Quantum computer and quantum bit control method

Abstract

In the present invention, a quantum computation includes a plurality of gate operations, and the plurality gate operations are executed in synchronization with a precession of quantum bits so that time for each of the plurality of gate operations is a positive integer multiple of a prescribed time length.

Description

Quantum Computer and Quantum Bit Control Method

[0001] The present invention relates to a quantum computer and a quantum bit control method.

[0002] A quantum computer is considered to be capable of performing high-speed information processing for specific problems compared to existing computers. While existing computers handle binary values of 0 and 1, a quantum computer is characterized by handling these superposed states. Information processing using the superposed state by a quantum computer is called quantum computing. To handle the superposed state, a quantum computer requires an element that realizes a quantum bit.

[0003] A quantum bit can be realized using a superconducting element, a cooled atom, a quantum dot by a semiconductor element, etc. Quantum computing is composed of multiple types of gate operations such as a single quantum bit gate, which is a basic operation, and a two-qubit gate. The gate operation uses two states of a quantum bit as 0 and 1, and controls the transition between 0 and 1 by applying an electromagnetic wave (energy) that resonates with the energy difference between the states. To accelerate and improve the accuracy of quantum computing, it is necessary to accelerate and improve the accuracy of each gate operation that constitutes the quantum computing.

[0004] WO2023004469A1US2024-220837

[0005] The two states 0 and 1 of a quantum bit have a phase that rotates between the states at a frequency proportional to the energy difference between the two states. This frequency is called the phase rotation frequency. To control the transition between 0 and 1 and perform a gate operation, it is necessary to apply an electromagnetic field having a frequency (resonance frequency) that matches the phase rotation frequency.

[0006] The states of 0 and 1 transition due to the interaction between the quantum bit and the electromagnetic field of the resonance frequency. The application of the electromagnetic field can be realized by a quantum bit control device such as a laser generator or a microwave generator. Usually, from the perspective of ease of implementation, the quantum bit control device generates a linearly polarized electromagnetic field to perform a gate operation.

[0007] A linearly polarized electromagnetic field can be decomposed into a rotational term and a counter-rotational term. The rotational term contributes as an interaction for the transition between 0 and 1. The counter-rotational term is unnecessary for the transition between 0 and 1 and causes a decrease in gate operation fidelity. Therefore, the rotational wave approximation is usually used to eliminate the contribution of the counter-rotational term. In order to use the rotational wave approximation, the gate operation must be performed at a frequency sufficiently slower than the phase rotation frequency.

[0008] In other words, the gate operation speed needs to be reduced, which in turn slows down the speed of quantum computations that consist of multiple gate operations. Furthermore, performing quantum computations within a range of gate operation speeds where the rotational wave approximation does not hold leads to a decrease in gate operation fidelity, resulting in a deterioration of quantum computation accuracy.

[0009] Patent document 1 mentions the above-mentioned problems related to the rotational wave approximation, but does not describe a solution.

[0010] Furthermore, Patent Document 2 describes how the fidelity of gate operations is improved by matching the CZ gate operation time to the period of Rabi oscillations. However, this is limited to CZ gate operations and cannot be applied to other gate operations. Also, the fact that it is limited to 2-qubit operations makes it not general-purpose. Moreover, it fails to solve the above-mentioned problems such as the reduction in quantum computation speed.

[0011] The objective of this invention is to provide a quantum computer capable of high-speed and high-precision quantum computation.

[0012] A quantum computer according to one aspect of the present invention comprises a qubit array and a qubit control device that performs gate operations on the qubit array in order to perform quantum computation consisting of a plurality of types of gate operations using the qubit array, wherein the qubit control device executes the plurality of types of gate operations in synchronization with the precession of the qubits and controls the time of each of the plurality of types of gate operations so that it is a positive integer multiple of a predetermined time length.

[0013] According to one aspect of the present invention, a quantum computer capable of high-speed and high-precision quantum computation can be provided.

[0014] This figure shows the energy diagram of two states used as a qubit. This figure shows a method for representing the state of a qubit using a Bloch sphere. This figure illustrates the phase rotation of two states used as a qubit. This figure shows an example of a qubit array. This figure shows the energy diagram of an electron spin used as a qubit. This figure illustrates a method for controlling the spin state using electron spin resonance. This figure illustrates the quantum computation in Example 1. This figure illustrates the quantum computation in Example 1. This figure illustrates the quantum computation in Example 1. This figure illustrates a method for controlling the spin state using a CCD. This figure illustrates the quantum computation in Example 2. This figure illustrates the quantum computation in Example 2. This figure illustrates the configuration of a quantum computer.

