Quantum bit array and method for controlling quantum bits

Abstract

The dynamic resonant frequency changing method has problems with phase tracking, and there is a concern that single-qubit gate errors may occur. The solution is a qubit control method that controls the spin state of qubits formed by charges trapped in a semiconductor device and performs a first step for measuring at least one of a current flowing through a first line and a second line or an amount of charges when controlling the spin state of qubits which are formed in the semiconductor device and formed by target charges specified by the first line and the second line; and a second step for controlling at least one of the current flowing through the first line and the second line and the amount of charges on the basis of the result of the measurement in the first step.

Description

[Technical Field]

[0001] The present invention relates to a device for integrating quantum bits and a method for controlling the device. [Background technology]

[0002] Quantum computers are thought to be capable of faster information processing than existing computers. While existing computers handle only the binary values ​​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] Here, we will explain how to realize a single quantum bit gate using a semiconductor element. Each quantum bit to which a static magnetic field is applied in the Z direction has a resonant frequency that depends on the element and the magnitude of the static magnetic field. By irradiating microwaves with the same frequency as the resonant frequency, the quantum bit state can be changed by a phenomenon called Rabi oscillation.

[0005] 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.

[0006] Conventional technology uses a control method in which a unique resonant frequency is set (assigned) to each quantum bit (hereinafter referred to as the "fixed resonant frequency method"). However, because frequency is a finite resource, it is easy to imagine that when there are a large number of quantum bits to handle, it becomes difficult to set different resonant frequencies for all quantum bits. In fact, one million quantum bits are required to solve practical problems, and it is difficult to control all quantum bits using the fixed resonant frequency method. Therefore, a method has been studied in which the resonant frequency of the quantum bit to be controlled (selected quantum bit) is changed relative to the quantum bits not to be controlled (unselected quantum bits) to separate the selected quantum bit in terms of frequency.

[0007] Patent Document 1 discloses a circuit configuration in which the resonant frequency of each of a plurality of quantum bits can be adjusted, which may make it possible to avoid the above-mentioned problems. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Special Publication No. 2018-532255 Summary of the Invention [Problem to be solved by the invention]

[0009] The above patent documents do not mention the issue of phase shift caused by changing the frequency of the selected quantum bit. Each quantum bit, which uses 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 thought of as precessing around the Z axis at its respective resonance 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 quantum bit a different resonance frequency, and by irradiating it with microwaves that match this resonance frequency, it is possible to perform single-qubit gate operation on only the selected quantum bit (hereinafter referred to as the "dynamic resonance frequency change method").

[0010] In quantum computers that use precessing spins as qubits, the phase of the microwaves irradiated relative to the phase of the spin precession determines which axis in the XY plane the rotation axis of a single qubit gate operation will be, so it is necessary to constantly track the precession phases of all qubits during quantum computation.

[0011] However, in the dynamic resonant frequency change method, which changes the resonant frequency of a selected qubit relative to the other unselected qubits, it is difficult to constantly track the phase fluctuations that accompany the frequency fluctuations. This is because constantly tracking the fluctuations in the resonant frequency requires constantly tracking the fluctuations in the static magnetic field (sensed by the qubit) at each qubit position, which is expected to be technically difficult. In addition, directly measuring the qubits in real time to monitor the phase is also difficult due to the nature of the qubit, which is "a change in the quantum state due to measurement."

[0012] As such, the dynamic resonant frequency change method has issues with phase tracking, and there is a concern that errors may occur in the single-qubit gate. [Means for solving the problem]

[0013] A representative example of the invention disclosed in the present application is as follows: A quantum bit array comprising: a semiconductor layer, an insulating layer disposed on the semiconductor layer, a plurality of first electrodes disposed on the insulating layer and configured to trap charges of a predetermined spin state in the semiconductor layer by applying a voltage thereto, a plurality of second electrodes disposed on the insulating layer and configured to form a magnetic field acting on the charges by passing a current therethrough, a current application unit configured to pass a current through at least one of the second electrodes to form a magnetic field acting on the charges when changing the spin state of the charges, a microwave generation source configured to irradiate the charges with microwaves, and a current measurement unit configured to measure the current flowing through the second electrodes.

[0014] Another aspect of the present invention is a method for controlling the spin state of a quantum bit formed by a charge trapped in a semiconductor device, the method comprising the steps of: a first step of measuring at least one of the current and the amount of charge flowing through the first line and the second line; and a second step of controlling at least one of the current and the amount of charge flowing through the first line and the second line based on the measurement results of the first step, when controlling the spin state of a quantum bit formed by a target charge identified by a first line and a second line formed in the semiconductor device. [Effects of the Invention]

