave and the quantum bit can be controlled. Controlling the phase difference controls the direction of the spin rotation axis, and the rotation angle can be controlled by the duration during which the microwave and the resonance frequency match. By selecting multiple arbitrary quantum bits and independently modulating the local magnetic field for each quantum bit, it becomes possible to perform different operations on multiple quantum bits in parallel.

[0023] According to this embodiment, parallel calculation of multiple quantum bits can be performed with high precision in a quantum bit array having gate-defined quantum dots.

[0024] [Quantum Computer System] First, we will explain how to realize a single quantum bit gate using quantum bits that use electron spins in semiconductor elements. Each quantum bit to which a static magnetic field is applied has a resonant frequency that depends on the element and the amplitude of the static magnetic field. By irradiating it with microwaves having the same frequency as the resonant frequency, the state of the quantum bit can be changed through a process called Rabi oscillation.

[0025] A real quantum computer has a large number of qubits and requires selective operations to be performed on each qubit. To achieve selective operations, it is necessary to prevent overlap of the resonant frequencies of the controlled qubits and the non-controlled qubits.

[0026] In the conventional technology, a control method is used in which a unique resonant frequency is set (assigned) to each quantum bit (hereinafter referred to as a fixed resonant frequency method). However, frequency is a finite resource, and frequency intervals of approximately the Rabi frequency are required to avoid crosstalk. Therefore, when there are a large number of quantum bits to handle, it is difficult to set different resonant frequencies for all quantum bits.

[0027] In fact, one million qubits are required to solve practical problems, and it is difficult to control all qubits using a fixed resonant frequency method. Therefore, we consider a method to frequency-separate the selected qubit by changing the resonant frequency of the controlled qubit (selected qubit) relative to the uncontrolled qubit (unselected qubit).

[0028] Each quantum bit, using the degree of freedom of electron spin due to a semiconductor element to which a static magnetic field is applied in the Z direction, can be considered to precess around the Z axis at its respective resonant frequency. The frequency of this precession is roughly proportional to the magnitude of the static magnetic field (magnetic flux density) applied. Therefore, by locally changing the magnitude of the static magnetic field applied to the selected quantum bit, it is possible to give the non-selected quantum bits a different resonant frequency, and by irradiating microwaves that match this resonant frequency, it is possible to perform single-qubit gate operation on only the selected quantum bit (hereinafter referred to as a dynamic resonant frequency change method using a local magnetic field, and the method described in Patent Document 1).

[0029] As another method of dynamic resonant frequency alteration, a Stark shift effect can be achieved by locally changing the electric field applied to a selected quantum bit, thereby causing a different resonant frequency to be imparted to unselected quantum bits. (Hereinafter, this method will be referred to as the dynamic resonant frequency alteration method using Stark shift, as described in Patent Document 2.) Figure 1A shows a schematic diagram of a quantum computer system 200 for performing a single quantum bit gate using the dynamic resonant frequency alteration method using a local magnetic field in this embodiment. First, a control unit 201 issues a command to a microwave generator 202, and microwaves 212 are irradiated via a microwave irradiation antenna unit 211 to multiple quantum bits 203 in a quantum dot array 210 (typically, the entire quantum dot array 210).

[0030] For example, when a command to perform a single quantum bit gate is sent to control unit 201 from host 220, which is configured as a general server, control unit 201 sends the quantum bit address for which the gate operation is to be performed (an address specifying which quantum bit in the quantum bit array is to be gated) and parameter information for various gate operations to quantum bit array controller 205. Quantum bit array controller 205 issues a command to current application unit 206 based on this information.

[0031] Current application unit 206 applies current 208 to wiring 207a corresponding to the specified quantum bit address at a specified timing and for a specified duration, generating local magnetic field 209 (a magnetic field generated locally around quantum bit 203a). Here, the current flowing through wiring 207a is sent outside the chip through wiring not shown in the figure, suppressing heat generation within the chip in order to maintain an extremely low temperature environment near the quantum bit.

[0032] This allows a single quantum bit gate to be selectively applied to the selected quantum bit 203 a using the principle of dynamic resonance frequency change using a local magnetic field. On the other hand, when selecting another quantum bit 203 b, the selection can be performed by passing a current through wiring 207 b.

[0033] It is desirable that the directions of the magnetic field vectors at the quantum bit position of the local magnetic field 209 and the microwave 212 are orthogonal to each other, thereby enabling one-qubit gate operation by Rabi oscillation.

[0034] When reading out the state of the quantum bit, the quantum state of quantum bit 203 is measured using readout unit 204. Note that although quantum dot array 210 in this figure shows only two quantum bits and two wires, in reality it has multiple of these and configurations necessary for operations such as electron capture, initialization, readout, and two-qubit gate.