[0015] The embodiments will be described in detail below with reference to the drawings. However, the present invention is not to be construed as being limited to the embodiments described below. It will be easily understood by the parties involved that the specific configuration can be modified without departing from the spirit or purpose of the present invention.

[0016] In the configuration of the invention described below, the same reference numerals are used in common across different drawings for parts that are identical or have similar functions, and redundant explanations may be omitted. If there are multiple elements with the same or similar functions, they may be described using different subscripts. However, subscripts may be omitted in some cases.

[0017] In this specification, notations such as "Part 1," "Part 2," and "Part 3" are used to identify components and do not necessarily limit their number, order, or content. Furthermore, the numbers used to identify components are used context by context, and a number used in one context does not necessarily indicate the same component in another context. Moreover, the identification of a component by one number does not prevent considering the function of a component identified by another number.

[0018] The positions, sizes, shapes, and ranges of each component shown in drawings, etc., may not represent their actual positions, sizes, shapes, and ranges in order to facilitate understanding of the invention. Therefore, the present invention is not necessarily limited to the positions, sizes, shapes, and ranges disclosed in drawings, etc.

[0019] Figure 1A is an energy diagram 1 of the two states used as a qubit.

[0020] The energy of state |0> is E1, and the energy of state |1> is E2. The energy difference can be written as ΔE = E2 - E1. The state of a qubit is generally a superposition of state |0> and state |1>, and is often visualized and represented using Bloch sphere 2.

[0021] Figure 1B shows an example of a representation of a qubit state using Bloch sphere 2.

[0022] The south pole of Bloch Sphere 2 corresponds to state |0〉 and the north pole corresponds to state |1〉. The state of a qubit is represented by state vector 3, which is a vector that passes through a point on Bloch Sphere 2 specified by latitude θ and longitude φ, starting from the origin of Bloch Sphere 2. The phase between the states of a qubit rotates at a frequency proportional to the energy difference ΔE between the two states. This period is called the phase rotation frequency.

[0023] Figure 2 shows how the state of a qubit undergoes phase rotation using Bloch sphere 2.

[0024] The frequency F of phase rotation 4 is given by the relationship F = ΔE / h, where h is Planck's constant. In order to control the state of a qubit and perform gate operations, it is necessary to provide an electromagnetic field with a frequency (resonance frequency) that matches the phase rotation frequency. The provision of an electromagnetic field with a resonance frequency component can be realized using qubit control devices such as laser generators or microwave generators (see Figure 10).

[0025] Typically, for ease of implementation, qubit control devices perform gate operations by irradiating qubits with a linearly polarized electromagnetic field. This linearly polarized field can be decomposed into a rotational term and a counter-rotational term. The rotational term contributes as an interaction for the transition between 0 and 1. The counter-rotational term is unnecessary for the transition between 0 and 1 and causes a decrease in gate operation fidelity. Therefore, the counter-rotational term is usually canceled using a rotational wave approximation. In this case, to satisfy the rotational wave approximation, the gate operation must be performed at a frequency sufficiently smaller than the phase rotation frequency.

[0026] In other words, if the gate operation time is t0, the relationship 1 / F << t0 must be satisfied. Thus, the rotational wave approximation becomes a bottleneck, slowing down the speed of quantum computations that consist of multiple gate operations. Furthermore, if quantum computations are performed in a range of gate operation speeds where the rotational wave approximation does not hold, the gate operation fidelity decreases, leading to a deterioration in the accuracy of the quantum computation.

[0027] The following examples describe a method for solving the challenge of balancing speed and accuracy in quantum computation, which is limited by the rotational wave approximation. While the following examples use semiconductor devices as qubits, the method is not necessarily limited to these; qubits using superconducting devices or cold atoms would also be acceptable.

[0028] This first embodiment will explain using a qubit that utilizes electron spin in a semiconductor device as an example. In a qubit that utilizes electron spin in a semiconductor device, two levels (two states) of electrons, an up-spin state and a down-spin state, in a static magnetic field are used to make it function as a qubit.

[0029] Figure 3 is an enlarged cross-sectional view of a quantum bit array 210 using electron spin in a semiconductor device.

[0030] The qubit array 210 can be realized, for example, in a semiconductor substrate SUB such as silicon, by an arrangement of electrons 208 trapped by a potential shape P formed by a voltage applied by a gate electrode 207.

[0031] This section explains qubits that utilize electron spin in semiconductor devices. In qubits using electron spin in semiconductor devices, two energy levels—an up-spin state and a down-spin state—are used to function as a qubit. In this example, the down-spin state of the electron is denoted as |0〉 and the up-spin state as |1〉.