[0015] In the dynamic resonant frequency changing method, it is possible to deal with the occurrence of errors in the single quantum bit gate. Problems, configurations and effects other than those described above will become clear from the following description of the embodiments. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 shows two views of a two-dimensional quantum bit array according to an embodiment. [Figure 2] FIG. 1 is a schematic block diagram of a system for performing single-qubit gates. [Figure 3]A graph showing the change over time t in the current value, the resonant frequency fq1 of the selected quantum bit, the resonant frequency fq2 of the unselected quantum bit, the amplitude Brb of the magnetic flux density of the microwave pulse, and the resulting Rabi frequency frb of the selected quantum bit in the dynamic resonant frequency change method. [Figure 4A] FIG. 1 is a graph showing the change over time in the phase of a selected quantum bit and an unselected quantum bit. [Figure 4B] FIG. 10 is a graph showing the frequency change of a selected quantum bit. [Figure 4C] A graph showing the relationship between gate fidelity and phase shift. [Figure 5] A block diagram showing the system configuration for measuring the current or charge flowing through a wiring with high precision. [Figure 6] FIG. 10 is a block diagram showing a configuration for detecting current values ​​or charge amounts of a plurality of wirings using a small number of current or charge readout units. [Figure 7A] 1 is a flow diagram illustrating an example of a calibration method. [Figure 7B] FIG. 10 is a table showing an example of calibration data. [Figure 7C] FIG. 10 is a table showing an example of correction data set based on calibration data. [Figure 8A] A diagram of qubit classification in a qubit array. [Figure 8B] A graph showing the time evolution of the resonant frequency of each of the three types of quantum bits. [Figure 9A] Graph showing the decrease in F due to crosstalk. [Figure 9B] A graph showing the reduction in F due to crosstalk on a logarithmic scale with 1-F on the vertical axis. [Figure 9C] FIG. 1 is a graph showing the change over time in the resonant frequency of a selected quantum bit using the single-irradiation method. [Figure 9D] FIG. 10 is a graph showing the temporal change in the resonant frequency of a selected quantum bit using another single irradiation method. [Figure 9E] Graph showing the change over time in the resonant frequency of a selected quantum bit using the two-time irradiation method. [Figure 10A]FIG. 11 is a graph showing the decrease in F due to crosstalk in the single irradiation method. [Figure 10B] A graph showing the reduction in F due to crosstalk when using the single irradiation method, with 1-F on the vertical axis and displayed on a logarithmic scale. [Figure 10C] Graph showing the decrease in F due to crosstalk caused by the two-time irradiation method. [Figure 10D] A graph showing the reduction in F due to crosstalk when using the two-time irradiation method, with the vertical axis being 1-F and plotted on a logarithmic scale. [Figure 10E] A graph showing the relationship between the angle θ and x in quantum gate operation. [Figure 10F] A graph showing the relationship between the angle θ and x in quantum gate operation. [Figure 10G] A graph showing the relationship between the angle θ and x in quantum gate operation. [Figure 11] Conceptual diagram of the two-time irradiation method. [Figure 12A] Conceptual diagram of the three-gate system. [Figure 12B] FIG. 10 is a quantum circuit diagram for explaining Example 3. [Figure 13A] A plan view showing the contour lines of the static magnetic field distribution generated when currents are passed through Ia, Ib, Ic, and Id in the direction of the arrows. [Figure 13B] FIG. 10 is a schematic diagram of an N-gate system according to a fourth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0017] The embodiments will be described in detail with reference to the drawings. However, the present invention should not be interpreted as being limited to the description of the embodiments shown below. Those skilled in the art will easily understand that the specific configuration can be changed without departing from the concept or spirit of the present invention.

[0018] In the configurations of the embodiments described below, the same parts or parts having similar functions are denoted by the same reference numerals in different drawings, and redundant explanations may be omitted.

[0019] When there are multiple elements having the same or similar functions, they may be described using the same reference numeral with different subscripts. However, when there is no need to distinguish between multiple elements, the subscripts may be omitted.

[0020] The designations "first," "second," "third," etc. 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, this does not prevent a component identified by a certain number from also serving the function of a component identified by another number.

[0021] 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.

[0022] All publications, patents, and patent applications cited herein are incorporated by reference in their entirety.

[0023] As used herein, elements referred to in the singular are intended to include the plural unless the context clearly indicates otherwise.

[0024] In this embodiment, we focus on the phase shift of selected quantum bits when a local magnetic field is applied by current in a quantum bit array chip using electron spins in silicon. In this embodiment, by detecting the current value or charge amount flowing through the wiring used to apply the local magnetic field to the spins, it becomes possible to estimate the phase shift that occurs during frequency shift. As a result, calibration can be performed by utilizing the amount of phase shift, achieving high fidelity in quantum gate operation.

[0025] As a specific circuit, in the frequency variation method, a circuit that accumulates current when a local magnetic field is applied stores and reads out the amount of charge, and the amount of phase shift is estimated from the obtained amount of charge and used for calibration. [Example]

[0026] [Basic configuration] We describe a quantum computer that uses semiconductor elements and electron spin as quantum bits. This quantum computer has multiple two-dimensional quantum bit arrays.

[0027] Figure 1 is a schematic diagram of a two-dimensional quantum bit array. This diagram shows a portion of quantum bit array 100, which has a large number of quantum bits. Quantum bit array 100 is implemented in a chip kept at an extremely low temperature of several mK to several K.

[0028] Quantum bit 101 is the selected quantum bit to be controlled, and the other quantum bits (for example, 102) are unselected quantum bits. Wire 103 and wire 104 are composite structures of wire and gate electrode located between each quantum bit in the Y and X directions, respectively, and are used to generate a local magnetic field by passing a current through them, as described below. They can also be used as gate electrodes to control the strength of the coupling between electron spins, and can also perform two-qubit gates through exchange interaction. Furthermore, wire 105 and wire 106 are composite structures of wire and gate electrode located between each quantum bit in the Y and X directions, respectively, and are used as gate electrodes to trap electrons that become quantum bits.

[0029] Cross-sectional view 120 is a cross-sectional view of a line on which a quantum bit, such as wiring 106, of quantum bit array 100 is located, and has a MOS (Metal Oxide Insulator) structure consisting of insulating layer 121, semiconductor layer 122, and a gate electrode layer formed by wiring 103 and 105 that constitute multiple gate electrodes.

[0030] By adjusting the voltage applied to the gate electrodes of wiring 103 and wiring 105, a potential 124 is generated in semiconductor layer 122, trapping electrons 123 etc. Note that these figures are schematic enlarged views of a portion of quantum bit array 100, and the actual gate dimensions and thickness of each layer do not represent the actual dimensions. [Single qubit gate operation] The up and down states of electron spin are considered to be the 0 and 1 states of the quantum bit. In this case, the superposition of the up and down states of electron spin makes it possible to physically generate a superposition of 0 and 1, enabling quantum computation. Furthermore, the operation of rotating the direction of the electron spin by any angle corresponds to the operation of a single quantum bit gate. This operation is performed by Rabi oscillation, which is caused by irradiating a microwave pulse 111 that matches the resonant frequency of the electron spin.

[0031] In FIG. 1, a substantially uniform static magnetic field is applied across the entire surface in the Z direction. This static magnetic field has a magnetic flux density of several tens of mT to several T, such as that produced by a superconducting magnet. The frequency of the spin precession is substantially proportional to the applied magnetic field (magnetic flux density). Each spin precesses around the Z axis at, for example, several tens of GHz. An oscillating magnetic field is then applied by microwave pulse 111 so that the polarization direction 110 is, for example, the X direction. The polarization direction may be any direction within the XY plane.