[0035] 1B shows an enlarged cross-sectional view of a portion of the quantum dot array 210. The quantum dot array 210 is an array of quantum dots QD formed by a potential shape P formed by a voltage applied by a gate electrode G in a semiconductor substrate SUB such as silicon. Quantum bits QB are stored in these quantum dots. The wiring 207a and 207b used for quantum bit addressing can be formed by sharing the gate electrode G for forming the potential shape P. Alternatively, a separate gate electrode may be provided.

[0036] 1C is a perspective view schematically illustrating an example of the structure of the quantum dot array 210. In this example, the wiring layer has two layers, but the number of layers is not limited to two, and the number of layers may be one, or three or more.

[0037] A silicon channel C is formed in the X and Y directions on a semiconductor substrate SUB, and quantum dots QD and potential barriers PB are alternately arranged two-dimensionally in the silicon channel C.

[0038] As the first layer of gate wiring in the MOS structure, a plurality of quantum dot control gate lines (XQ) 2022 and interaction control gate lines (XJ) 2021 are formed, arranged in the X direction, and as the second layer of gate wiring, a plurality of quantum dot control gate lines (YQ) 2032 and interaction control gate lines (YJ) 2031 are formed, arranged in the Y direction. The quantum dot control gate lines (XQ) 2022 and the quantum dot control gate lines (YQ) 2032 control the voltage of the quantum dot QD, and electrons or holes of a predetermined spin state are captured as quantum bits in the quantum dot QD formed in the silicon channel C.

[0039] The interaction control gate line (XJ) 2021 and the interaction control gate line (YJ) 2031 control the voltage of the potential barrier PB. Furthermore, the interaction control gate line (XJ) 2021 and the interaction control gate line (YJ) 2031 can form a magnetic field that acts on the quantum bit by passing a current through them. The current application unit 206 passes a current for forming a magnetic field through any of the interaction control gate lines (XJ) 2021 and the interaction control gate line (YJ) 2031.

[0040] Furthermore, the microwave irradiation antenna unit 211 irradiates the quantum bit formed by the electron or hole with microwaves of a fixed frequency. The spin state of the electron or hole is controlled by controlling the timing and duration of the current applied by the current application unit 206. The control unit 201 realizes parallel operation by instructing the current application unit 206 to apply different currents to at least any two of the interaction control gate line (XJ) 2021 and the interaction control gate line (YJ) 2031.

[0041] To make the diagram easier to understand, this figure shows the distance between the first gate wiring and the silicon channel C expanded in the Z direction. Although not shown, an insulating layer is disposed between the first gate wiring and the semiconductor substrate SUB where the silicon channel C is located. By adopting this array structure, large-scale integration of quantum dots is achieved while suppressing an increase in the total number of wirings. [Concept of Serial and Parallel Operation] Figures 2A and 2B show schematic diagrams illustrating the effectiveness of parallel operation, one of the features of this embodiment. The vertical axis represents frequency f, and the horizontal axis represents time t. The wavy lines also represent microwave amplitude, and do not represent frequency modulation. Figure 2A shows an example of serial operation, for example, when the Rx gate and Ry gate, which are single-qubit gates, are operated on different qubits. On the other hand, Figure 2B shows an example of parallel operation recommended in this embodiment.

[0042] Figure 2A: In serial computation, a microwave pulse MP is applied to the entire quantum dot array to perform computation. The Rx gate and Ry gate are switched by adjusting the phase of the microwave. In Figure 2A, the vertical axis represents frequency, and the solid and dotted lines represent the resonant frequencies of the two quantum bits, respectively (similar to Figure 2B). The resonant frequency can be changed by changing the magnitude of the static magnetic field applied to the quantum bits.

[0043] The quantum bit's resonant frequency is changed from f0 to f1, and a microwave pulse MP with a center frequency of f1 is irradiated. This is performed sequentially. The Ry gate shifts the initial phase of the microwave pulse MP by 90 degrees relative to the Rx gate. The irradiation time MPT of the microwave pulse MP corresponds to the rotation angle of the gate.

[0044] In this method, the type of gate operation is determined by the phase and duration of the microwave pulse MP irradiated onto the entire quantum bit array, so different gate operations cannot be performed simultaneously on two different quantum bits.

[0045] Figure 2B: In parallel operation, the operation is performed by applying a current pulse. The Rx gate and Ry gate are switched by adjusting the timing of the current pulse, which changes the quantum bit's resonance frequency from f0 to f1. The duration of the current pulse, CPT, corresponds to the gate rotation angle.

[0046] The microwave MD with a frequency of f1 is irradiated almost continuously, and the quantum bit is set to have a resonant frequency of f0. The resonant frequency of the quantum bit to be manipulated is changed from f0 to f1 by the local magnetic field generated by the applied current pulse.

[0047] where f0 and f1 are different frequencies, approximately the Rabi frequency f ｒａｂｉ There is a frequency difference of more than twice that of |f1-f0|>2f ｒａｂｉ This reduces the effect of crosstalk when no calculation is being performed.