[0032] When a static magnetic field is applied to an electron spin, the energy of the electron's down-spin and up-spin states splits due to the Zeeman effect. This energy split is called the Zeeman energy. The Zeeman energy Ez can be written as EZ = gμBB0, where B0 is the magnitude of the static magnetic field. Here, g is the g-factor and μB is a physical constant called the Bohr magneton. Figure 4A shows the energy diagram of the electron spin.

[0033] Next, we will explain the gate operation method. Since the down-spin state of an electron is |0〉 and the up-spin state is |1〉, the gate operation is performed by controlling the electron spin state. The electron spin state can be manipulated, for example, using electron spin resonance.

[0034] Figure 4B illustrates a method for controlling the spin state using electron spin resonance.

[0035] A static magnetic field 8 is applied to the electron spin in the z direction, creating an energy difference of Zeeman energy Ez between the electron's down-spin state |0〉 and up-spin state |1〉. At this time, the phases of the |0〉 and |1〉 states rotate. This phase rotation is called precession. The frequency fL of precession 5 is given by the relationship fL = Ez / h, where h is Planck's constant. The period T of precession is given by T = h / Ez.

[0036] Electron spin state control is performed using electron spin resonance. Specifically, microwaves 6 with a frequency that matches (resonates with) the frequency of precession are irradiated onto the electron spin. When the frequency 6 of the microwaves irradiating the electron spin matches the precession of the electron spin state, Rabi oscillations 7 occur, which oscillate between the down-spin and up-spin states of the electron. By controlling the microwave irradiation time and its relative phase with the precession, the spin can be controlled in any direction, and the desired gate operation can be performed.

[0037] Next, the interaction between electron spin and microwaves will be described.

[0038] As an example, a static magnetic field 8 is applied in the z direction to the electron spin, and microwaves 6 with a resonance frequency fL of linearly polarized light in the x direction are applied. The Hamiltonian in the laboratory system can be written as shown in the following (Equation 1).

[0039]

[0040] For simplicity

[0041] it can be written as shown in the following (Equation 2).

[0042]

[0043] fL is the precession frequency, and fRabi is the Rabi frequency.

[0044] Microwaves 6 of linearly polarized light in the x direction are applied to the electron spin that is precessing at the frequency fL. Therefore, it is necessary to shift to the first rotating coordinate system defined by the precession frequency fL and decompose the microwaves 6 of linearly polarized light in the x direction into a rotating term and a counter-rotating term. The Hamiltonian Hrot when shifted to the rotating coordinate system of the frequency can be written as shown in the following (Equation 3) by transforming the Hamiltonian Hlab in (Equation 2).

[0045]

[0046] The first term in (Equation 3) is the rotating term 12. When viewed from the first rotating coordinate system, the rotating term 12 is independent of time and takes a constant value, and the spin state is controlled by this rotating term. For example, when the phase φ of the microwaves is set to 0 degrees, the electron spin rotates about the x axis, and when the phase φ of the microwaves is set to 90 degrees, the electron spin rotates about the y axis. That is, by changing the phase φ of the microwaves, the rotation axis of the spin changes, and operations such as X gate operation and Y gate operation can be realized.

[0047] The second term is the counter-rotating term, and it rotates at a period of 1 / 2fL, which is half of the precession motion, when viewed from the first rotating coordinate system. Since the counter-rotating term leads to a decrease in the gate operation fidelity, it is a term that is usually canceled using the rotating wave approximation.

[0048] The condition for the rotational wave approximation to hold is fRabi ≪ fL. When fRabi ≪ fL, the second term in (Equation 3) that rotates with a period of 1 / 2 fL is sufficiently faster than the gate operation period (period of Rabi oscillation), so it is averaged out and hardly contributes to the gate operation.

[0049] However, fRabi≪fL means that the gate operation period is sufficiently longer than the precession period, which reduces the gate operation speed and thus the speed of quantum computation, which consists of multiple types of gate operations. Conversely, if gate operations are performed at a gate operation speed that does not satisfy the rotating wave approximation, the gate operation fidelity decreases, leading to a decrease in the accuracy of quantum computation.

[0050] Therefore, in this invention, instead of using the rotating wave approximation, the contribution of the second term in (Equation 3) is made zero by performing a gate operation at a time that is a multiple of the period of the counter-rotation term in the second term of (Equation 3), that is, a multiple (positive integer multiple) of the period of half of the precession, 1 / 2 fL. In other words, the gate operation is performed at a time that is a multiple of the period 1 / 2 fL so that the contribution of the second term in (Equation 3) becomes zero when integrated.