[0032] The microwave pulse 111 is irradiated almost uniformly over the entire surface of the quantum bit array 100. Then, by selectively changing the resonant frequency of the spins, only the desired spins are made to resonate with the frequency of the microwave pulse. This allows Rabi oscillations to occur only in the desired spins, enabling single quantum bit gate operations to be performed.

[0033] In this configuration, the rotation axis of the spin due to Rabi oscillation is limited to the XY plane, and the direction of the rotation axis within the XY plane is determined by the relative phase between the phase of the microwave pulse and the phase of the spin. In other words, by precisely controlling the phase of the microwave pulse, it is possible to rotate the spin around an axis in any direction within the XY plane. By repeating this operation at least twice by changing the rotation axis (i.e., by changing the phase of the microwave pulse) and irradiating microwave pulses consecutively, it is possible to perform any single-qubit gate operation.

[0034] The microwave pulse 111 is generated by the microwave generating antenna structure 190 shown in Fig. 1. This antenna structure is realized by an electromagnetic field leaking from a high-frequency transmission line structure such as a microstrip line structure or a coplanar waveguide structure. [Dynamic resonance frequency change method] To select a desired quantum bit, a local magnetic field is generated by passing a current through wires such as wires 103 and 104. For example, the I a , I b , I c , I d A current flows through each of the four wires in the direction of the arrow. In this case, a current flows in the opposite direction through the two parallel wires that make up a pair. The current I in the X direction a , I b selects the qubit in the Y direction, and the Y-direction current I c , I d performs quantum bit selection in the X direction, so quantum bit 101 at this intersection is selected.

[0035] First, one-dimensional quantum bit selection will be explained using cross-sectional diagram 120. When a direct current is passed through the wiring, static magnetic fields 127 and 128 are generated, and a resultant magnetic field 126 is generated between the wiring. Here, static magnetic fields in the same direction reinforce each other, and magnetic fields in opposite directions weaken each other. A quantum bit located at a position where the magnetic fields reinforce each other is subjected to a local static magnetic field in the Z direction, which can impart a resonant frequency difference approximately proportional to the magnitude of the local static magnetic field applied to other surrounding quantum bits, thereby enabling quantum bit selection. In addition, the resonant frequency of the selected quantum bit can be varied by turning the current on and off and adjusting the current value.

[0036] The one-dimensional qubit selection described above can be easily extended to two dimensions. When the qubit selection described above is performed in both the X and Y directions, only the qubit at the intersection has a different resonant frequency from the surrounding qubits, enabling two-dimensional qubit selection. Therefore, by applying a microwave pulse with a frequency that matches the resonant frequency of the selected qubit, which has polarization 125 in the X direction, Rabi oscillations can be generated only in the selected qubit 101, realizing a single-qubit gate. [System diagram] 2 shows a schematic block diagram of a system 200 for performing single-qubit gating. A host 220 is, for example, a general-purpose computer that controls the entire system. When a command to perform a single-qubit gating is issued from the host 220 to a control unit 201, the control unit 201 sends the qubit address for which the gating operation is to be performed and parameter information for various gating operations to a controller 205 in the dynamic resonant frequency changer 210. The qubit address is an address that specifies which qubit in the qubit array is to be gated; for example, the qubit address can be identified by numbering the wires 105 and 106 in FIG. 1 and identifying the wires at their intersections.

[0037] Based on this information, controller 205 issues a command to current application unit 206. Current application unit 206 applies current 208 to wiring 207 (corresponding to wiring 103 and 104 in FIG. 1) corresponding to the specified quantum bit address, generating local static magnetic field 209. Wiring 207 and quantum bits are composed of the semiconductor elements shown in FIG. 1, and are maintained at extremely low temperatures as described above. Here, the current flowing through wiring 207 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 bits.

[0038] Furthermore, when a command is issued from control unit 201, microwave pulse generation unit 202 generates microwave pulse 111 with adjusted frequency and irradiates the quantum bit array. This makes it possible to selectively apply a single quantum bit gate to selected quantum bit 101 based on the principle of the dynamic resonant frequency change method described above. Furthermore, when reading out the state of the quantum bit, the quantum state of selected quantum bit 101 is measured using readout unit 204.

[0039] Although Figure 2 shows only one quantum bit and two wires, in reality there are multiple of these as shown in Figure 1, and there are configurations required for trapping, initializing, reading out electrons, and operating a two-qubit gate. [Dynamic frequency] Figure 3 shows the dynamic resonance frequency change method. a ~I d and the resonant frequency f of the selected qubit 101. q1 , the resonant frequency f of the unselected qubit 102 q2 , the amplitude B of the magnetic flux density of the microwave pulse 111 rb and the Rabi frequency f of the selected qubit 101 rb The corresponding change with time t is shown.

[0040] Figure 1 I a ~I d A static magnetic field is generated by the current flowing through the qubit, and the selected qubit 101 has a resonant frequency f q1 It has a resonant frequency f q1By irradiating a microwave pulse 111 that coincides with the spin axis of the selected quantum bit, the rotation axis of the selected quantum bit can be controlled to any angle, which is the action of a one-bit quantum operation. As mentioned above, the direction of the rotation axis in the XY plane is determined by the relative phase between the microwave pulse phase and the spin phase.

[0041] The inventors, a ~I d We focused on the phenomenon where the current does not reach the initially intended value due to parasitic capacitance, resistance, etc., and the static magnetic field is unstable, resulting in an unstable resonance frequency. Due to this phenomenon, the control of the relative phase between the microwave pulse phase and the spin phase does not work as expected, and we discovered that the spin rotation axis cannot be precisely controlled.

[0042] Times t1 and t4 are the start and end times of the positive resonant frequency shift in the selected quantum bit 101. Times t2 and t3 are the start and end times of the application of microwave pulse 111. Times t4 and t5 are the start and end times of the negative resonant frequency shift in the selected quantum bit 101.

[0043] The reason for varying the resonant frequency of the selected qubit 101 in both the positive and negative directions is to prevent the selected qubit from being out of phase with the unselected qubits due to the variation in the resonant frequency. a and I b As shown in Figure 1, the wires are parallel and carry current in opposite directions. c and I d The same is true for the period t2 to t3 and the period t3 to t4. The magnetic field formed is, for example, a magnetic field with the same magnitude but opposite direction. This allows the resonant frequency f q1 is the frequency of the resonance when no current is flowing from f0 to f during the period t1-t4. + shifts in the positive direction.