[0048] In this method, the gate operation is determined by the timing and duration CPT of the applied current pulse (i.e., the applied local magnetic field), allowing different gate operations to be performed simultaneously on two different quantum bits. While this example uses two quantum bits, parallel operations are also possible for more quantum bits. By controlling the first application duration of the first magnetic field and the second application duration of the second magnetic field to overlap at least partially, parallel operation of the first quantum bit and the second quantum bit becomes possible. For these reasons, the parallel operation method shown in FIG. 2B is recommended in this embodiment. [Operation method using current application, issues with Stark shift] As a method for selectively changing the resonant frequency of a quantum bit, FIG. 3A shows the Stark shift, and FIG. 3B shows a method for changing the resonant frequency of a quantum bit using a local magnetic field.

[0049] 3A: In Stark shifting, the voltage applied to the gate electrode G located near the quantum bit QB is changed to change the potential profile P of the quantum dot that captures the quantum bit QB, thereby induced changes in the resonant frequency. This resonant frequency change is generally nonlinear with respect to the applied electric field, and there is a risk that the change in the potential profile may cause the quantum bit to escape capture, as well as adverse effects such as resonant frequency shifts and capture escapes on surrounding quantum bits. Considering these effects, this method is disadvantageous for large-scale quantum bit arrays.

[0050] Figure 3B: The method using the local magnetic field MF induced by the application of current has the advantage of high controllability because the resonant frequency shift of the quantum bit QB is linear with the applied current value and there is little disturbance in the potential profile, making it advantageous for large quantum bit arrays.

[0051] Therefore, in this embodiment, it is more desirable to change the resonant frequency from f0 to f1 by using an applied current pulse to induce a local magnetic field MF, as shown in FIG. 2B. By adopting the technique shown in FIG. 3B, it is possible to further improve the accuracy of parallel computation using a quantum bit array. [Method for Controlling Phase and Rotation Angle] When performing gate operations on a quantum bit by matching the microwave frequency with the quantum bit's resonant frequency, the direction of the rotation axis is controlled by the phase difference between the microwave and the quantum bit, and the rotation angle is controlled by the duration during which the microwave and the resonant frequency match. The phase difference between the quantum bit's resonant frequency f1 after the change and the microwave frequency f1 is the same as the phase difference immediately before the change from f0 to f1. Therefore, the phase difference between the quantum bit's resonant frequency f1 after the change and the microwave frequency f1 can be adjusted by changing the timing of the change from f0 to f1.

[0052] Assuming that the static magnetic field generated by the current is applied with an ideal rectangular pulse and that the phase remains fixed at the moment of application and only the resonance frequency changes, as described above, the phase difference just before the frequency change (f0) can be considered to be equal to the phase difference after the frequency change (f1). Also, if the static magnetic field is not an ideal rectangular pulse, the current and rectangular pulse can be measured in advance and the current value can be corrected.

[0053] Figure 4A shows a phase control method in a dynamic resonant frequency change method using a local magnetic field. In a simple example, microwaves are continuously irradiated at a fixed frequency f1. There is a frequency difference Δf = f1 - f0 between the microwave frequency f1 and the quantum bit's resonant frequency f0, and the quantum bit's phase relative to the microwave is expressed as φ(t) = 2πΔft. In other words, the phase difference changes every moment with time t, with a period of 1 / Δf. Therefore, to set a desired phase difference, all one needs to do is wait until φ(t) reaches that phase.

[0054] Since one cycle occurs at t = 1 / Δf, the timing when the desired phase (any of 0 to 2π) is reached always occurs within a waiting time of 1 / Δf or less. Therefore, by adjusting the timing of current application and setting the desired waiting time before applying the current pulse, it becomes possible to control the microwave phase for the quantum bit, and switch the desired gates for Rx and Ry.

[0055] Furthermore, the timing adjustment accuracy is determined by the frequency of Δf (approximately f ｒａｂｉ Since it is sufficient to perform phase adjustment with sufficient accuracy for the microwave frequency f1 (typically about 10 to 20 GHz), this has the advantage of being much easier than adjusting the phase with accuracy for the microwave frequency f2 (typically about 10 to 20 GHz).

[0056] Furthermore, the rotation angle of the gate operation is determined by the duration of the applied current pulse. Furthermore, when a microwave pulse is applied, the resonant frequency of the quantum bit may shift due to the effects of heat generated by microwave loss before and after application. However, when operating using an applied current pulse, the microwave is irradiated almost continuously, which has the advantage of reducing such effects. [G-Factor Variation Correction] Quantum dot arrays created using semiconductor manufacturing processes have the problem of element variation. The embodiment described below aims to perform parallel calculations of multiple quantum bits with high precision, taking into account the variation in the resonant frequency of the quantum bits in a quantum bit array having gate-defined quantum dots (quantum dot structures are electrically formed by applying a voltage to the gate).