[0051] Figure 5 shows an example of quantum computation using the present invention.

[0052] Quantum computation 9 consists of multiple types of gate operations, and the gate operation time is a multiple of 1 / 2fL (a positive integer multiple). In order to perform such quantum computation 9, it is necessary to always synchronize each gate operation with the precession 5. Synchronizing each gate operation with the precession 5 means matching the frequency of the precession 5 with the frequency of the microwave used to execute the gate operation. By synchronizing each gate operation with the precession 5, the phase state of the qubit can be determined, and the rotation axis of the spin in each gate operation can be correctly changed by controlling the microwave phase. In other words, by synchronizing the precession 5 and the gate operation and controlling the microwave phase, desired gate operations such as X-rotation gates and Y-rotation gates can be realized. Furthermore, by synchronizing, there is no discrepancy between the gate operation time and the precession period, and as a result, the second term of (Equation 3) integrates and approaches zero, leading to improved fidelity of the gate operation and thus improved accuracy in quantum computation.

[0053] When using the rotating wave approximation, the time required for a single gate operation must be significantly longer than 1 / fL. However, by using the present invention, a single gate operation can be performed in as little as 1 / 2fL.

[0054] Furthermore, since the anti-rotation term of the second term in (Equation 3) integrates to zero, problems such as a decrease in the fidelity of gate operations do not occur. In other words, by using this invention, a quantum computer capable of high-speed and high-precision quantum computation can be realized.

[0055] The spin rotation is driven by Rabi oscillations 7 at the Rabi frequency fRab, and its rotation angle can be controlled by the microwave irradiation time. The Rabi frequency FRab is

[0056] Because of this relationship, the amplitude of the applied microwave, Bac, can also be used to control it.

[0057] When the microwave amplitude is constant, the spin rotation angles that can be performed in the quantum computation example 9 shown in Figure 5 are discrete. Therefore, in order to achieve the desired discrete rotation angle, it is necessary to adjust the constant microwave amplitude Bac.

[0058] An example of quantum computation using the present invention will be described.

[0059] The gate operations required to perform any quantum computation (quantum algorithm) are called the universal gate set, and three gate operations are well known: the Hadamard gate, the CNOT gate, and the T gate. The Hadamard gate is used to put qubits into a superposition state and is an operation that rotates the spin state by 90 degrees.

[0060] The CNOT gate acts on two qubits, rotating (inverting) the target qubit by 180 degrees when the control qubit is 1. The T gate rotates the phase by 45 degrees and is used to create specific quantum states. To perform these gate operations, it is sufficient to achieve spin rotation angles of 45, 90, and 180 degrees.

[0061] To achieve this, adjust the microwave amplitude Bac so that it satisfies the following equation (Equation 4).

[0062]

[0063] By doing so, the minimum gate operation time of the quantum computing method in this invention, that is, the rotation angle of the spin rotating in a time of 1 / 2 fL, which is half the period of precession, becomes 45 degrees.

[0064] By adjusting the microwave amplitude Bac in this way, a T-gate can be executed in 1x the time of half the precession period (1 / 2fL), an Hadamard gate in 2x the time, and a CNOT gate in 4x the time. By combining these, any quantum algorithm can be executed.

[0065] Here, for example, the multiple types of gate operations 1 to N shown in Figure 5 are performed using different numbers of qubits.

[0066] For example, gate operations using a single qubit include the X gate, Y gate, Z gate, Hadamard gate (H gate), and phase gates (S gate, T gate). Gate operations using two qubits include the CNOT gate (controlled NOT gate), SWAP gate, and CZ gate (controlled Z gate). Gate operations using three qubits include the Toffoli gate (controlled controlled NOT gate). Furthermore, gate operations using three or more qubits also exist.

[0067] Thus, by performing the multiple types of gate operations 1 to N shown in Figure 5 using different numbers of qubits, a general-purpose gate operation can be realized.

[0068] Furthermore, as shown in the quantum computation 10 in Figure 6A, the gate operation time is constant, and the rotation angle can be adjusted by adjusting the amplitude of the microwave amplitude B_ac.

[0069] In this example, the time for each gate operation is 1 / 2fL multiplied by M (where M is a positive integer). This allows gate operations to be performed at a constant time interval, which has the advantage of making it easier to synchronize with other control devices and measuring devices.

[0070] Furthermore, quantum computations like the one shown in Figure 6B, quantum computation 11, can be considered in which both the gate operation time and the amplitude of the microwave Bac are varied with each gate operation. This has the advantage of enabling a wider range of rotation angles and allowing for the implementation of diverse quantum computations.