[0044] On the other hand, during the period t4-t5, - On the other hand, the resonant frequency fq2 is not affected by the local magnetic field and remains unchanged at f0. The resonant frequency f + By applying a microwave pulse 111 having a frequency that matches the Rabi frequency f rb is the amplitude B of the magnetic flux density felt by the spin rb and contributes to the speed of single qubit gate operations, where (t4-t1)=(t5-t4)>(t3-t2) By satisfying this relationship, single quantum bit gate operation can be performed correctly. Note that the order of the positive and negative resonance frequency fluctuations can be reversed, and the timing of irradiating the microwave pulse can be either the positive or negative resonance frequency fluctuation, or both. [Phase Tracking] As mentioned above, the phase of the spin is important in single-qubit gate operations. Because phase is a relative concept, the phase of the qubit and the phase of the microwave pulse at time t2, when the microwave pulse 111 is applied at the beginning of quantum computation, are both defined as an initial phase of 0 (phase difference of 0). However, since there is some flexibility in this definition, any phase and phase difference may be used.

[0045] From time t2, the control unit 201 has a reference clock that matches the resonant frequency of the quantum bit, and is equipped with a function (phase tracking function) that tracks and counts the phase of the quantum bit using the reference clock. Regarding phase tracking using such a reference clock, see, for example, "The role of master clock stability in quantum information processing" Harrison Ball, William D Oliver and Michael J Biercuk. npj Quantum Information (2016) 16033. It should be noted that if the phase is reset during quantum computation, it will become impossible to track the phase of the continuously rotating quantum bit (the phase will be lost), so it is important to note that phase tracking cannot be reset during quantum computation.

[0046] FIG. 4A shows the time change of the phase φ(t) of the quantum bit when the operation of FIG. 3 is performed. Here, the phase 402 of the selected quantum bit and the phase 401 of the unselected quantum bit are also shown. A phase shift occurs between the two phases due to the frequency shift. This phase shift is used to selectively operate the desired quantum bit. Here, it can be expressed as phase = (time integral of frequency) × 2π. In other words,

[0047]

number

[0048]

number

[0049] In the fixed resonant frequency method, the frequency of each quantum bit is constant, so the phase increases linearly over time (repeating in a 2π cycle). Therefore, phase tracking can be easily achieved by using the high-precision reference clock signal described above, but for the reasons mentioned above, this is not suitable for large-scale integration. In the dynamic resonant frequency change method, when a reference clock signal is used, there are issues with phase tracking at the frequency switching points of t1, t4, and t5, as shown below.

[0050] The challenges of phase tracking will be explained using a concrete example. For example, to know at any time the current phase (which cannot be measured directly) of a quantum bit precessing at 20 GHz, a 20 GHz reference clock (sine wave) is prepared, and its phase is considered to match the phase of the precession. Then, when applying microwaves, the phase of the microwaves can be set using the phase information of the reference clock. In other words, the above-mentioned "phase tracking and counting" is synonymous with "using the phase information of the reference clock."

[0051] If the precession of the qubit deviates from 20 GHz due to some noise factor, the phase of the qubit and the phase of the reference clock will also deviate, but this change cannot be measured directly. However, if the noise factor is caused by the rise of the applied current described below in Figure 4B, it is believed that the method of this embodiment can estimate and correct the phase deviation between the qubit phase and the reference clock.

[0052] Figure 4B shows the frequency f of the selected qubit around t1 in Figure 3. q1 At t1, ideally, the change from f0 to f + In reality, however, the frequency may change instantaneously to f after a delay of a finite delay time τ (line 411), a linear change (line 412), a transient change (line 413), or a combination of these. +Therefore, if phase tracking is performed assuming that the frequency is the ideal line 410, an error (phase shift) occurs.

[0053] This phase shift amount (the amount of phase shift between the reference phase and the actual quantum bit) Δφ is

[0054]

number

[0055] The unstable part of Figure 4B causes f + The amount of current (proportional to frequency) that flows until the frequency stabilizes is unknown. + If we do not know whether the phase shift has been reached, we cannot know the amount of phase shift, which is the integral value of the frequency, so we need to control the trajectory regardless of the length of τ. Here, we estimate the allowable amount of phase shift Δφ necessary to maintain the accuracy of quantum computing.

[0056] Figure 4C shows the relationship between the gate fidelity (F), which indicates the performance of a quantum gate, and the phase shift (F = cos 2 (Δφ)). Therefore, by setting Δφ<2π×0.0016 (rad), F>99.99% can be achieved.

[0057] Next, we estimate the typical phase shift. Typically, τ=1 ns, |f + -f0|=10MHz. In this case, in FIG. 4B, f tracking A line 410, F real If we set this to line 411, then from (Equation 2), Δφ=2π|f +-f0|τ=2π×0.01.

[0058] Also, f tracking A line 410, F real If we take line 412 as the line, then Δφ=π|f + -f0|τ=2π×0.005. These cannot satisfy F=99.99%.

[0059] The phase shift amount Δφ is proportional to the area surrounded by ideal line 410 of the frequency assumed in phase tracking and the line of the actual quantum bit resonance frequency (lines 411 to 413 or a combination of these) in FIG. 4B.

[0060] Therefore, to further reduce Δφ, either (1) the transition time τ is reduced, or (2) f tracking and f real However, it is usually difficult to reduce the difference between (1) and (2).

[0061] So, considering (2), f real For example, by using a circuit simulator, it is possible to estimate f real The time waveform of can be predicted with high accuracy, thereby making it possible to reduce the phase shift amount Δφ. [Solution method using current and charge measurement] Furthermore, the amount of resonant frequency shift of the quantum bit is approximately proportional to the magnetic flux density at the quantum bit position, and according to Ampere's circuital law, the magnetic flux density is proportional to the amount of current flowing through the wiring. Therefore, for Δφ, from (Equation 2),

[0062]

number

[0063] At time τ, if we measure the voltage V of the capacitor, we get Q from V=Q / C. real It is also possible to measure the current I flowing through the wiring using a current mirror circuit, for example. real These methods allow the measurement of I real or Q real can be detected.