[0057] 4B shows an operation method when the variation in the resonant frequency of the quantum bits is taken into consideration. In FIG. 4B, the vertical axis represents frequency, and the dotted line QB1 and the solid line QB2 represent the resonant frequencies of two quantum bits, respectively. When the quantum bit frequency variation width is Δf variance And the microwave frequency width is Δf mw is shown.

[0058] In a semiconductor quantum dot structure, for example, due to variations in the semiconductor manufacturing process, the g-factor of the electron spin (a factor that represents the relationship between the magnetic moment of an electron and its angular momentum) may vary among quantum dots. variance As shown above, the frequency of the quantum bit varies.

[0059] By obtaining the resonant frequency of each quantum dot in advance and adjusting the amount of current applied to each quantum dot, this variation can be corrected and the resonant frequency can be matched to the microwave frequency. To measure the resonant frequency of a quantum dot, it is possible to measure the electron spin resonance (ESR) of the quantum dot by sweeping the frequency, as is well known.

[0060] Since the amount of change in the resonant frequency is approximately proportional to the amount of applied current, this adjustment is relatively easy. mw Frequency width Δf mw is the Rabi frequency f rabi or more (Δf mw >f rabi ) The average value of the quantum bit frequency f average and the variation width Δf variance From f mw -Δf mw / 2>Δf variance / 2+f average The relationship between the two is to be satisfied.

[0061] As a result, even if the resonant frequency of the quantum bit varies, as shown in FIG. 4B, it can be adjusted to the microwave frequency as shown by the dotted line QB1 and the solid line QB2, and the variation width Δf variance It is possible to perform quantum gate operations on the quantum bits within the

[0062] Also, the microwave frequency f mw By setting the frequency band with a small number of quantum dots in the quantum dot resonance frequency distribution, quantum dots can be used efficiently. [Phase Management Method] If there is variation in the g-factor in the quantum dot array, the resonance frequency of the quantum bit stored in each quantum dot will vary because it is proportional to the g-factor. Therefore, phase management of each quantum bit becomes important. The g-factor of each quantum dot is obtained in advance and stored in memory in the host 220, for example, and this g-factor information is used to manage the phase of the quantum bit.

[0063] As is well known, the g-factor of a quantum dot can be measured by measuring the spin resonance of the quantum dot while sweeping the magnetic field and frequency.

[0064] An example of a phase management method is shown in Figure 5A, which shows three quantum bits q1, q2, and q3, with time t (quantum operation sequence) on the horizontal axis.

[0065] If we denote each quantum bit as q1, q2, and q3, then depending on the g-factor of the quantum dot in question, a different resonant frequency f q1 , f q2 , f q3 Therefore, the time t and the resonant frequency f q1 , f q2 , f q3 Using this, the phase of each quantum bit is φ q1 =2πf q1 t, φ q2 =2πf q2 t, φ q3 =2πf q3 t. This can be considered as an Rz gate with appropriate phase rotation (t i=0 reference).

[0066] Furthermore, when quantum operations or shuttling Sh are performed, the phase changes according to those operations (t i=1 , t i=2 , t i=3(See references below.) These can be calculated in advance using information on the g-factors obtained in advance, and therefore the host 220 determines the current application pulse timing for the one-qubit gate, taking into consideration these phase management steps in compiling the quantum circuit (the stage of generating a quantum operation sequence from the quantum circuit).

[0067] The above control is performed by setting the quantum operation sequence to t for all quantum bits as shown in FIG. 5A. i It is convenient to divide the quantum circuit into synchronized sections shown in Fig. 1 and manage them. When compiling a quantum circuit, it is sufficient to calculate the input-output relationship of the phase for each section.

[0068] It is also possible to achieve phase adjustment (Rz gate) using an applied current. That is, by shifting the resonant frequency of the desired quantum bit for a certain period of time using an applied current, the phase changes, and this can be used to realize an Rz gate.

[0069] Furthermore, by adjusting the direction of the applied current to shift the quantum bit's resonant frequency in the opposite direction to the microwave, the frequency difference with the microwave frequency can be increased and the desired phase can be adjusted in a short time. This reduces the time required for phase adjustment and enables high-speed quantum computing. [Rabi frequency variation correction] In addition to correcting the g-factor variation described above, adjusting the applied current can also correct, for example, unevenness in the Rabi frequency distribution.

[0070] FIG. 5B shows a partial cross-sectional view of the quantum dot array. Microwave 212 is irradiated over the entire quantum dot array, but uneven irradiation power may occur. For example, quantum bit QB2 is closer to microwave irradiation antenna unit 211 than quantum bit QB1, resulting in a stronger microwave intensity. In such cases, variations in the Rabi frequency of each quantum dot occur. However, this can be corrected by acquiring the Rabi frequency corresponding to each quantum dot in advance and adjusting the duration of the applied current during calculation. The Rabi frequency can be determined from the measurement results by measuring Rabi oscillations, and measurement techniques are known.

