Quantum logic gate manipulation device, quantum logic gate manipulation method, and program

Abstract

To provide a quantum logic gate operation device, a method and a program which have quick gate execution speed while holding heat insulation performance, and realize entanglement quantum gate operation being resistive to ZI interaction error, residual ZZ interaction error and phase relaxation error.SOLUTION: A quantum logic gate operation device comprises: a 2 quantum bit system of a control quantum bit 11 and a target quantum bit 12; a crossing resonance drive pulse irradiation unit which irradiates the control quantum bit with crossing resonance drive pulses of a natural frequency of the target quantum bit; an echo pulse irradiation unit which irradiates the control quantum bit with echo pulses which reverse a quantum state; and a control unit which emits the crossing resonance drive pulses of a first phase in a first period of quantum logic gate operation, continuously changes the phase while holding strength of the pulses in a second period, controls the crossing resonance drive pulse irradiation unit so as to emit the crossing resonance drive pulses of a second phase in a third period, and controls the echo pulse irradiation unit so as to irradiate the echo pulses in the second period.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] This disclosure relates to a quantum logic gate manipulation device, a quantum logic gate manipulation method, and a program. [Background technology]

[0002] Entangled quantum gates are a means of realizing the quantum logic gate operations necessary for quantum computers. Entangled quantum gates induce entanglement interactions between coupled qubits with different frequencies. This allows quantum information to be transmitted from one qubit to another. An example of a mechanism for manipulating entangled quantum gates is the cross-resonance gate (see, for example, Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] "Procedure for systematically tuning up crosstalk in the cross resonance gate", Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta, Phys. Rev. A 93, 060302 (2016) [Non-Patent Document 2] “Cross-Cross Resonance Gate”, Kentaro Heya and Naoki Kanazawa, PRX Quantum 2, 040336 (2021) [Overview of the project] [Problems that the invention aims to solve]

[0004] Conventionally, two methods have been proposed for cross-resonance gates: Direct Control-X (hereinafter also referred to as "DCX") and Two-pulsed echoed Control-X (hereinafter also referred to as "TPCX") (see, for example, Non-Patent Document 2).

[0005] DCX excels in its fast gate execution speed but has the disadvantage of being untolerant of errors during gate operations (ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors). On the other hand, TPCX excels in its tolerance to errors during gate operations but has the disadvantage of being untolerant of gate execution speed.

[0006] This invention was made in view of these circumstances, and its purpose is to realize entangled quantum gate operations that are fast while maintaining thermal insulation and are resistant to errors during gate operations (ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors). [Means for solving the problem]

[0007] To solve the above problems, a quantum logic gate manipulation device according to one aspect of the present invention comprises a two-qubit system in which a control qubit and a target qubit are coupled, a cross-resonance drive pulse irradiation unit that irradiates the control qubit with a cross-resonance drive pulse having the intrinsic frequency of the target qubit, an echo pulse irradiation unit that irradiates the control qubit with an echo pulse to invert the quantum state of the control qubit, and a control unit. The control unit controls the cross-resonance drive pulse irradiation unit to irradiate with a cross-resonance drive pulse of a first phase during a first period of quantum logic gate manipulation, to irradiate with a cross-resonance drive pulse while continuously changing the phase of the cross-resonance drive pulse from a first phase to a second phase while maintaining the intensity of the cross-resonance drive pulse during a second period of quantum logic gate manipulation, to irradiate with a cross-resonance drive pulse of a second phase during a third period of quantum logic gate manipulation, and controls the echo pulse irradiation unit to irradiate with an echo pulse during the second period.

[0008] In one embodiment, the control unit may control the echo pulse irradiation unit so as to frequency-modulate the echo pulse.

[0009] In one embodiment, the frequency modulation may be a frequency modulation that follows the modulation of the resonance frequency of the control qubit.

[0010] In one embodiment, the frequency modulation may be obtained by further adding the change in the anharmonicity of the control qubit.

[0011] In one embodiment, the first phase may be 0 and the second phase may be π.

[0012] In one embodiment, the control qubit and the target qubit may be superconducting qubits.

[0013] In one embodiment, the control unit may include an arbitrary waveform generator.

[0014] In one embodiment, the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit may be integrated. [[ID=2C]]

[0015] In one embodiment, the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit may be separate.

[0016] In one embodiment, the control unit may control the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit so as to repeatedly execute a set of a change in the phase of the cross-resonance drive pulse and irradiation of the echo pulse.

[0017] Another aspect of the present invention is a quantum logic gate operation method that performs a quantum logic gate operation using a two-qubit system in which a control qubit and a target qubit are coupled. This method includes a cross-resonance drive pulse irradiation step of irradiating the control qubit with a cross-resonance drive pulse having the intrinsic frequency of the target qubit, and an echo pulse irradiation step of irradiating the control qubit with an echo pulse to invert the quantum state of the control qubit. In the cross-resonance drive pulse irradiation step, a cross-resonance drive pulse of a first phase is irradiated during the first period of the quantum logic gate operation, a cross-resonance drive pulse is irradiated during the second period of the quantum logic gate operation while maintaining the intensity of the cross-resonance drive pulse and continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase, a cross-resonance drive pulse of the second phase is irradiated during the third period of the quantum logic gate operation, and in the echo pulse irradiation step, an echo pulse is irradiated during the second period.