[0064] Therefore, for example, the I real or Q real By detecting this information and using it during actual quantum computation, the phase shift Δφ can be made closer to 0. Alternatively, I real or Q real is detected, and I is controlled by threshold control and feedback control. real or Q real can be controlled, thereby making the phase shift amount Δφ approach zero.

[0065] Since there are multiple wirings, by inserting a switching circuit, it is possible to detect the current values ​​or charge amounts of multiple wirings with a small number of current or charge readout units 500.

[0066] A schematic diagram of a configuration with a switching circuit inserted is shown in Figure 6. In this figure, for a quantum bit array 100, switching units 601 and 602 are connected to the wiring in the X and Y directions, respectively, and a current or charge readout unit 500 is located at the end of these.

[0067] An example of the calibration method is shown in Figure 7A. When a command to start calibration (S700) is sent from the host 220 to the control unit 201, the control unit 201 sends a command to set the switches (S701) to the controller 205, and the wiring to which the current is applied by the current application unit 206 and the wiring from which the current or charge readout unit 500 reads out the current are selected by switching units 601 and 602.

[0068] Thereafter, wiring current application (S702) is performed by the current application unit 206, and charge amount measurement (S703) is performed by the current or charge readout unit 500, and then the measurement results are stored in memory by the controller 205.

[0069] The measurement results stored in memory are the IDs of the wires 103 and 104 and the corresponding Q real or I real is.

[0070] FIG. 7B shows the I real This is an example of calibration data, which is the measurement result of the above. The data shown is taken immediately after t1 in Figure 3 (reference time 0 seconds). As shown in Figure 4B, the period immediately after the current switching timing is particularly problematic, so data may be recorded from t1 to t5 in Figure 3, or data may be extracted and recorded around t1, t4, and t5. By using such data for calibration, the phase shift Δφ can be brought closer to 0.

[0071] By repeating the above sequence until all wiring is completed (S705), individual I real or Q real This allows accurate detection of I, taking into account the effects of parasitic capacitance specific to each wiring. real or Q real can be detected, the phase shift amount Δφ can be effectively brought close to 0.

[0072] One method is to real or Q real The I or Q to be sent is controlled by threshold control or feedback control. In feedback control, a general feedback circuit is used to real or Q real Detect, for example, I tracking or Q tracking The supplied I or Q can be controlled so that the difference between them becomes zero, thereby making the phase shift amount Δφ approach zero.

[0073] Alternatively, in threshold control, I real or Q real By changing the operation when I is smaller than the threshold and when it is larger than the threshold, real or Q real I tracking or Q tracking For example, by using a threshold, I real or Q real The integral value is controlled by making the current value constant when the integral value reaches a predetermined value. [Feedforward] For example, based on the calibration data shown in Figure 7B, the desired I real or Q real The I and Q to be supplied are determined in advance to obtain this, and the current is controlled based on this data.

[0074] Figure 7C shows an example of correction data set based on the calibration data. By using a constant current source or charge pump circuit to pass a predetermined amount of current or charge through the wiring, Ireal or Q real can be controlled with high precision.

[0075] For example, in the case of a charge pump circuit, a constant charge Q stored in a capacitor is counted and sent to a wire. The current I(t) flowing through the wire has the relationship I(t) = Q × f(t), where f(t) is the frequency at which the charge Q is sent to the wire (the frequency at which it is counted). When Q is constant, I(t) is proportional to f(t), so if it is possible to control f(t) to gradually increase from 0 until it reaches the desired current amount, then I, as shown by line 412 in Figure 4B, can be obtained. real This allows for highly accurate control of I in Equation 4. tracking I real By matching these, the phase shift amount Δφ can be made close to 0. [Summary of the effects of Example 1] As a result, the amount of phase shift between the reference phase and the actual quantum bit can be reduced, enabling single quantum bit gate operations to be performed with low error. [Example]

[0076] In this example, the basic configuration is the same as in Example 1, but the microwave pulse irradiation method is different in order to reduce the influence of crosstalk on unselected quantum bits. In this case, the influence of errors due to the phase shift between the reference phase and the actual quantum bit is expected to become more significant, so the phase shift reduction method described in Example 1 is more effective. As a result, it is possible to reduce the amount of phase shift between the reference phase and the actual quantum bit while reducing the influence of crosstalk on unselected quantum bits, thereby performing single quantum bit gate operation with low error.

[0077] The frequency shift depicted in Figure 8A and subsequent figures is caused by a magnetic field, and the magnitude of the shift is proportional to the magnetic field. The magnetic field is controlled by the current flowing through each line. First, we will briefly explain the gist of Examples 2 and subsequent figures in relation to the drawings.

[0078] Specifically, a first magnetic field (magnetic field t1-t4 in Figures 8B and 9E) is applied to a target charge (801 in Figure 8A) by current flowing through a first line (word line) and a second line (bit line), and then a second magnetic field (magnetic field t4-t5 in Figures 8B and 9E) having the same magnitude but opposite direction as the first magnetic field is applied, and microwaves are irradiated to the charge for at least a portion of the period during which the first magnetic field is applied and at least a portion of the period during which the second magnetic field is applied (see Figures 9E, 8A to 10G).

[0079] More preferably, a third magnetic field is formed by passing a current through the first line, followed by a fourth magnetic field having the same magnitude but opposite direction as the third magnetic field (1202 in Figure 12A), a fifth magnetic field is formed by passing a current through the second line, followed by a sixth magnetic field having the same magnitude but opposite direction as the fifth magnetic field (1203 in Figure 12A), the magnitudes of the third magnetic field, fourth magnetic field, fifth magnetic field and sixth magnetic field are smaller than the first magnetic field and second magnetic field, and microwaves are irradiated to the charge for at least a portion of the period during which the third magnetic field is applied, at least a portion of the period during which the fourth magnetic field is applied, at least a portion of the period during which the fifth magnetic field is applied and at least a portion of the period during which the sixth magnetic field is applied (see Figures 11 to 12B).

