Quantum device gate operation method, quantum device, quantum computer, and quantum calculation system

Abstract

To provide a quantum device gate operation method, a quantum device, a quantum computer, and a quantum calculation system which can easily be large-sized.SOLUTION: A gate operation method for a gate-type quantum device includes: a first control for controlling a ratio of a superposed state in a ground state by performing quantum annealing on a degenerated transverse magnetic field Ising Hamiltonian; a second control for releasing the degeneration without changing the ratio of the superposed state by applying a longitudinal magnetic field; and a third control for returning to an original Hamiltonian without changing the controlled ratio of the superposed state by performing quantum annealing in a state where only a transverse magnetic field is applied.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a gate operation method for a quantum device, a quantum device, a quantum computer, and a quantum computing system. [Background technology]

[0002] In recent years, quantum computers have been expected to enable calculations that are fundamentally impossible to achieve using classical computing. There are two main types of quantum computing known: quantum annealing and gate-based methods.

[0003] For example, Patent Document 1 discloses a method for realizing a unitary quantum gate for one or more quantum bits, the method including an operation of designing control pulses for the unitary quantum gate, the operation of designing the control pulses including an operation of defining a universal quantum control cost function, the control cost function including quantum bit leakage penalty terms representing i) coherent quantum bit leakage and ii) incoherent quantum bit leakage across all frequency components in the evolution of a time-dependent Hamiltonian that realizes the unitary quantum gate, the operation of designing the control pulses further including an operation of adjusting parameters of the time-dependent Hamiltonian evolution in accordance with the control cost function to change the control cost so as to reduce leakage errors, the method further including an operation of generating a control pulse using the adjusted parameters, and an operation of applying the control pulses to one or more quantum bits to realize the unitary quantum gate. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2021-512396 Summary of the Invention [Problem to be solved by the invention]

[0005] However, compared to quantum annealing, conventional gate-based quantum devices have had relatively difficult scaling up and integration to increase the number of qubits, and as a result, gate-based quantum devices tend to have fewer qubits than quantum annealing devices.

[0006] The present invention has been made in consideration of the above circumstances, and one of its objects is to provide a gate operation method for a quantum device, a quantum device, a quantum computer, and a quantum computing system that can be easily scaled up. [Means for solving the problem]

[0007] A gate operation method for a gate-type quantum device according to one aspect of the present invention includes a first control that controls the ratio of superposition states of the ground state by quantum annealing to a degenerate transverse magnetic field Ising Hamiltonian, a second control that removes the degeneracy without changing the ratio of the superposition states by applying a longitudinal magnetic field, and a third control that returns to the original Hamiltonian without changing the ratio of the controlled superposition states by quantum annealing to a state in which only a transverse magnetic field is applied. [Effects of the Invention]

[0008] According to the present invention, gate-type quantum devices can be easily scaled up. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram showing an example of a schematic configuration of a quantum computing system according to an embodiment. [Figure 2] FIG. 2 is a diagram for explaining the procedure of gate-based quantum computing. [Figure 3] FIG. 3 is a diagram illustrating an example of an overall view of quantum computing of a quantum computer and a quantum device according to an embodiment. [Figure 4] FIG. 4 is a diagram illustrating an example of state transitions caused by gate operations of a quantum computer and a quantum device according to an embodiment. [Figure 5] FIG. 5 is a diagram for explaining an example of a state transition due to the first control shown in FIG. [Figure 6] FIG. 6 is a diagram for explaining an example of control of the overlap state in the first control shown in FIG. [Figure 7] FIG. 7 is a diagram for explaining an example of a change in Hamiltonian due to gate operations of a quantum computer and a quantum device in one embodiment. [Figure 8] FIG. 8 is a graph showing an example of the calculation result of the overlap ratio of the first control shown in FIG. 4 in the example of the X-axis rotary gate. [Figure 9] FIG. 9 is a graph showing an example of the calculation result of the overlap ratio of the third control shown in FIG. 4 in the example of the X-axis rotary gate. [Figure 10] FIG. 10 is a graph showing an example of the results of a demonstration conducted using a commercial service regarding the first control shown in FIG. 4 in the example of an X-axis rotating gate. [Figure 11] FIG. 11 is a diagram for explaining the energy levels of the first control shown in FIG. 4 in the example of the C-NOT gate. [Figure 12] FIG. 12 is a diagram for explaining the energy level of the third control shown in FIG. 4 in the example of the C-NOT gate. [Figure 13] FIG. 13 is a graph showing an example of the calculation result of the overlap ratio of the first control shown in FIG. 4 in the example of the C-NOT gate. [Figure 14] FIG. 14 is a graph showing an example of the results of a demonstration conducted using a commercial service regarding the first control shown in FIG. 4 in the example of the C-NOT gate. [Figure 15] FIG. 15 is a diagram showing the relationship between the direction of the current flowing through the superconducting circuit in a superconducting flux qubit and the state of the qubit. [Figure 16] FIG. 16 is a diagram illustrating a circuit of a superconducting flux qubit. [Figure 17] FIG. 17 is a diagram for explaining the change in potential in a superconducting flux qubit. [Figure 18] FIG. 18 is a diagram illustrating a circuit with a coupler between two superconducting flux qubits. DETAILED DESCRIPTION OF THE INVENTION

[0010] An embodiment of the present invention will be described below. In the following description of the drawings, identical or similar parts are denoted by identical or similar reference numerals. However, the drawings are schematic. Therefore, specific dimensions and the like should be determined in light of the following description. Furthermore, it goes without saying that the dimensional relationships and ratios of parts included in the drawings differ from one another. Furthermore, the technical scope of the present invention should not be interpreted as being limited to the embodiment.