[0018] Another aspect of the present invention is a program which causes a computer to perform a quantum logic gate operation using a two-qubit system in which a control qubit and a target qubit are coupled. The program includes a cross-resonance drive pulse irradiation step in which a cross-resonance drive pulse having the intrinsic frequency of the target qubit is irradiated onto the control qubit, and an echo pulse irradiation step in which an echo pulse is irradiated onto the control qubit to invert the quantum state of the control qubit. In the cross-resonance drive pulse irradiation step, a cross-resonance drive pulse of a first phase is irradiated during the first period of the quantum logic gate operation, a cross-resonance drive pulse is irradiated during the second period of the quantum logic gate operation while maintaining the intensity of the cross-resonance drive pulse and continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase, a cross-resonance drive pulse of the second phase is irradiated during the third period of the quantum logic gate operation, and in the echo pulse irradiation step, an echo pulse is irradiated during the second period.

[0019] Furthermore, any combination of the above components, as well as any conversion of the expressions of this disclosure between methods, apparatus, systems, recording media, computer programs, etc., are also valid forms of this disclosure. [Effects of the Invention]

[0020] According to this disclosure, it is possible to realize entangled quantum gate operations that maintain thermal insulation, have a high gate execution speed, and are resistant to errors during gate operations (ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors). [Brief explanation of the drawing]

[0021] [Figure 1] This is a schematic diagram illustrating the principle of a cross-resonance gate. [Figure 2] This figure shows the temporal change of the cross-resonance drive pulse irradiated by DCX. [Figure 3] This figure shows the temporal change of the cross-resonance drive pulse irradiated by TPCX. [Figure 4] This figure shows the temporal changes in the echo pulses irradiated by TPCX. [Figure 5] This is a functional block diagram of a quantum logic gate manipulation device according to the first embodiment. [Figure 6] This figure shows the temporal change of the cross-resonance drive pulse irradiated by OPCX. [Figure 7] This figure shows the temporal change of the echo pulse irradiated by OPCX. [Figure 8] This is an enlarged view of Figure 6 around the second period. [Figure 9] This figure shows the phase change of the cross-resonance drive pulse of an OPCX on the complex plane. [Figure 10] This figure shows the phase change of the cross-resonance drive pulse of TPCX on the complex plane. [Figure 11] This figure shows the relationship between drive intensity and drive frequency for OPCX and TPCX. [Figure 12]This figure shows the temporal change of the cross-resonance drive pulse irradiated by a two-pass type OPCX. [Figure 13] This figure shows the temporal change of the echo pulse irradiated by a two-pass OPCX. [Figure 14] This is a processing flow diagram of the quantum logic gate manipulation method according to the second embodiment. [Figure 15] This figure shows the changes in the main terms of the Cartan coefficient as gate operations are performed. [Figure 16] This figure shows the changes in the secondary terms of the Cartan coefficient as a result of gate operations. [Figure 17] This figure shows the change in the amount of leakage of the Kartan coefficient associated with the execution of gate operations. [Modes for carrying out the invention]

[0022] Before describing specific embodiments, we will refer to Figure 1 to explain the fundamental knowledge. Figure 1 is a schematic diagram illustrating the principle of a cross-resonance gate. The two-qubit system 100 in Figure 1 is configured as a system in which a control qubit 101 and a target qubit 102 are coupled via a coupling resonator 103. In this example, both the control qubit 101 and the target qubit 102 are formed from superconducting qubits such as transmons, but this is not necessarily limited to this. The resonance frequency (also called the "natural frequency") of the control qubit 101 is f c and the resonance frequency (also called the "natural frequency") of the target qubit 102 f t It is different. For example, f c =8.0GHz, f t For example, the frequency is 8.8 GHz, but it is not limited to these values. Furthermore, the two-qubit system 100 shown in Figure 1 has two qubits coupled via a coupling resonator, but this is not necessarily the only option. For example, the two-qubit system may be formed by direct coupling. The important point here is that qubits with different natural frequencies are coupled.

[0023] The control qubit 101 and the target qubit 102 each have a state of 0 (represented as |0>) and a state of 1 (represented as |1>). Here, the states 0 and 1 of the control qubit 101 are represented as |0> c and |1> c respectively, and the states 0 and 1 of the target qubit 102 are represented as |0> t and |1> t respectively.

[0024] In this system, a microwave pulse having the natural frequency f t of the target qubit 102 is irradiated from the microwave source 104 to the control qubit 101. This microwave pulse is called a "cross-resonance drive pulse". At this time, the state of the control qubit 101 does not change before and after the irradiation of the cross-resonance drive pulse. That is, |0> c →|0> c or |1> c →|1> c (The left side of the right arrow indicates the state before the irradiation of the cross-resonance drive pulse, and the right side indicates the state after the irradiation. The same applies hereinafter). On the other hand, the state of the target qubit 102 changes according to the state of the control qubit 101. Specifically, when the state of the control qubit 101 is the state 0 (|0> c ), the state of the target qubit 102 does not change. That is, if |0> c , then |0> t →|0> t or |1> t →|1> t . On the other hand, when the state of the control qubit 101 is the state 1 (|1> c ), the state of the target qubit is inverted. That is, if |1> c , then |0> t →|1> t or |1> t →|0> tIn particular, a 2-input, 2-output cross-resonance gate that operates in this manner corresponds to a control bit inversion (CNOT) gate and is locally equivalent to a 90-degree rotation along the ZX axis. In addition, cross-resonance drives can implement rotations along the (A*ZX+B*IX) axis, which result in arbitrary rotations of the target qubit depending on the state of the control qubit (A and B are arbitrary real coefficients), by applying an additional microwave irradiation called a crosstalk correction drive. Here, a rotation along the ZX axis refers to an operation in which the target rotates positively when the control side is 0, and negatively when the control side is 1. Furthermore, an operation in which the target is stationary when the control is 0, and acts when the control is 1, is called a rotation along the (ZX-IX) axis.