[0080] More preferably, a seventh magnetic field is formed by passing a current through another line parallel to the first line, followed by a eighth magnetic field having the same magnitude but opposite direction as the seventh magnetic field, and a ninth magnetic field is formed by passing a current through another line parallel to the second line, followed by a tenth magnetic field having the same magnitude but opposite direction as the ninth magnetic field (in a specific example, current is passed through the bit line and word line that are far from the target bit in Figure 13A), the magnitudes of the seventh magnetic field, the eighth magnetic field, the ninth magnetic field, and the tenth magnetic field are smaller than the first magnetic field and the second magnetic field, and microwaves are irradiated to the charges for at least a portion of the period during which the seventh magnetic field is applied, at least a portion of the period during which the eighth magnetic field is applied, at least a portion of the period during which the ninth magnetic field is applied, and at least a portion of the period during which the tenth magnetic field is applied (see Figures 13A to 13B). [Issues of crosstalk to unselected qubits] 8A shows a classification diagram of qubits in qubit array 800. Shown are selected qubit 801, which is the target of single-qubit gate operation, qubit string 803, whose resonant frequency is shifted by a local magnetic field for Y-direction (bit line) selection, qubit string 804, whose resonant frequency is shifted by a local magnetic field for X-direction (word line) selection, and other unselected qubits 802.

[0081] 8B shows the time evolution of the resonant frequencies 813, 814, and 815 of the three types of quantum bits. The resonant frequency 815 of the selected quantum bit 801 changes from frequency f0 to frequency f 2+ and the frequency f 2+ After the microwave pulse 111, which coincides with the frequency f 2- and then returns to frequency f0 around time t5.

[0082] On the other hand, the resonant frequency 813 of the unselected quantum bit 802 is fixed at f0 without frequency fluctuation. Furthermore, the resonant frequency 814 of the quantum bit string 803 on the bit line and the quantum bit string 804 on the word line varies from a frequency f0 to f2+ Half the frequency f 1+ Shift up to f 2- Half the frequency f 2- and then returns to frequency f0.

[0083] where frequency f 2+ The influence of microwave pulse 111 coincident with the selected quantum bit 801 affects not only selected quantum bit 801 but also, to a certain extent, unselected quantum bit 802 and quantum bit strings 803 and 804 on the bit line and word line. This influence is called crosstalk.

[0084] Crosstalk is the effect on quantum bits of the microwave pulse frequency and the detuned resonant frequency, and generally the greater the frequency difference, the smaller the effect. However, in order to increase the detuning, it is necessary to increase the local magnetic field, which requires an increase in the amount of current to the wiring, which poses a problem of non-negligible heat generation inside the refrigerator. Therefore, the following describes a method to reduce the effect of this crosstalk.

[0085] In particular, this embodiment shows a method for reducing crosstalk 820 to unselected quantum bits 802. In embodiment 3, a method for reducing crosstalk 821 to quantum bit strings 803 and 804 on bit lines and word lines is shown. [Method for reducing crosstalk to non-selected qubits] Figure 9A shows the effect of crosstalk on a quantum bit using the parameter F. The horizontal axis, x, is the value obtained by normalizing the difference between the resonant frequency of the quantum bit and the frequency of the microwave pulse by the Rabi frequency. A π gate is assumed for the quantum gate. When considering the effect of crosstalk, F = 1 when the quantum bit is not affected at all by the microwave pulse. This is achieved when the frequency difference is sufficiently large as x → ∞. It can be seen that the smaller x becomes, the closer the frequencies become, and F decreases due to the influence of the microwave pulse.

[0086] Figure 9B shows a graph of Figure 9A plotted on a logarithmic scale with the vertical axis representing 1-F. When performing quantum gate operations on a selected qubit, for example, the unselected qubit 802 has x = 10 (903), resulting in F = approximately 99%, the qubit arrays 803 and 804 on the bit and word lines have x = 8 (902), resulting in F = approximately 95%, and the qubit nearest to the selected qubit 801 has x = 5 (901), resulting in F = approximately 90%. However, in practice, F = 99.99% or higher is desired, so a reduction in F due to the effects of crosstalk is a serious problem.

[0087] Figure 9C shows the temporal change in the resonant frequency of the selected qubit 801 in one method of performing a θ rotation gate using Rabi oscillations (called the single-irradiation method). Here, θ is the spin rotation angle, taking values ​​from 0 to 2π. This is the same as Figure 8B, where t4 - t1 = t5 - t4. In this case, the phase difference between the selected qubit and the unselected qubits or qubits on the bit / word lines can be canceled out, as shown in Figure 4A, but the effects of crosstalk described above still occur.

[0088] Figure 9D shows the temporal change in the resonant frequency of the selected qubit 801 when the quantum gate operation time is reduced by approximately half, with t4 - t1 > t5 - t4, using the single-irradiation method. In this case, too, the phase shift between the unselected and selected qubits can be canceled by utilizing the 2π phase periodicity. However, due to the imbalance between the (+) frequency shift and the (-) frequency shift, it is not possible to simultaneously cancel all phase shifts among qubits on the bit and word lines or nearby qubits.

[0089] Figure 9E shows the temporal change in the resonant frequency of the selected quantum bit 801 using the method proposed in this example. As shown in the figure, the method of this example irradiates microwave pulses twice, each at an angle of θ / 2 (called the two-time irradiation method). This method can reduce the quantum gate operation time to about half that of the one-time irradiation method shown in Figure 9C. In addition, because the (+) frequency shift and (-) frequency shift are well balanced, all phase shifts can be simultaneously canceled out in unselected quantum bits, quantum bits on the bit and word lines, and nearby quantum bits, as in Figure 9C. Another feature of this method is that it can also cancel the effects of crosstalk, as shown below.

[0090] 10A and 10B show the effect of crosstalk on F in the single-exposure scheme, and FIGS. 10C and 10D show the effect of crosstalk on F in the double-exposure scheme, using linear and log plots, respectively.

[0091] As shown in FIG. 10A, in the single irradiation method, it is difficult for the line 1011 of the π gate, the line 1013 of the 2π / 3 gate, and the line 1012 of the π / 2 gate to achieve F=1.

[0092] As shown in Figure 10B, which shows Figure 10A in logarithmic scale, for example, to make F = 1-10^(-4), x needs to be around 100. In order to make F approach 1, x needs to be set to a large value, and in order to apply a large local magnetic field, a large current needs to be applied, and from the perspective of the heat generation that would result, it would be difficult from a design perspective to increase x to 10 or more.