[0071] Calibration, such as the one described above, to obtain the g-factor (resonant frequency) and Rabi frequency variations of each quantum dot in advance must be performed before quantum computing. Specifically, the g-factor and Rabi frequency of each quantum dot can be obtained by changing parameters such as magnetic field strength and obtaining RAP (Rapid Adiabatic Passage) and Rabi oscillations. [Addressing g-factor variations and heat generation] If the g-factor variations are large, a relatively large current must be applied when selecting a quantum bit with a resonant frequency far from the microwave frequency, and the resulting heat generation poses an issue.

[0072] A method for reducing this effect is shown in Figure 6A. It is shown in the same notation as Figure 4B. The width of the quantum bit frequency variation due to the g-factor variation is Δf variance When this is the case, the amount of applied current can be reduced by imposing a restriction that the quantum bit QB in the quantum dot having a resonant frequency far from the microwave frequency is not used for calculation.

[0073] By acquiring the resonance frequency of each quantum dot in advance, such constraints can be used during compilation. Specifically, as shown in the figure, a prohibited area 600 of the quantum bit QB is defined and calculations are performed.

[0074] Figure 6B shows another method for reducing the amount of current. It is shown using the same notation as in Figure 4B. The amount of current can be reduced by generating microwaves MD at two frequencies and using the microwave with the closest resonant frequency. In addition, by making the two microwaves MD1 and MD2 intermittent continuous waves, heat generation due to microwave loss can be reduced.

[0075] Furthermore, the microwave irradiation time can be reduced by turning it off during operations other than the quantum bit operation, such as initialization, readout, and shuttling. mw_min is the sum of the phase adjustment time of the quantum bit whose resonance frequency is farthest from the microwave frequency and the time to apply the π gate, that is, t mw_min = 1 / (2f rabi )+2 / (Δf variance), any quantum operation can be performed. Two or more microwave frequencies may also be used. [Two-qubit operation] The above parallel operations can also be used in combination with two-qubit operations. For example, the SWAP gate and CZ gate are known for two-qubit operations in silicon quantum dots, and both of these utilize the exchange interaction caused by the overlap of wave functions by lowering the barrier gate between two adjacent quantum dots. Such two-qubit operations can be performed independently of or in combination with the above parallel operations. This makes it possible to realize one- and two-qubit gates, enabling universal quantum computing.

[0076] [Shuttling] In a quantum dot array, the movement of electrons while maintaining their spin state (quantum information) is called shuttling. In this example, a quantum bit selection method using shuttling is used to reduce the number of current application wirings.

[0077] Figure 7 shows a portion of a quantum dot array. There are two quantum dots (quantum dot QD1 and quantum dot QD2). The electron that becomes the quantum bit QB can be shuttled between the two quantum dots by controlling the gate voltage. A current is applied to the gate electrode directly above quantum dot QD1. This applies a static magnetic field MF2 due to the local current to quantum dot QD1 in addition to the static magnetic field MF1 applied externally in the direction of the arrow, shifting the resonant frequency relative to quantum dot QD2.

[0078] Microwaves are irradiated almost continuously at the resonant frequency of quantum dot QD1. Single quantum bit gate operation is performed by shuttling between quantum dot QD1 and quantum dot QD2, rather than by changing the applied current as in Example 1. When there is an electron in quantum dot QD2, it is out of resonance and the electron is not manipulated. However, by transferring an electron to quantum dot QD1 by shuttling, it becomes resonant with the microwave, and spin manipulation is performed.

[0079] By controlling the timing of shuttling from quantum dot QD2 to quantum dot QD1 and the time spent in quantum dot QD1, arbitrary single quantum bit gate operations can be performed. This corresponds to replacing the control of the timing and duration of current application in Example 1 with control of the timing of shuttling and the time spent in quantum dot QD1. This method can reduce the current application wiring and the control precision of current application. It can also reduce the impact of reduced phase precision due to switching of applied current.

[0080] Here, the local magnetic field modulation method for creating a frequency difference between quantum dots may use, for example, a minute magnetic body (micromagnet) or a minute superconductor structure other than current application. These methods can reduce the influence of heat generation without power consumption due to current application. Furthermore, in superconductors, the ON / OFF of the local magnetic field modulation can be controlled by destroying the superconducting state by current application or other methods.

[0081] Furthermore, shuttling does not necessarily have to be performed between two quantum dots. By using shuttling between quantum dots that are one or more apart, the effects of crosstalk (unintended magnetic field modulation), which occurs when the magnetic fields of quantum dots surrounding the desired quantum dot are also modulated by the local magnetic field modulation method described above, can be reduced, allowing for highly accurate quantum manipulation.