[0025] [Conventional Technology 1: DCX] As the first example of a conventional technology for realizing cross-resonance gates, we will explain DCX. In DCX, a cross-resonance drive pulse is irradiated onto the control qubit 101 only once during quantum gate operation. As a result, the quantum information of one qubit (control qubit 101) is propagated to the other qubit (target qubit 102), as described above. However, DCX has the problem of not being error-tolerant. Figure 2 shows an example of the temporal change of the cross-resonance drive pulse irradiated by DCX. In this example, the horizontal axis (time) is in units of ns (nanoseconds). As shown in the figure, the irradiation time of the cross-resonance drive pulse (gate execution time) is approximately 125 ns. The vertical axis (amplitude) is normalized to a magnitude of 1, with phase 0 represented as positive and phase π as negative (Figures 3 and 4 are similar).

[0026] Here, we will explain the three types of errors that exist in cross-resonance gates. When a cross-resonance drive pulse is applied to the control qubit 101 (hereinafter, this operation may also be referred to as "applying a cross-resonance drive" or "applying a gate"), an interaction called the ZX interaction acts between the control qubit 101 and the target qubit 102. The ZX interaction is a desirable interaction for a cross-resonance gate. However, in reality, in addition to the ZX interaction, there are undesirable interactions that act on cross-resonance gates, specifically called the ZI interaction and the residual ZZ interaction. These can cause errors when the cross-resonance gate is executed.

[0027] (Error 1: ZI interaction error) As mentioned above, in a cross-resonance gate, the control qubit 101 has its own intrinsic frequency f c and different frequencies f t The cross-resonance drive pulse is irradiated. At this time, an effect called drive-induced AC Stark shift occurs, and the resonance frequency of control qubit 101 changes to its original natural frequency f. c It shifts from [a certain frequency]. The error caused by such a frequency shift is called the ZI interaction error.

[0028] (Error 2: Residual ZZ interaction error) Even when no cross-resonance drive is applied, a residual interaction (residual ZZ interaction) exists between the control qubit 101 and the target qubit 102, originating from the coupling between the two qubits. This residual ZZ interaction is undesirable for a cross-resonance gate and can cause errors. Errors caused by such residual ZZ interactions are called residual ZZ interaction errors.

[0029] (Error 3: Phase relaxation error) The phase of the quantum state of control qubit 101 fluctuates over time (in other words, the phase relaxes over time). Errors that arise from this temporal relaxation of the phase are called phase relaxation errors.

[0030] DCX has been found to be incompatible with these three errors (i.e., ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors), which is a major drawback.

[0031] [Conventional Technology 2: TPCX] As a second example of a conventional technique for realizing cross-resonance gating, we will describe TPCX. TPCX is a method developed to provide resistance to the three errors mentioned above. Irradiated TPCX is characterized by the irradiation of the cross-resonance drive pulse twice.

[0032] In TPCX, first, in the first half of the gate operation, the first cross-resonance drive pulse is irradiated onto the control qubit 101. After this first irradiation, a pulse (called an "echo pulse" or "X-π pulse") to invert the quantum state of the control qubit 101 is irradiated onto the control qubit 101. Therefore, after the first cross-resonance drive pulse is irradiated, the quantum state of the control qubit 101 is inverted. Then, in the second half of the gate operation, the second cross-resonance drive pulse is irradiated onto the control qubit 101. However, the phase of the second cross-resonance drive pulse is set to be out of phase with the phase of the first cross-resonance drive pulse. Finally (after the second irradiation), an echo pulse to invert the quantum state of the control qubit 101 is irradiated onto the control qubit 101. Figure 3 shows an example of the temporal change of the cross-resonance drive pulse irradiated in TPCX. Figure 4 shows an example of the temporal change of the echo pulse irradiated in TPCX. The first cross-resonance drive pulse is irradiated between t0 and t1. The first echo pulse is delivered between t1 and t2. The second cross-resonance drive pulse is delivered between t2 and t3. The second echo pulse is delivered between t3 and t4.

[0033] Here, we focus on the following properties: Of the ZX, ZI, and ZZ interactions, the ZX interaction follows the phase of the irradiated cross-resonance drive pulse. That is, when a positively signed cross-resonance drive pulse is irradiated, a positively signed ZX interaction occurs. Conversely, when a negatively signed cross-resonance drive pulse is irradiated, a negatively signed ZX interaction occurs. On the other hand, the ZI and ZZ interactions always have a specific phase, regardless of the sign of the irradiated cross-resonance drive pulse. That is, whether the sign of the cross-resonance drive pulse is positive or negative, the ZI and ZZ interactions are always positive or negative. Furthermore, when the quantum state of control qubit 101 is inverted by an echo pulse, the phases of all ZX, ZI, and ZZ interactions are inverted.