[0093] On the other hand, as shown in FIG. 10C, in the double irradiation method, the line 1021 of the π gate, the line 1023 of the 2π / 3 gate, and the line 1022 of the π / 2 gate each have x where F=1 periodically.

[0094] As shown in Fig. 10D by logarithmic scale in Fig. 10C, by appropriately setting x according to the rotation angle of the spin in the quantum gate operation, F = 1 can be realized. In this way, it is theoretically possible to realize quantum gate operation that reduces the influence of crosstalk by using the double irradiation method.

[0095] Figure 10E shows the relationship between the angle θ of the quantum gate operation and x. The black line indicates the region where F is approximately 99.5% or higher. This figure shows that the desired θ (+2nπ, n is an integer) can be achieved by appropriately selecting x.

[0096] As shown in FIG. 10F, the larger θ becomes, the finer the period in the x direction where F=1 becomes, so that a desired θ can be achieved within a small range of x.

[0097] Figure 10G shows an example of how to achieve a desired θ. For example, if you operate in the range of θ = π to 3π, by using a combination of (θ, x) that satisfies the condition on line 1024, you can set x for any θ (excluding the periodicity between 0 and 2π) and, in principle, achieve F = 1.

[0098] In this embodiment, the waveform of the microwave pulse is assumed to be, for example, a rectangular wave. However, the influence of crosstalk can also be reduced by using, for example, a Gaussian waveform or a Sech waveform. In this case, if the waveform is long enough, the influence of crosstalk can be reduced almost without depending on the frequency. In this case, the crosstalk reduction method using the above-mentioned two-time irradiation method is also effective. [Example]

[0099] In this embodiment, the basic configuration is the same as in embodiment 2, but the quantum gate operation method is different in order to reduce crosstalk on the bit line and word line. In this case, the influence of errors due to the phase shift between the reference phase and the actual quantum bit is expected to become more significant, so the phase shift reduction method described in embodiment 1 is more effective. As a result, it is possible to reduce the amount of phase shift between the reference phase and the actual quantum bit while reducing the influence of crosstalk on the bit line and word line, thereby performing single quantum bit gate operation with low errors.

[0100] Figure 11 shows a conceptual diagram of the double-exposure method. We have already shown in Example 2 that crosstalk 820 to unselected quantum bits 802 can be eliminated by the double-exposure method. On the other hand, crosstalk 821 to quantum bit strings 803 and 804 on the bit and word lines (called B / W crosstalk) cannot be eliminated. Therefore, a method for eliminating this B / W crosstalk will be described below. [Methods for reducing crosstalk on bit lines and word lines] A two-time irradiation method is adopted to eliminate crosstalk to the unselected quantum bit 802. Furthermore, to realize a unitary matrix for any single quantum bit gate, it is necessary to change the phase and perform two spin rotations using Rabi oscillations. Therefore, if the two-time irradiation method is used for one spin rotation, a total of four microwave pulse irradiations are required. Using this quantum gate operation using four pulse irradiations as the basic unit, a method of performing three consecutive gate operations (called the three-gate method) can eliminate B / W crosstalk.

[0101] A conceptual diagram of the three-gate method is shown in Figure 12A. The first, second, and third quantum gate operations are 1201, 1202, and 1203, respectively, and each quantum gate operation can realize a quantum operation corresponding to an arbitrary unitary matrix U.

[0102] In quantum gate operation 1201, U is input to the selected qubit 801. t , U as crosstalk to the qubit string 804 on the word line w , U as crosstalk to the qubit string 803 on the bit lineb In addition, crosstalk to the unselected quantum bit 802 is eliminated by the double irradiation method.

[0103] Next, in quantum gate operation 1202, quantum gate operation is performed only on the quantum bit string 804 on the word line, and U is applied to the quantum bits on the word line including the selected quantum bit 801. w † is effective.

[0104] Finally, in quantum gate operation 1203, a quantum gate operation is performed only on the quantum bit string 803 on the bit line, and U is applied to the quantum bits on the bit line including the selected quantum bit 801. b † is effective.

[0105] The above operations are shown in FIG. 12B as a quantum circuit diagram 1204. Here, this series of quantum circuit diagrams 1204 must finally be transformed into quantum circuit diagram 1205, in which the desired quantum gate operation U1 is performed only on the selected quantum bit, and B / W crosstalk is removed (i.e., an I (identity) gate is performed). To achieve this,

[0106]

number

[0107] In the third embodiment, a three-gate method was described that removes the influence of crosstalk on the three types of quantum bits shown in FIG. 8A (unselected quantum bits 802, quantum bit array on word lines 804, and quantum bit array on bit lines 803).

[0108] However, the method of Example 3 is based on the ideal situation where all three types of quantum bits have the same frequency (i.e., three types of frequencies). In reality, there are quantum bits that have frequencies other than the three types mentioned above due to the influence of the leakage magnetic field described below.

[0109] In this embodiment, the basic configuration is the same as in embodiment 3, but the quantum gate operation method is different in order to reduce crosstalk due to leakage magnetic fields. In this case, the influence of errors due to the phase shift between the reference phase and the actual quantum bit is expected to become more significant, so the phase shift reduction method described in embodiment 1 is more effective. As a result, it is possible to reduce the amount of phase shift between the reference phase and the actual quantum bit while reducing the influence of crosstalk due to leakage magnetic fields, and perform single quantum bit gate operation with low errors.

[0110] Figure 13A shows I a ,I b ,I c ,I d The figure shows the contour lines of the static magnetic field distribution generated when a current is passed in the direction of the arrow. The current is passed in order to apply a local static magnetic field to the selected quantum bit 101, but this also affects nearby quantum bits. The effects of this "stray magnetic field" cannot be eliminated by the crosstalk elimination method of Example 3 alone.

[0111] Figure 13B shows a schematic diagram of the "N-gate method" for eliminating crosstalk due to leakage magnetic fields. The N-gate method is an extension of the three-gate method of Example 3. For example, suppose there are six different frequencies of frequency-shifted qubits due to leakage magnetic fields, the influence of which cannot be ignored.

[0112] These six types include the frequency of the selected qubit, the qubits in the vicinity of the selected qubit, and the qubits on the bit line and word line. In this case, N=6, which is called a 6-gate method.