[0082] This example illustrates various local magnetic field modulation methods, including those described in Examples 1 and 2. [Local Magnetic Field Modulation Method by Current Application] Figure 8 illustrates various local magnetic field modulation methods using a magnetic field M generated by applying a current to a gate electrode G. The objective here is to locally modulate a magnetic field parallel to the direction of an externally applied static magnetic field, thereby selecting quantum dots using resonance with microwaves. Here, the magnetic field parallel to the direction of the externally applied static magnetic field Bext is illustrated by an arrow. This is because, although the magnetic field direction vector is actually modulated, only the static magnetic field perpendicular to the microwave polarization is important in spin manipulation using electron spin resonance (ESR). A magnetic field parallel to the direction of the externally applied static magnetic field Bext and a magnetic field perpendicular to the substrate are referred to as a substrate-parallel magnetic field and a substrate-perpendicular magnetic field, respectively. [Local Magnetic Field Type vs. Gradient Magnetic Field Type] There are two types of local magnetic field modulation methods: a local magnetic field type and a gradient magnetic field type. The local magnetic field type modulates only the magnetic field at the selected quantum dot position, leaving the magnetic fields of other unselected quantum dots unmodulated. Quantum bit selection is achieved by matching the microwave frequency to the resonant frequency of the selected quantum dot. On the other hand, the gradient magnetic field type generates a magnetic field gradient in the quantum dot array, and selection is achieved by matching the microwave frequency to the frequency of the desired quantum dot. [Single-wire method vs. dual-wire method] Furthermore, there are two methods for modulating local magnetic fields by applying current: the single-wire method and the dual-wire method. The differences between these methods are also described in Patent Document 1. The single-wire method applies current to a single gate electrode to locally modulate the magnetic field directly below or around it. On the other hand, the dual-wire method applies current to two gate electrodes in parallel or opposing directions to locally modulate the magnetic field directly below or around them. [Static Magnetic Field Direction] In addition to the four (2 × 2) combinations of the above methods, there are two other types of relationship between the externally applied static magnetic field direction (Bext) and the substrate direction: a magnetic field parallel to the substrate and a magnetic field perpendicular to the substrate. The various combinations described above are shown in Figure 8. In addition to these local magnetic field modulation methods using current application, effective quantum bit selection can be achieved by designing the device shape taking into account other factors such as device shape and quantum bit controllability.[Two-dimensional array selection method] An example of a quantum bit selection method in a two-dimensional quantum bit array using the various local magnetic field modulation methods described above is shown below. Each figure shows the relationship between the direction of the externally applied static magnetic field (Bext) and the substrate surface.

[0083] In this example, we use a two-wire method with a magnetic field perpendicular to the substrate, which can reduce crosstalk during quantum bit selection. Furthermore, to increase the flexibility of quantum operations such as two-qubit gates using shuttling, quantum bits are sparsely stored in each quantum dot.

[0084] Figure 9A shows a method described in Patent Document 1, referred to here as the crossbar method. In this crossbar method, selection is performed in both the horizontal (X) and vertical (Y) directions using a local magnetic field generated by two current lines, and quantum bits A and B located at the intersection of the two vertical and horizontal lines are selected. Microwaves matched to the resonant frequency of the quantum dot at the intersection are applied almost continuously, and quantum gate operation is performed by controlling the duration and timing of the applied currents C1 and C2 in either or both the vertical and horizontal directions. Selected quantum bits A and B can perform different operations in parallel by changing the timing and duration of the applied current C2 in the vertical direction. Furthermore, the effects of crosstalk can be reduced by using shuttling to move unselected quantum bits to quantum dots farther from the current-applying gate electrode.

[0085] In Figure 9B, horizontal quantum bit selection is performed using a local magnetic field generated by two-wire currents, and vertical quantum bit selection is performed using a gradient magnetic field generated by two-wire currents. Microwaves matched to the resonant frequency of the quantum dots in the selected row are applied almost continuously, and quantum gate operation is performed by controlling the duration and timing of either or both of the vertical and horizontal applied currents C1 and C2. Selected quantum bits A and B can perform different operations in parallel by changing the timing and duration of the vertical applied current C2. This method can also be achieved by using micromagnets or superconducting wiring instead of current as the gradient magnetic field used for vertical selection, thereby reducing the impact of heat generation due to current application.

[0086] In Figure 9C, horizontal qubit selection is performed using a local magnetic field generated by two-wire currents, and vertical qubit selection is performed by horizontal shuttling. The microwave frequency is matched to the quantum dots in the selected column. Since all qubits in the quantum dots in the selected column are selected, horizontal shuttling moves unselected qubits out of the selected column. Selected qubits A and B can perform different operations in parallel by changing the timing and duration of the vertical current C2 applied. Compared to the methods in Figures 9A and 9B, the amount of applied current can be reduced, mitigating the effects of heat generation.