[0071] From the perspective of thermal noise experienced by the qubit, we will examine the energy difference between the two states used by the qubit and the frequency of its precession.

[0072] Since the quantum states of qubit arrays used in quantum computers need to be observed at very low energies, it is desirable to operate them in an environment with low thermal noise. For example, qubit arrays using superconducting elements or quantum dots made of semiconductor elements can be cooled to about 10 mK to 100 mK using a dilution refrigerator.

[0073] At this time, if Ep is the energy difference between the two states of the qubit, it is desirable that Ep / kb > 10 mK, where kb is the Boltzmann constant. Otherwise, it becomes difficult to distinguish the energy difference between the two states of the qubit due to thermal noise, and it cannot be used as a qubit. Converting Ep from Ep / h to frequency gives approximately 200 MHz. In other words, it is desirable that the frequency of precession be 200 MHz or higher.

[0074] Controlling a qubit requires electromagnetic waves with a frequency that matches the qubit's precession frequency. A higher precession frequency means a higher Ep (precession frequency), making it more resistant to thermal noise. However, when transmitting electromagnetic waves (microwaves) to a qubit using coaxial cables, microstrip lines, or antennas, it generally becomes more difficult to efficiently transmit the electromagnetic waves to the qubit as the frequency increases.

[0075] To efficiently transmit electromagnetic waves to qubits, it is desirable to keep the precession below 50 GHz and the frequency of the electromagnetic waves used below 50 GHz.

[0076] In this second embodiment, we will explain quantum computation when spin manipulation (gate manipulation) is performed using a method called CCD (concatenated continuous driving).

[0077] It is known that applying CCDs can mitigate the effects of quantum computation errors called diffusing and decoherence, which originate from environmental noise (coherence protection).

[0078] CCD is described, for example, in the non-patent document A. J. 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).

[0079] This non-patent document describes only the coherence protection of qubits. In this embodiment, we investigate a method for realizing high-speed and high-precision quantum computation using a CCD. As described in the above non-patent document, CCDs have amplitude modulation and phase modulation methods. This embodiment 2 will be explained using the phase modulation method, but the present invention is also applicable to the amplitude modulation method.

[0080] Figure 7 illustrates a method for controlling the spin state using a CCD.

[0081] In a CCD, microwaves are constantly irradiated onto the qubit, causing continuous Rabi oscillations. The phase or amplitude of the microwaves is modulated into a sine or cosine wave, and the gate operation of the CCD is performed by changing the modulation parameter θm and the microwave phase φ.

[0082] By setting the modulation period of the phase or amplitude of the modulated microwave to the Rabi oscillation period, the effectiveness of the CCD can be maximized, and quantum computation errors can be mitigated through coherence protection. In a phase-modulated CCD, the phase of the irradiated microwave is modulated. The microwave is modulated at a frequency of the Rabi frequency, Frab, as shown in (Equation 5) below, where εm is the CCD frequency and θm is the phase modulation parameter.

[0083]

[0084] Next, we will explain the interaction between electron spin and microwaves. A static magnetic field 8 is applied to the electron spin in the z direction, and a phase-modulated microwave 13 with linear polarization and frequency fL is applied in the x direction. In this case, the Hamiltonian of the laboratory system can be written as shown in (Equation 6) below.

[0085]

[0086] In CCD, it is necessary to consider the transition from the laboratory system to the second rotating coordinate system. First, we transition to the first rotating coordinate system defined in (Equation 7).

[0087]

[0088] In this case, the Hamiltonian in the first rotating coordinate system can be written as follows (equation 8).

[0089]

[0090] The first and second terms of (Equation 8) are rotation terms 14 as viewed from the first rotating coordinate system. The third term of (Equation 8) is the anti-rotation term as viewed from the first rotating coordinate system. The anti-rotation term of the third term of (Equation 8) is a factor that reduces the fidelity of the gate operation, so its contribution needs to be set to 0.

[0091] The contribution of the anti-rotation term in the third term of (Equation 8) can be set to zero by applying the usual rotational wave approximation, that is, the condition fRabi ≪ fL, or, as explained in Example 1, the contribution of the anti-rotation term in the third term of (Equation 8) can be set to zero by making the gate operation time of the CCD a positive integer multiple of half the precession period.

[0092] Even if we apply the standard rotational wave approximation, i.e., the condition fRabi ≪ fL, and perform the CCD gate operation at a speed sufficiently slower than the precession period of 1 / fL, applying the CCD offers the advantage of providing coherence protection. In other words, applying the CCD offers the advantage of enabling robust gate operation even in noisy environments such as thermal noise, electromagnetic noise, and nuclear spin noise.