[0113] In this way, let N be the number of types of qubit frequencies + 1 at which the influence of crosstalk cannot be ignored (above a certain threshold). As shown in Figure 13B, by combining N gate operations, quantum gate operations can be performed only on selected qubits. All quantum gates U1 to U6 are performed using the double irradiation method, and the crosstalk (N *,* ), the parameters of each quantum gate can be calculated by a normal computer to realize the desired quantum gate U1', just like the three-gate method. Also, the quantum gates for quantum bits other than the selected quantum bit do not necessarily have to be I, and any quantum gate operation can be set.

[0114] According to the above-described embodiment, a quantum bit array with integrated quantum bits and dynamic resonant frequency change can perform single quantum bit gate operations with low error. This enables the realization of practical quantum computers, which consume less energy, reduce carbon emissions, prevent global warming, and contribute to the realization of a sustainable society. [Explanation of symbols]

[0115] Quantum bit 101, wire 103, wire 104, wire 105, wire 106

Claims

1. a semiconductor layer; an insulating layer disposed on the semiconductor layer; a plurality of first electrodes disposed on the insulating layer, the first electrodes trapping charges 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 forming a magnetic field acting on the charges by passing a current therethrough; a current applying unit that applies a current to at least one second electrode to form a magnetic field acting on the charge when changing the spin state of the charge; a microwave generating source that irradiates the charge with microwaves; a current measuring unit that measures a current flowing through the second electrode; Equipped with a plurality of charges are trapped in the semiconductor layer; the second electrode applies a first magnetic field to target charges that are a portion of the charges whose spin states are to be changed among the plurality of charges; Based on data of the current flowing through the second electrode measured by the current measurement unit, A quantum bit array, characterized in that a current flowing through the second electrode is controlled to apply the first magnetic field.

2. The current measuring unit measures the amount of charge flowing through the second electrode during a predetermined period. The quantum bit array of claim 1 .

3. The control of the current is feedback control or feedforward control. The quantum bit array of claim 1 .

4. a control unit having a function of setting both the phase of the precession of the spin of the charge and the phase of the microwave at the time of irradiation of the microwave as initial phases, generating a reference clock that coincides with the frequency of the precession of the spin of the charge, and tracking the phase of the precession using the reference clock; The quantum bit array of claim 1 .

5. the second electrode applies the first magnetic field to the target charge and then applies a second magnetic field having the same magnitude but opposite direction as the first magnetic field; the microwave generation source irradiates the charge with microwaves for at least a portion of a period during which the first magnetic field is applied and at least a portion of a period during which the second magnetic field is applied; The quantum bit array of claim 1 .

6. the second electrode is composed of a plurality of first lines extending in a first direction and a plurality of second lines extending in a second direction, forming a matrix; the target charge is identified at a predetermined first line and a predetermined second line; the current applying unit applies the first magnetic field to the target charge by passing a current through the predetermined first line and the predetermined second line, and then applies the second magnetic field to the target charge; The quantum bit array of claim 5.

7. moreover, the current applying unit applies a current to the predetermined first line to form a third magnetic field, and then forms a fourth magnetic field; the current applying unit applies a current to the predetermined second line to form a fifth magnetic field, and then forms a sixth magnetic field; The quantum bit array of claim 6.

8. moreover, the current applying unit applies a current to a first line other than the predetermined first line to form a seventh magnetic field, and then forms an eighth magnetic field; the current applying unit applies a current to second lines other than the predetermined second line to form a ninth magnetic field, and then forms a tenth magnetic field. The quantum bit array of claim 7.

9. A method for controlling a quantum bit, which controls a spin state of a quantum bit formed by a charge trapped in a semiconductor device, comprising: When controlling the spin state of a quantum bit formed by a target charge specified by a first line and a second line formed in the semiconductor device, a first step of measuring at least one of a current and an amount of charge flowing through the first line and the second line; a second step of controlling at least one of the current and the amount of charge flowing through the first line and the second line based on the measurement result of the first step; A method for controlling quantum bits to perform

10. providing a reference clock for tracking the phase of the quantum bit undergoing precession, and setting the phase of the microwave based on the phase of the reference clock, assuming that the phase of the reference clock and the phase of the precession coincide with each other; In the second step, the microwave is irradiated at a timing when a magnetic field is applied to the target charge by the current flowing through the first line and the second line. The method for controlling a quantum bit according to claim 9.

11. applying a first magnetic field to the target charge by currents flowing through the first line and the second line, and then applying a second magnetic field having the same magnitude as the first magnetic field but opposite in direction; The microwave is applied to the charge for at least a portion of a period during which the first magnetic field is applied and at least a portion of a period during which the second magnetic field is applied. The method for controlling a quantum bit according to claim 10.

12. generating a third magnetic field by passing a current through the first line, and then generating a fourth magnetic field having the same magnitude as the third magnetic field but opposite in direction; generating a fifth magnetic field by passing a current through the second line, and then generating a sixth magnetic field having the same magnitude as the fifth magnetic field but opposite in direction; the magnitudes of the third magnetic field, the fourth magnetic field, the fifth magnetic field, and the sixth magnetic field are smaller than the magnitudes of the first magnetic field and the second magnetic field; The microwave is irradiated to the charge for at least a portion of a period during which the third magnetic field is applied, at least a portion of a period during which the fourth magnetic field is applied, at least a portion of a period during which the fifth magnetic field is applied, and at least a portion of a period during which the sixth magnetic field is applied. The method for controlling a quantum bit according to claim 11.

13. generating a seventh magnetic field by passing a current through another line parallel to the first line, and then generating an eighth magnetic field having the same magnitude as the seventh magnetic field but opposite in direction; generating a ninth magnetic field by passing a current through another line parallel to the second line, and then generating a tenth magnetic field having the same magnitude but opposite direction as the ninth magnetic field; the magnitudes of the seventh magnetic field, the eighth magnetic field, the ninth magnetic field, and the tenth magnetic field are smaller than the first magnetic field and the second magnetic field; The microwave is irradiated to the charge for at least a portion of a period during which the seventh magnetic field is applied, at least a portion of a period during which the eighth magnetic field is applied, at least a portion of a period during which the ninth magnetic field is applied, and at least a portion of a period during which the tenth magnetic field is applied. The method for controlling a quantum bit according to claim 12.

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