[0087] Figure 9D shows a similar method to Figure 9C, but with two vertically aligned currents applied alternately to almost all columns. This selects each column. The quantum bit to be operated on is moved to the selected column by shuttling, and parallel computation is performed by adjusting each current. This method creates a periodic magnetic field distribution that reverses direction horizontally, increasing the frequency difference between the unselected and selected columns and reducing the effects of crosstalk.

[0088] As described above, by combining the local magnetic field modulation method shown in FIG. 8 with shuttling, it is possible to select / deselect quantum bits and perform parallel operations even in a two-dimensional quantum bit array.

[0089] Using a two-dimensional quantum bit array may enable efficient quantum error correction. As an example, the method described in the non-patent document Jones, Cody, et al. "Logical qubit in a linear array of semiconductor quantum dots," Physical Review X 8.2 (2018): 021058, can be used. Furthermore, as another example, by entangling a vertical quantum bit string and using it as one logical quantum bit encoded by, for example, a Steen code, a transversal gate can be implemented in which all vertical quantum bits perform the same one- or two-qubit gate operations in parallel. Such a vertical transversal gate is compatible with the parallel computing method of this embodiment and can efficiently perform error-tolerant quantum computation.

[0090] In this example, we demonstrate that a method called concatenated continuous driving (CCD) can mitigate the effects of quantum computing errors called dephasing and decoherence (coherence protection), enabling highly accurate parallel computation. CCD is described, for example, in non-patent literature AJ Ramsay et al., "Coherence protection of spin qubits in hexagonal boron nitride," Nat. Commun. 14, 461 (2023) (https: / / doi.org / 10.1038 / s41467-023-36196-7 (accessed May 10, 2024)).

[0091] Although this non-patent document only describes one quantum bit, this is used in the present embodiment to perform parallel calculations. As described in the non-patent document, CCDs can be classified into amplitude modulation and phase (frequency) modulation methods, but in this embodiment, phase (frequency) modulation is used. In order to apply this method to parallel calculations, the microwave frequency is matched to the quantum bit frequency, and phase (frequency) modulation is performed by utilizing quantum bit resonance frequency modulation using local magnetic field modulation by applied current. [CCD Basics] In a phase-modulated CCD, the Hamiltonian due to microwaves is expressed as Ωcos[ωt+φ-2ε m Ω -1 sin(Ωt-θ m This is expressed as Ψ(t) = ωt + φ - 2ε m Ω -1 sin(Ωt-θ m ) and rewrite it as Ωcos[Ψ(t)]. Here, ω is the angular frequency corresponding to the microwave carrier frequency, Ω is the angular frequency corresponding to the Rabi frequency, t is time, φ is the initial phase of the microwave, ε m and θ m is a modulation parameter.

[0092] This can be rewritten as the time change in frequency f(t), which is the differential of the phase term Ψ(t), as f(t) = ω-2ε m cos(Ωt-θ m) is the frequency modulation of the microwave.

[0093] In the CCD, the phase or frequency is modulated to a sine wave or cosine wave while the Rabi oscillation is always in progress, and the modulation parameter θ m and the initial phase φ of the microwave are changed to perform quantum gate operations. The state of the quantum bit is defined in the second rotating frame, and quantum computation is performed by reading out the quantum bit state at an appropriate timing when the second rotating frame and the experimental system frame coincide. [Parallel computation using CCD] Example 4 is similar to Examples 1 to 3 in that microwaves are continuously irradiated and parallel computation is possible by applying a local magnetic field, but the local magnetic field is modulated as described below.

[0094] Figure 10A shows phase-modulated CCD parallel operation when there is no g-factor variation. The vertical axis represents the applied current value for generating the local magnetic field, and the horizontal axis represents time. In this example, the applied current (local magnetic field) is a sine wave, and the phase is modulated at a predetermined timing, as explained below. To modulate the phase, the frequency can be temporarily changed.

[0095] To apply CCDs to parallel computing, we focus on the fact that Ψ(t) is the relative phase difference between the microwave and the quantum bit. In other words, we can realize a Hamiltonian similar to the above by using local magnetic field modulation instead of microwaves.

[0096] To achieve this, first, a continuous wave of a single frequency is applied so that the Hamiltonian of the microwave becomes a single frequency Ωcos[ωt]. Then, by modulating the local magnetic field by applying a current, the resonance frequency of the quantum bit is adjusted to −2ε, which is the modulation part of f(t). m cos(Ωt-θ m By appropriately setting the timing of the local magnetic field modulation to achieve the desired φ, the phase difference between the quantum bit and the microwave coincides with Ψ(t), realizing a Hamiltonian similar to that of a phase-modulated CCD.