[0034] Thus, by setting the phases of the first and second cross-resonance drive pulses to be out of phase, and by irradiating with an echo pulse before the second cross-resonance drive pulse, the ZX interaction acts as an interaction with the same sign throughout the first and second halves of the gate operation. Therefore, the ZX interaction acts as an effective interaction throughout the entire gate operation. On the other hand, the ZI and ZZ interactions act as interactions with opposite signs in the first and second halves of the gate operation. Therefore, the effects of the ZI and ZZ interactions cancel each other out throughout the entire gate operation. In this way, TPCX makes it possible to achieve the desired ZX interaction while eliminating undesirable ZI interactions, residual ZZ interactions, and phase relaxation errors.

[0035] However, TPCX has the disadvantage of a slow gate execution speed. Generally, when applying a gate, the gate drive speed is determined by the pulse area of ​​the cross-resonance drive pulse shown in Figures 2 and 3. That is, the gate operation ends when this pulse area reaches a predetermined value. Therefore, to increase the gate execution speed, it is necessary to apply the largest possible pulse area in the shortest possible time. As shown in Figure 3, TPCX has two rising and falling edges of pulses, and also performs echo pulse irradiation. These time periods (also called pulse edges) correspond to the pulse gap period. Therefore, TPCX has a slower gate execution speed compared to DCX due to this pulse gap period. In reality, the pulse edge occupies about 10% to 20% of the pulse area.

[0036] The OPCX described below, using embodiments, aims to solve the problems of DCX and TPCX, and to achieve both high error tolerance and fast gate execution speed.

[0037] [First Embodiment] Figure 5 shows a functional block diagram of the quantum logic gate manipulation device 1 according to the first embodiment. The quantum logic gate manipulation device 1 comprises a two-qubit system 10, a cross-resonance drive pulse irradiation unit 20, an echo pulse irradiation unit 30, and a control unit 40. The two-qubit system 10 is formed by coupling a control qubit 11 and a target qubit 12. The cross-resonance drive pulse irradiation unit 20 irradiates the control qubit 11 with a cross-resonance drive pulse having the intrinsic frequency of the target qubit 12. The echo pulse irradiation unit 30 irradiates the control qubit 11 with an echo pulse to invert the quantum state of the control qubit 11.

[0038] The control of cross-resonance drive pulse irradiation and echo pulse irradiation in this embodiment will be described below with reference to Figures 6 to 8.

[0039] Figure 6 shows the temporal change of the cross-resonance drive pulse irradiated by OPCX. As shown in the figure, the cross-resonance drive pulse is irradiated between t10 and t13. That is, in OPCX, the cross-resonance drive pulse is irradiated only once, over the entire period of the gate operation. In this respect, OPCX differs from TPCX, in which the cross-resonance drive pulse is irradiated twice. However, between t10 and t11 (hereinafter referred to as the "first period"), the phase of the cross-resonance drive pulse is 0. Between t11 and t12 (hereinafter referred to as the "second period"), the cross-resonance drive pulse is irradiated while the intensity of the cross-resonance drive pulse remains constant, and the phase continuously changes from 0 to π. Between t12 and t13 (hereinafter referred to as the "third period"), the phase of the cross-resonance drive pulse is π.

[0040] Figure 7 shows the temporal change of the echo pulse irradiated by OPCX. As shown in the figure, the echo pulse is irradiated between t11 and t12, i.e., during the second period.

[0041] Figure 8 is a magnified view of the area around the second period in Figure 6. Figure 8 shows the real and imaginary parts of the cross-resonance drive pulse in complex number form. As shown in the figure, during the second period, a cross-resonance drive pulse of non-zero intensity is irradiated, and its phase is inverted.

[0042] Thus, OPCX performs phase inversion of cross-resonance drive pulses and irradiation with echo pulses. Therefore, like TPCX, OPCX is resistant to ZI interactions, residual ZZ interactions, and phase relaxation errors.

[0043] Figure 9 shows the phase change of the cross-resonance drive pulse of the OPCX on the complex plane. As shown, the vector of the cross-resonance drive pulse, which was constant in intensity and phase (0) until t11, begins to change phase at t11. In the second period (t11 to t12), the cross-resonance drive pulse changes phase from 0 to π, smoothly tracing along the cylinder while rotating, while maintaining a constant intensity. The echo pulse is irradiated during the second period. When the echo pulse irradiation ends at t12, the cross-resonance drive pulse continuously changes phase to π, and thereafter continues to irradiate with constant intensity and constant phase (π).

[0044] For comparison, Figure 10 shows the phase change of the TPCX cross-resonance drive pulse on the complex plane. As shown, the vector of the cross-resonance drive pulse, which was constant in intensity and phase (0) until t1, begins to decrease in intensity before the echo pulse is irradiated. At t1, the intensity of the cross-resonance drive pulse becomes zero. Between t1 and t2, the echo pulse is irradiated. When the echo pulse irradiation ends at t2, the phase of the cross-resonance drive pulse vector discontinuously reverses to π, and the intensity (absolute value of the intensity) increases until it becomes constant.