[0093] Next, we consider the second rotating coordinate system defined in (Equation 9).

[0094]

[0095] In this case, the Hamiltonian in the second rotating coordinate system can be calculated as shown in (Equation 10).

[0096]

[0097] The first term of (Equation 10) is the rotation term 15 as viewed from the second rotating coordinate system, which takes a constant value independent of time when viewed from the second rotating coordinate system, and this rotation term 15 is used to perform gate operations in the CCD.

[0098] The rotation term 15 generates spin rotation 17. By appropriately adjusting the phase modulation parameter θm of the rotation term 15 and the microwave phase φ, the spin is rotated in the X or Y direction, and the desired gate operation is performed. The CCD frequency ε_m determines the speed of spin rotation 17 in the CCD, that is, the speed of the gate operation. The period of the gate operation by the CCD, TCCD, is TCDD = 1 / εm.

[0099] The second term in (Equation 10) is the counter-rotation term as seen from the second rotating coordinate system, and is a term that is usually canceled out using the rotating wave approximation. The counter-rotation term in the second term of (Equation 10) rotates with a period of 1 / 2fRabi, which is half the period of the Rabi oscillation, so the condition for the rotating wave approximation to hold is εm ≪ fRabi. When εm ≪ fRabi, the term in the second term of (Equation 10) that rotates with a period of 1 / 2fRabi is sufficiently faster than the gate operation period of the CCD, 1 / εm, so it is averaged out and hardly contributes to the gate operation of the CCD.

[0100] However, εm≪fRabi means that the gate operation period of the CCD is made sufficiently longer than the period of the Rabi oscillation, which reduces the gate operation speed of the CCD and decreases the speed of quantum computation, which consists of multiple types of gate operations. Conversely, if the gate operations of the CCD are performed at a gate operation speed that does not satisfy the rotating wave approximation, the fidelity of the CCD's gate operations decreases, leading to a decrease in the accuracy of quantum computation.

[0101] Therefore, in this invention, when transitioning to the second rotating coordinate system, instead of using the rotational wave approximation, the CCD gate operation is performed at a time that is a multiple of the period 1 / 2 fRabi of the second term of (Equation 10), and the contribution of the anti-rotation term of the second term of (Equation 10) is set to zero. In other words, the CCD gate operation is performed at a time that is a multiple of the period 1 / 2 fRabi such that the anti-rotation term of the second term of (Equation 10) integrates to zero.

[0102] Figure 8 shows an example of quantum computation using the present invention.

[0103] Quantum computation 16 consists of multiple types of gate operations (gate operation 1 to gate operation N), and the gate operation time is a multiple of 1 / 2 fRabi. In order to perform such quantum computation, it is necessary to always synchronize each gate operation with the precession and Rabi oscillation. Synchronizing each gate operation with precession 5 means matching the frequency of precession 5 with the frequency of the microwave used to execute the gate operation, and synchronizing each gate operation with the Rabi oscillation means matching the frequency of the Rabi oscillation with the CCD frequency εm. By synchronizing each gate operation with precession 5 and the Rabi oscillation, the phase state of the qubit can be determined, and the rotation axis of the spin in each gate operation can be correctly changed by controlling the microwave phase. In other words, desired gate operations such as X rotation gates and Y rotation gates can be realized by controlling the microwave phase. Furthermore, by synchronizing, there is no discrepancy between the gate operation time and the Rabi oscillation period, and as a result, the second term of (equation 8) integrates and approaches zero, leading to improved fidelity of the gate operation and improved accuracy of quantum computation.

[0104] When using the rotational wave approximation, the time required for one gate operation must be significantly longer than 1 / fRabi. However, by using the present invention, it is possible to perform a gate operation on one CCD in as little as 1 / 2fRabi.

[0105] Furthermore, since the anti-rotation term of the second term in (Equation 10) integrates to zero, problems such as a decrease in the fidelity of gate operations do not occur. In other words, by using this invention, a quantum computer capable of high-speed and high-precision quantum computation can be realized. In addition, since the CCD provides a coherence protection effect, a quantum computer capable of high-precision quantum computation even in environments with external noise can be realized.

[0106] The spin rotation 17 in the CCD rotates at the CCD frequency εm, and its rotation angle can be controlled by the microwave irradiation time and the CCD frequency εm. When the CCD frequency εm is constant, the spin rotation angles that can be performed in the quantum computation example shown in Figure 8 are discrete. Therefore, in order to achieve the desired discrete rotation angle, it is necessary to adjust the constant CCD frequency εm.

[0107] An example of quantum computation using the present invention will be described.