[0097] Since the quantum operation part is contained only in the local magnetic field modulation part, desired quantum operations can be performed in parallel by modulating each quantum bit with different timing and duration. m Quantum gate operation can be performed by controlling the

[0098] Figure 10B shows the parallel operation of a phase-modulated CCD when there is a variation in the g-factor between quantum dots. The variation in the g-factor can be corrected by offsetting the current (DC component). The variation in the Rabi frequency of each quantum dot can also be corrected by controlling the applied current.

[0099] Parallel computing using phase-modulated CCDs not only protects coherence, but also has the advantage of being able to reduce the current value used to select quantum bits and suppress the effects of heat generation, since frequency modulation below the Rabi frequency is sufficient.

[0100] According to the above-described embodiment, a highly accurate and practical quantum computer can be realized, which reduces energy consumption, reduces carbon emissions, prevents global warming, and contributes to the realization of a sustainable society.

[0101] Quantum computer system 200, control unit 201, microwave generation unit 202, quantum bit array controller 205, current application unit 206, wiring 207, quantum dot array 210, microwave irradiation antenna unit 211, host 220, microwave pulse MP, microwave pulse irradiation time MPT, applied current pulse duration CPT, microwave MD, quantum bit QB

Claims

a plurality of electrodes disposed on the insulating layer, the electrodes forming an electromagnetic field acting on the quantum bits; a voltage application unit for applying a voltage to at least one of the electrodes to form the electromagnetic field acting on the quantum bits; a microwave generation source for irradiating the quantum bits with microwaves of a fixed frequency; and a control unit for modulating a first electromagnetic field applied to a first quantum bit at a first timing and modulating a second electromagnetic field applied to a second quantum bit at a second timing during the microwave irradiation, and for independently controlling the spin states of the first quantum bit and the second quantum bit by controlling the first timing and the second timing to be different from each other.

2. The quantum bit control device according to claim 1, wherein the control unit performs parallel operations on the first quantum bit and the second quantum bit by controlling a first application duration for applying the first electromagnetic field and a second application duration for applying the second electromagnetic field to overlap at least partially.

3. The quantum bit control device according to claim 2, wherein the control unit starts applying the first electromagnetic field at the first timing and starts applying the second electromagnetic field at the second timing during irradiation of the microwaves.

4. The quantum bit control device according to claim 3, wherein the control unit controls the first timing and the second timing by controlling the timing of the voltage applied to the electrodes.

5. The quantum bit control device according to claim 1, wherein the control unit applies different voltages to at least two of the plurality of electrodes.

6. The quantum bit control device according to claim 1, wherein the control unit selects the electrode to which a voltage is applied based on a resonance frequency of the spin of the quantum bit.

7. A quantum bit control device as claimed in claim 1, wherein the microwave generation source irradiates the quantum bit with at least two types of microwaves having different fixed frequencies, and the control unit controls the spin state based on a resonance frequency of the spin of the quantum bit using a microwave having the fixed frequency close to the resonance frequency.

8. The quantum bit control device according to claim 3, wherein the control unit controls the first timing and the second timing by moving the position of the quantum bit relative to the electrode.

9. The quantum bit control device according to claim 2, wherein the control unit changes the phase of the first electromagnetic field at the first timing and changes the phase of the second electromagnetic field at the second timing during irradiation of the microwaves.

10. A quantum computer system comprising the quantum bit control device of claim 1.

11. A method for controlling quantum bits constituted by electrons or holes trapped in a semiconductor layer in a quantum dot array comprising a semiconductor layer, an insulating layer disposed on the semiconductor layer, and a plurality of electrodes disposed on the insulating layer, the method comprising: a microwave irradiation step of irradiating microwaves of a predetermined frequency onto at least a portion of the quantum dot array; and an electromagnetic field application step of forming an electromagnetic field acting on at least one of the quantum bits by applying a voltage to the electrodes, wherein in the electromagnetic field application step, during microwave irradiation, a first electromagnetic field applied to a first quantum bit is modulated at a first timing, and a second electromagnetic field applied to a second quantum bit is modulated at a second timing, and the first timing and the second timing are controlled to be different, thereby independently controlling the states of the first quantum bit and the second quantum bit.

12. A quantum bit control method according to claim 11, wherein in the electromagnetic field application step, parallel operations of the first quantum bit and the second quantum bit are performed by controlling the first application duration for applying the first electromagnetic field and the second application duration for applying the second electromagnetic field so that they at least partially overlap.

13. A quantum bit control method according to claim 12, wherein in the electromagnetic field application step, the first timing and the second timing are controlled to be different from each other by controlling the timing of the voltage applied to the electrodes.

14. A quantum bit control method according to claim 12, wherein in the electromagnetic field application step, the first timing and the second timing are controlled to be different from each other by controlling the timing of moving the position of the quantum bit relative to the electrode.

15. A quantum bit control method according to claim 12, wherein in the electromagnetic field application step, the first timing and the second timing are controlled to be different from each other by controlling the timing of modulating the frequency of the voltage applied to the electrodes.

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