[0045] The control of cross-resonance drive pulse irradiation and echo pulse irradiation as described above is performed by the control unit 40. In this embodiment, the control unit 40 controls the cross-resonance drive pulse irradiation unit 20 to irradiate a cross-resonance drive pulse of the first phase during the first period of the quantum logic gate operation. The control unit 40 then controls the cross-resonance drive pulse irradiation unit 20 to irradiate a cross-resonance drive pulse while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase during the second period of the quantum logic gate operation, while maintaining the intensity of the cross-resonance drive pulse. The control unit 40 then controls the cross-resonance drive pulse irradiation unit 20 to irradiate a cross-resonance drive pulse of the second phase during the third period of the quantum logic gate operation. The control unit 40 then controls the echo pulse irradiation unit 30 to irradiate an echo pulse during the second period.

[0046] The effects of this embodiment will be explained below using Figure 11. Figure 11 shows the relationship between the drive intensity Ω and drive frequency Δ of the OPCX and TPCX. The horizontal axis shows the intensity of the cross-resonance drive pulse (however, the intensity, which has units of energy, is converted to units of frequency (MHz) by dividing it by Planck's constant. Also, a phase of 0 is considered positive and a phase of π is considered negative). In this example, the drive intensity Ω = 300 MHz for both the OPCX and TPCX. The drive frequency Δ on the vertical axis corresponds to the difference between the frequency of the microwave pulse irradiated onto the control qubit and the natural frequency of the control qubit. In this example, the microwave pulse frequency = 8.8 GHz and the natural frequency of the control qubit = 8.0 GHz, so Δ = 800 MHz. Figure 11 shows how the echo pulse modulates the drive frequency Δ and drive intensity Ω in the OPCX and TPCX.

[0047] In OPCX, the phase inversion of the cross-resonant drive pulse corresponds to temporarily changing the drive frequency Δ while keeping the drive intensity Ω at +300MHz. In this example, the phase is inverted from 0 to π in 20ns. This temporary change in drive frequency Δ is 25MHz. Therefore, the change in the cross-resonant drive pulse in OPCX is shown by the upward solid arrow from point P to Q and the downward solid arrow returning from point Q to point P in the figure. On the other hand, the change in the cross-resonant drive pulse in TPCX is a change in drive intensity Ω from +300MHz to -300MHz while keeping the drive frequency Δ at 800MHz, and is shown by the dashed arrow from point P through point S to point R in the figure.

[0048] The smoothness of the temporal change of a pulse can be evaluated by the non-adiabatic transition ε shown in equation (1) below (adiabatic theorem).

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[0049] From this perspective, we compare OPCX and TPCX. In OPCX, indicated by the two solid arrows, when the state changes from P to Q to P, the total change in the angular deviation relative to the origin is 0.57° × 2 = 1.14°. The distance to the origin gradually increases from point P, reaches a maximum at point Q, then decreases, and returns to its original value at point P. On the other hand, in TPCX, indicated by the dashed arrow, when the state changes from P to S to R, the magnitude of the change in the angular deviation relative to the origin is 41.1°. The distance to the origin gradually decreases from point P, reaches a minimum at point S, then increases, and returns to its original value at point R. As can be seen from the above, the magnitude of the change in angular deviation is smaller for OPCX than for TPCX. Therefore, for the same value of ε, OPCX can change the state in a shorter time (see the numerator of equation (1)). Also, the distance from the origin is longer for OPCX than for TPCX. Therefore, OPCX can make the value of ε smaller (see the denominator of equation (1)).

[0050] From the above, it can be seen that OPCX can perform gate operations in a shorter time than TPCX without increasing the value of ε (in other words, without compromising quality). Furthermore, as shown in Figure 8, in OPCX, the cross-resonance drive pulse is irradiated even during the period when the echo pulse is irradiated (the second period). That is, the ZX interaction is also at work during the second period. In contrast, in TPCX, the cross-resonance drive pulse is not irradiated during the period when the echo pulse is irradiated (t1~t2 in Figures 3 and 10). In this case, the ZX interaction is not at work during the period t1~t2. From this point of view as well, it can be seen that OPCX can achieve gate operations faster than TPCX.

[0051] Furthermore, OPCX has an advantage in terms of error tolerance. Specifically, because OPCX has a small ε value, it can reduce errors. In addition, OPCX has a shorter gate operation time than TPCX, which further reduces the probability of errors occurring.

[0052] As described above, this embodiment makes it possible to realize entangled quantum gate operations that maintain thermal insulation, have a high gate execution speed, and are resistant to ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors.

[0053] This embodiment includes various individual embodiments, as described below.

[0054] [Frequency modulation of echo pulses] In one embodiment, the control unit 40 may control the echo pulse irradiation unit 30 to frequency modulate the echo pulse. As mentioned above, in OPCX, a cross-resonance drive pulse is irradiated even during the period when the echo pulse is irradiated (second period). At this time, it is desirable that the echo pulse is modulated. This point will be explained below.

[0055] When a superconducting qubit is irradiated with non-resonant microwaves, different energy levels within the superconducting qubit become coupled via the irradiated microwave photons. As a result, a mutually anti-crossing effect (drive-induced AC Stark effect) is produced, as described below.