[0108] The gate operations necessary to perform any quantum computation (quantum algorithm) are called the universal gate set, and three gate operations are well known: the Hadamard gate, the CNOT gate, and the T gate. To realize these gate operations, it is sufficient to achieve spin rotation angles of 45 degrees, 90 degrees, and 180 degrees. To achieve this, the CCD frequency εm is adjusted so that (Equation 11) is given below.

[0109]

[0110] By doing so, the minimum gate operation time of the quantum computing method in this invention, that is, the rotation angle of a spin that rotates in a period of 1 / 2fRabi, which is half the Rabi oscillation period, becomes 45 degrees.

[0111] By adjusting the CCD frequency εm in this way, a T-gate can be executed in a time equal to half the period of the Rabi oscillation (1 / 2fRabi), an Hadamard gate in twice the time, and a CNOT gate in four times the time. By combining these, any quantum algorithm can be executed.

[0112] Here, for example, the multiple types of gate operations 1 to N shown in Figure 8 are performed using different numbers of qubits.

[0113] For example, gate operations using a single qubit include the X gate, Y gate, Z gate, Hadamard gate (H gate), and phase gates (S gate, T gate). Gate operations using two qubits include the CNOT gate (controlled NOT gate), SWAP gate, and CZ gate (controlled Z gate). Gate operations using three qubits include the Toffoli gate (controlled controlled NOT gate). Furthermore, gate operations using three or more qubits also exist.

[0114] Thus, by performing the various gate operations 1 to N shown in Figure 8 using different numbers of qubits, a general-purpose gate operation can be realized.

[0115] Furthermore, as shown in the quantum computation 10 in Figure 9A, the gate operation time is constant, and the rotation angle can be adjusted by adjusting the amplitude of the microwave amplitude Bac.

[0116] In this example, the time for each gate operation is M times 1 / 2fRabi (where M is a positive integer). This allows gate operations to be performed at a constant time, which has the advantage of making it easier to synchronize with other control devices and measuring devices.

[0117] Furthermore, quantum computations like the one shown in Figure 9B, quantum computation 11, can be considered in which both the gate operation time and the amplitude of the microwave Bac are varied with each gate operation. This has the advantage of enabling a wider range of rotation angles and allowing for the implementation of diverse quantum computations.

[0118] Furthermore, the state of a qubit is defined in a second rotating coordinate system, and the readout of the qubit state must be performed at an appropriate timing when the qubit state in the second rotating coordinate system and the experimental system coincide. From the perspective of the laboratory system, the second rotating coordinate system rotates with a Rabi oscillation period of 1 / fRabi, so the readout should be performed at a time that is a positive integer multiple of the Rabi oscillation period after the microwave is applied, i.e., at time K / Rabi (where K is a positive integer).

[0119] Referring to Figure 10, the configuration of the quantum computer in Example 3 will be described.

[0120] The quantum computer 301 shown in Figure 10 consists of a quantum operation generation unit 302, a qubit control device 303, a qubit array 210, a precession frequency measurement unit 305, a Rabi oscillation frequency measurement unit 306, a readout unit 307, and a quantum computation result output unit 308.

[0121] The quantum computation generation unit 302 constructs the quantum computation that the user wants to perform using an appropriate quantum algorithm and multiple types of gate operations. The qubit control device 303 controls the quantum state of the qubit array 304 in order to perform multiple types of gate operations on the qubit array 304. The qubit control device 303 is equipped with a microwave generator that generates microwaves for performing gate operations.

[0122] The readout unit 307 reads out the quantum state of the qubit array. By reading out the quantum state of the qubit array and passing the result to the Rabi oscillation frequency measurement unit 306 and the precession frequency measurement unit 305, the Rabi oscillation frequency and precession frequency of the qubit array are determined.

[0123] The obtained Rabi oscillation frequency and precession frequency results are sent to the qubit control device 303, where the waveform shaping unit and timing control unit set an appropriate gate time synchronized with the precession so that the anti-rotation term integrates to zero during gate operation.

[0124] The quantum state of the qubit array after multiple types of gate operations is read by the readout unit 307, and the result is passed to the quantum computation result output unit 308 to output the result of the quantum computation that the user wants to perform.

[0125] The precession frequency measurement unit 305, for example, determines the frequency characteristics of the qubit array 304 by sweeping the frequency of the electromagnetic field output from the qubit control device 303 and analyzing the frequency characteristics read out by the readout unit 307. Since the quantum state of the qubit array used in a quantum computer needs to be observed at very small energies, it must operate in an environment with low thermal noise.