[0056] Driving frequency ω d is the transition frequency ω ge , ω ef We will now describe the time evolution when the system is sufficiently far from any of the three energy levels. In this case, each energy level in the three-level system is shifted by the influence of the AC Stark shift for both the ge transition and the ef transition. To verify this, we will consider the rotating coordinate system of the drive.

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[0057] From the above, it can be concluded that the resonance frequency ω of a superconducting qubit can be increased by irradiation with non-resonant microwaves. q (Energy difference between the first excited level and the ground level) and anharmonicness α qIt can be seen that a property called (the energy difference between the first and second excitation transitions) is modulated. At this time, the driving frequency of the echo pulse is the modulation component δω of the resonance frequency. q It is necessary to modulate accordingly.

[0058] In general, modern superconducting quantum computers generate qubit-controlled microwave pulses by multiplying a steady microwave generated from a local oscillator with a fixed drive frequency (~several GHz) with an arbitrary microwave waveform generated from an arbitrary waveform generator with a variable frequency (~several hundred MHz). Therefore, the modulation of the echo pulse's drive frequency is performed by the latter arbitrary waveform generator. The modulation frequency δω is set to the microwave waveform A(t) that is to be output from the arbitrary waveform generator. q B(t)=A(t)exp(-iδω) q t) is the waveform that is actually output.

[0059] More specifically, the degree of disharmonic α q The value of δα q By modulating only this component, the modulation (called DRAG) applied to the echo pulse to suppress non-adiabatic transitions also changes. In this modulation, a modulation obtained by multiplying the time derivative of the echo pulse waveform by a coefficient is applied to the complex component of the echo pulse. That is,

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[0060] According to this embodiment, echo pulses can be irradiated more appropriately during the second period.

[0061] [CNOT gate and root CNOT gate] In the example above, a CNOT gate was realized by appropriately setting the first and second periods. However, it is not limited to this; a square root gate, the root CNOT gate, can also be realized by appropriately setting the first and second periods.

[0062] In a two-qubit system irradiated with a cross-resonance drive pulse, rotation along the ZX axis occurs with angular velocity ω. In this case, the CNOT gate is locally equivalent to a 90-degree rotation along the ZX axis, and the root CNOT gate is locally equivalent to a 45-degree rotation along the ZX axis. The CNOT gate can be realized by setting the irradiation time t of the cross-resonance drive pulse to t = π / (2ω), and the root CNOT gate to t = π / (4ω).

[0063] According to this embodiment, various logic gates can be implemented.

[0064] [Degrees of freedom of rotation axis and rotation angle] In the example above, the phase of the cross-resonance drive pulse was changed from 0 to π by rotation around ZX. However, this is not the only way; the phase change of the cross-resonance drive pulse can be achieved by rotation around any axis or by rotation at any angle.

[0065] According to this embodiment, the degree of freedom in applications can be increased.

[0066] [Superconducting qubit] In one embodiment, the control qubit 11 and the target qubit 12 may be superconducting qubits such as transmons.

[0067] According to this embodiment, a quantum logic gate manipulation device can be realized using superconducting qubits.

[0068] [Arbitrary waveform generator] In one embodiment, the control unit may include an arbitrary waveform generator.

[0069] According to this embodiment, a quantum logic gate manipulation device can be realized using an existing device, such as an arbitrary waveform generator.

[0070] [Integrated implementation form] In one embodiment, the cross-resonance drive pulse irradiation unit 20 and the echo pulse irradiation unit 30 may be integrated. That is, the cross-resonance drive pulse irradiation unit 20 and the echo pulse irradiation unit 30 may be formed in a single integrated piece of hardware.

[0071] According to this embodiment, the number of devices in the system can be reduced, thus enabling a simpler configuration.

[0072] [Separate implementation type] In one embodiment, the cross-resonance drive pulse irradiation unit 20 and the echo pulse irradiation unit 30 may be separate components. That is, the cross-resonance drive pulse irradiation unit 20 and the echo pulse irradiation unit 30 may be formed as individual, independent hardware.

[0073] According to this embodiment, the degree of freedom in configuration can be increased.

[0074] [Multiple execution type OPCX] When phase inversion and echo pulse irradiation are performed in an OPCX gate, a very small amount of unwanted entanglement generation error can occur. This unwanted entanglement generation error can be eliminated by modifying the echo pulse waveform. However, a simpler method is to perform phase inversion and echo twice during OPCX execution to cancel out the unwanted entanglement error.

[0075] Figure 12 shows the temporal change of the cross-resonance drive pulse irradiated by a double-execution type OPCX. Figure 13 shows the temporal change of the echo pulse irradiated by a double-execution type OPCX. As shown in the figures, in this embodiment, the set of phase inversion of the cross-resonance drive and echo pulse irradiation in the OPCX is repeated twice. The number of repetitions is not limited to two, but can be any number.

[0076] Thus, by repeatedly performing phase inversion and echo operations on the cross-resonance drive during OPCX gate execution, more robust error tolerance can be achieved. However, there is a trade-off: increasing the number of echoes increases the execution time required to generate the desired entanglement, but it also increases the perturbation order of errors that can be eliminated.