[0126] The precession frequency measurement unit 305 sets the gate operation time to an integer multiple of half the precession period. The qubit control device 303 executes multiple types of gate operations (see Figure 5) using the integer multiples of half the precession period set by the precession frequency measurement unit 305.

[0127] Furthermore, the Rabi oscillation frequency measurement unit 306 sets the gate operation time to an integer multiple of half the period of the Rabi oscillation. The qubit control device 303 performs multiple types of gate operations using the integer multiple of half the period of the Rabi oscillation set by the Rabi oscillation frequency measurement unit 306 (see Figure 8).

[0128] For example, quantum bit arrays using superconducting elements or quantum dots made of semiconductor elements are operated by cooling them to about 10 mK to 100 mK using a dilution refrigerator. In cooling systems, atoms in a vacuum chamber are cooled to extremely low temperatures using laser cooling to operate.

[0129] According to the above embodiment, a quantum computer capable of high-speed and high-precision quantum computation can be provided.

[0130] 1 Energy diagram 2 Bloch sphere 3 State vector 4 Phase rotation 5 Precession 6 Microwave 7 Rabi oscillation 8 Static magnetic field 9 Quantum computation 10 Quantum computation 11 Quantum computation 12 Rotation term 13 Phase-modulated microwave 14 Rotation term 15 Rotation term viewed from the second rotation coordinate system 16 Quantum computation 17 Spin rotation in CCD 207 Gate electrode 208 Electron 210 Qubit array 301 Quantum computer 302 Quantum operation generation unit 303 Qubit control unit 305 Precession frequency measurement unit 306 Rabi oscillation frequency measurement unit 307 Readout unit 308 Quantum computation result output unit

Claims

1. A quantum computer comprising: a qubit array; and a qubit control device that performs gate operations on the qubit array in order to perform quantum computation consisting of a plurality of types of gate operations using the qubit array, wherein the qubit control device executes the plurality of types of gate operations in synchronization with the precession of the qubits, and controls the time of each of the plurality of types of gate operations so that it is a positive integer multiple of a predetermined time length.

2. The quantum computer according to claim 1, characterized in that the qubit control device changes the positive integer based on the type of the plurality of gate operations.

3. The quantum computer according to claim 1, characterized in that the qubit control device performs the plurality of gate operations using a different number of qubits.

4. The quantum computer according to claim 1, characterized in that the qubit control device uses half the period of the precession as the predetermined time length.

5. The quantum computer according to claim 1, characterized in that the qubit control device performs the plurality of gate operations in synchronization with the Rabi oscillations of the qubit.

6. The quantum computer according to claim 5, characterized in that the qubit control device uses half the period of the Rabi oscillation as the predetermined time length.

7. The quantum computer according to claim 1, characterized in that the qubit control device has a microwave generator that generates microwaves.

8. The quantum computer according to claim 7, characterized in that the qubit control device modulates the phase or amplitude of the microwave to perform the plurality of gate operations.

9. The quantum computer according to claim 7, characterized in that the qubit control device matches the frequency of the microwaves to the frequency of the precession and performs the plurality of gate operations.

10. The quantum computer according to claim 8, characterized in that the qubit control device matches the modulation period of the phase or amplitude of the modulated microwave to the period of the Rabi oscillation and performs the plurality of gate operations.

11. The quantum computer according to claim 10, characterized in that the qubit control device reads out the results of the plurality of gate operations at a timing equal to the period of the Rabi oscillation.

12. The quantum computer according to claim 1, characterized in that the qubit control device sets the frequency of the precession between 200 MHz and 50 GHz and executes the plurality of gate operations in synchronization with the precession of the qubit.

13. The quantum computer according to claim 1, comprising a precession frequency measuring unit that sets the time of the gate operation to an integer multiple of half the period of the precession, wherein the qubit control device performs the plurality of gate operations using an integer multiple of half the period of the precession set by the precession frequency measuring unit.

14. The quantum computer according to claim 6, comprising a Rabi oscillation frequency measuring unit that sets the time of the gate operation to an integer multiple of half the period of the Rabi oscillation, wherein the qubit control device performs the multiple types of gate operations using an integer multiple of half the period of the Rabi oscillation set by the Rabi oscillation frequency measuring unit.

15. The quantum computer according to claim 1, characterized in that the qubit array is composed of semiconductor qubits or superconducting qubits.

16. A qubit control method for performing a quantum computation consisting of multiple types of gate operations on a qubit array having qubits using a qubit control device, the method comprising: a step of performing the multiple types of gate operations in synchronization with the precession of the qubits using the qubit control device; and a step of controlling the time of each of the multiple types of gate operations so that it is a positive integer multiple of a predetermined time length.

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