[0077] [Second Embodiment] The second embodiment is a quantum logic gate operation method that performs quantum logic gate operations using a two-qubit system in which a control qubit and a target qubit are coupled. Figure 14 is a processing flow diagram of the quantum logic gate operation method according to this embodiment. This method includes a cross-resonance drive pulse irradiation step S1 and an echo pulse irradiation step S2. In the cross-resonance drive pulse irradiation step S1, the method irradiates the control qubit with a cross-resonance drive pulse of a first phase having the intrinsic frequency of the target qubit. At this time, the first phase cross-resonance drive pulse is irradiated during the first period of the quantum logic gate operation, the cross-resonance drive pulse is irradiated while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase while maintaining the intensity of the cross-resonance drive pulse, and the second phase cross-resonance drive pulse is irradiated during the third period of the quantum logic gate operation. In the echo pulse irradiation step S2, the method irradiates the control qubit with an echo pulse to invert the quantum state of the control qubit. During this time, an echo pulse is irradiated during the second period.

[0078] According to this embodiment, it is possible to perform entangled quantum gate operations using a two-qubit system that maintain adiabatic properties, have a high gate execution speed, and are resistant to ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors.

[0079] [Third Embodiment] The third embodiment is a program. This program causes a computer to perform a cross-resonance drive pulse irradiation step S1 and an echo pulse irradiation step S2. In the cross-resonance drive pulse irradiation step S1, the control qubit is irradiated with a cross-resonance drive pulse having the intrinsic frequency of the target qubit. At this time, during the first period of the quantum logic gate operation, a cross-resonance drive pulse of the first phase is irradiated, during the second period of the quantum logic gate operation, the cross-resonance drive pulse is irradiated while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase while maintaining the intensity of the cross-resonance drive pulse, and during the third period of the quantum logic gate operation, a cross-resonance drive pulse of the second phase is irradiated. In the echo pulse irradiation step S2, the control qubit is irradiated with an echo pulse to invert the quantum state of the control qubit. At this time, the echo pulse is irradiated during the second period.

[0080] According to this embodiment, a program can be implemented in software that performs entangled quantum gate operations using a two-qubit system, while maintaining adiabatic properties, achieving high gate execution speed, and being resistant to ZI interaction errors, residual ZZ interaction errors, and phase relaxation errors.

[0081] [evaluation] According to the inventors' evaluation, OPCX achieves performance equivalent to TPCX in terms of error tolerance. Regarding gate operation speed, TPCX is about 20% slower than DCX, while OPCX is only about 10% slower than DCX.

[0082] Below, with reference to Figures 15 to 17, we will compare DCX, TPCX, and OPCX in terms of entanglement rate (Cartan coefficient) and leakage amount.

[0083] Figure 15 shows the progression of the main term of the Cartan coefficient during gate operation. The main term of the Cartan coefficient is a coefficient that takes values ​​from 0 to π / 4. When the main term of the Cartan coefficient is 0, no entanglement occurs, and when it is π / 4, it is equivalent to a CNOT gate. Therefore, the faster the main term of the Cartan coefficient reaches π / 4, the faster the gate is. In Figure 15, the time to reach π / 4 is 126 ns for the DCX gate, 137 ns for the OPCX gate, and 162 ns for the TPCX gate, indicating that the speed increases in this order. In the OPCX and TPCX gates, there is a region in the middle of the gate where the increase in the Cartan coefficient temporarily stagnates, which corresponds to the pulse edge and echo pulse execution portion of the cross-resonance drive. In the case of the OPCX gate, unlike the TPCX gate, it is not necessary to return the intensity of the cross-resonance drive to 0 once, so the time duration during which the increase in the Cartan coefficient stagnates is extremely short. (Note that the echo pulse length is the same for both OPCX and TPCX).

[0084] Figure 16 shows the changes in the Cartan coefficient subterms as the gate operation is performed. The Cartan coefficient subterms are coefficients corresponding to the unintended entanglement components that occur during gate execution. Therefore, it is desirable that this value be as small as possible at the end of the gate. Note that in the OPCX gate, a small amount of unwanted entanglement error occurs due to the phase rotation of the cross-resonance drive and the irradiation of the echo pulse. To eliminate this unwanted entanglement error, the echo pulse is irradiated twice. As a result, the entanglement error has been successfully eliminated. It can be seen that the amount of entanglement error for DCX, TPCX, and OPCX is the same at the end of the gate operation.

[0085] Figure 17 shows the change in the amount of leakage of the Cartan coefficient during gate operation. The amount of leakage represents the amount by which the superconducting qubit escapes from the low-energy level space during gate operation. Of particular importance is the amount of leakage after the gate operation is completed. Basically, more leakage is generated by irradiating with a stronger intensity of cross-resonance drive. In the numerical calculations here, the same cross-resonance drive intensity is used for DCX, TPCX, and OPCX, so it can be seen that the final leakage is roughly the same for all of them. This fact suggests that unintended leakage does not occur due to the phase inversion of the high-speed cross-resonance drive in OPCX, and the echo pulses irradiated simultaneously.

[0086] The comparative analysis using the above numerical calculations demonstrated that the OPCX gate can generate entanglement faster than the TPCX gate.

[0087] The present disclosure has been described above based on embodiments. These embodiments are illustrative, and it will be understood by those skilled in the art that various modifications are possible in the combination of their components and processing processes, and that such modifications are also within the scope of the present disclosure.

[0088] [SQUID] The above embodiment involved irradiating the control qubit with a microwave pulse whose driving frequency was modulated as an echo pulse. However, the implementation is not limited to this. For example, in the case of a superconducting qubit with a variable resonance frequency that incorporates a circuit element called a superconducting flux quantum interferometer (SQUID), an implementation can be realized by applying periodic modulation of the magnetic flux bias to the SQUID.

[0089] In understanding the technical concept abstracted from the embodiments and modifications, that technical concept should not be interpreted restrictively to the content of the embodiments and modifications. The embodiments and modifications described above are merely examples, and many design changes, such as changes, additions, and deletions of components, are possible. In the embodiments, the content in which such design changes are possible is emphasized with the notation "embodiment." However, design changes are also permitted in content without such notation. [Explanation of Symbols]

[0090] 1. Quantum logic gate manipulation device 10··2 qubit system 11. Controlled Qubit 12 ··Target qubit 20. Cross-resonance drive pulse irradiation unit 30. Echo pulse irradiation area 40. Control Unit 100··2 qubit system 101 ·· Controlled Qubit 102 ··Target qubit S1... A step in which a cross-resonance drive pulse having the eigenfrequency of the target qubit is irradiated onto the control qubit. S2... A step in which an echo pulse is irradiated onto the control qubit to invert the quantum state of the control qubit.

Claims

1. A two-qubit system in which a control qubit and a target qubit are coupled, A cross-resonance drive pulse irradiation unit irradiates the control qubit with a cross-resonance drive pulse having the intrinsic frequency of the target qubit, The control qubit is irradiated with an echo pulse irradiating an echo pulse to invert the quantum state of the control qubit, Control unit and A quantum logic gate manipulation device equipped with, The control unit, During the first period of the quantum logic gate operation, the cross-resonance drive pulse of the first phase is irradiated, During the second period of the quantum logic gate operation, the cross-resonance drive pulse is irradiated while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase, while maintaining the intensity of the cross-resonance drive pulse. During the third period of the quantum logic gate operation, the cross-resonance drive pulse irradiation unit is controlled to irradiate with the cross-resonance drive pulse of the second phase. A quantum logic gate manipulation device characterized by controlling the echo pulse irradiation unit to irradiate echo pulses during the second period.

2. The quantum logic gate manipulation device according to claim 1, characterized in that the control unit controls the echo pulse irradiation unit to frequency modulate the echo pulse.

3. The quantum logic gate manipulation device according to claim 2, characterized in that the frequency modulation is a frequency modulation that follows the modulation of the resonance frequency of the control qubit.

4. The quantum logic gate manipulation device according to claim 3, characterized in that the frequency modulation is further increased by the change in the anharmonicness of the control qubit.

5. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the first phase is 0 and the second phase is π.

6. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that it is a CNOT gate.

7. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that it is a root CNOT gate.

8. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the control qubit and the target qubit are superconducting qubits.

9. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the control unit includes an arbitrary waveform generator.

10. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit are integrated.

11. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit are separate components.

12. The quantum logic gate manipulation device according to claim 1 or 2, characterized in that the control unit controls the cross-resonance drive pulse irradiation unit and the echo pulse irradiation unit to repeatedly perform a phase change of the cross-resonance drive pulse and the irradiation of the echo pulse.

13. A quantum logic gate operation method that performs quantum logic gate operations using a two-qubit system in which a control qubit and a target qubit are coupled, A cross-resonance drive pulse irradiation step in which the control qubit is irradiated with a cross-resonance drive pulse having the intrinsic frequency of the target qubit, The steps include an echo pulse irradiation step in which an echo pulse is irradiated onto the control qubit to invert the quantum state of the control qubit, Includes, In the aforementioned cross-resonance drive pulse irradiation step, During the first period of the quantum logic gate operation, the cross-resonance drive pulse of the first phase is irradiated, During the second period of the quantum logic gate operation, the cross-resonance drive pulse is irradiated while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase, while maintaining the intensity of the cross-resonance drive pulse. During the third period of the quantum logic gate operation, the cross-resonance drive pulse of the second phase is irradiated. The method is characterized in that the echo pulse irradiation step involves irradiating an echo pulse during the second period.

14. A program that causes a computer to perform quantum logic gate operations using a two-qubit system in which a control qubit and a target qubit are coupled, A cross-resonance drive pulse irradiation step in which the control qubit is irradiated with a cross-resonance drive pulse having the intrinsic frequency of the target qubit, The steps include an echo pulse irradiation step in which an echo pulse is irradiated onto the control qubit to invert the quantum state of the control qubit, Includes, In the aforementioned cross-resonance drive pulse irradiation step, During the first period of the quantum logic gate operation, the cross-resonance drive pulse of the first phase is irradiated, During the second period of the quantum logic gate operation, the cross-resonance drive pulse is irradiated while continuously changing the phase of the cross-resonance drive pulse from the first phase to the second phase, while maintaining the intensity of the cross-resonance drive pulse. During the third period of the quantum logic gate operation, the cross-resonance drive pulse of the second phase is irradiated. The program is characterized in that, in the echo pulse irradiation step, an echo pulse is irradiated during the second period.

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