[0011] First, a schematic configuration of a quantum computing system according to an embodiment will be described with reference to Fig. 1. Fig. 1 is a configuration diagram showing an example of a schematic configuration of a quantum computing system 200 according to an embodiment.

[0012] [Quantum Computing Systems and Quantum Computers] 1, the quantum computing system 200 includes a quantum computer 100 and a computer 101. The quantum computing system 200 is configured to perform quantum computation.

[0013] The quantum computer 100 is also called a quantum computer. The quantum computer 100 includes a quantum device 110, which will be described later. The quantum computer 100 is configured to perform calculations using a quantum bit 115 of the quantum device 110, which can be in two states, for example, a superposition of a "0" state and a "1" state. The quantum computer 100 is connected to a computer 101 and is configured to receive at least one of data, information, and control signals from the computer 101, for example, and perform the quantum calculations described above.

[0014] The computer 101 is a conventional computer, a so-called classical computer. Although not shown, the computer 101 includes a processor such as a central processing unit (CPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), or a system-on-a-chip (SoC), a memory including a read only memory (ROM), an erasable programmable read only memory (EPROM), an electrically erasable programmable read only memory (EEPROM), a random access memory (RAM), a cache memory, and / or a buffer memory, and a storage device including a storage such as an HDD, an SSD, and / or an eMMC.

[0015] The quantum computing system 200 may include other devices instead of or in addition to the computer 101. For example, the quantum computing system 200 may include an input device configured to allow a user to input information through a user operation. The input device may include, for example, a keyboard, a touch panel, a mouse, a pointing device, and / or a microphone. The quantum computing system 200 may also include an output device configured to output information. The output device may include, for example, a display device such as a liquid crystal display, an EL (Electro Luminescence) display, a plasma display, an organic light-emitting diode (OLED) display, a mini LED display, or a micro LED display, and / or a printing device such as a printer. At least one of these input devices and output devices may be included in the quantum computer 100 and / or the computer 101.

[0016] The quantum computer 100 and the computer 101 may be configured to communicate via at least one of a wired and a wireless communication network. In this case, each of the quantum computer 100 and the computer 101 includes a communication device configured to include, for example, a network card, a communication module, an interface for connecting to other devices, etc. The communication network may be, for example, a local area network (LAN), a dedicated line, an in-house network, the Internet, a telephone line, a mobile communication network, Bluetooth (registered trademark), Wi-Fi (Wireless Fidelity), other communication lines, or a combination of these. Furthermore, the communication network may be either wired or wireless, or may be a combination of wired and wireless.

[0017] [Quantum Devices] Quantum device 110 includes control unit 111 and quantum bit 115. Quantum bit 115 in quantum device 110 includes at least one quantum bit. In the following description, unless otherwise specified, quantum bit 115 will be described as including multiple quantum pits.

[0018] Control unit 111 is configured to control quantum bits 115. More specifically, control unit 111 is configured to control, for each quantum bit of quantum bits 115, two quantum mechanical levels, that is, a superposition state (hereinafter simply referred to as a "superposition state") of two states (hereinafter, the respective states are also referred to as "0" and "1").

[0019] As described above, each quantum bit of quantum bits 115 has the property of being able to assume a superposition state in addition to "0" and "1" (quantum property). Quantum bits 115 having such a property can be realized using various systems, such as a superconducting system, a spin system, or a cooled electron system.

[0020] Next, the gate type method and quantum annealing method related to quantum computing will be described.

[0021] <Gate type method> Figure 2 is a diagram explaining the procedure for gate-based quantum computing. The gate-based method is a universal quantum computing method, that is, a method that can realize any quantum computation. The procedure for gate-based quantum computing is as follows: first, an initial state is prepared, as shown in Figure 2. What is prepared at this time is a vector. Next, a unitary operator corresponding to the algorithm is applied to each site to perform a unitary operation. The unitary operator is sometimes called a unitary matrix. Finally, a measurement is performed.

[0022] There are algorithms for which quantum acceleration is guaranteed using gate-based methods. However, executing such algorithms requires quantum error correction, which requires a large number of auxiliary qubits. Furthermore, when qubits are based on superconducting methods, which are the most actively researched method, it is said to be more difficult to scale than quantum annealing methods, which will be discussed later. This is thought to be because the superconducting method requires control of both DC magnetic fields and microwaves. Furthermore, in 2019, Google achieved a gate-based quantum device, a quantum computer, with approximately 60 qubits.

[0023] It is known that quantum gates can realize any unitary operation with a limited number of unitary operations. Such a combination of unitary operations is called a universal gate set. The following combinations are examples of universal gate sets in quantum gates:

[0024]

number

[0025] In this way, if a universal gate set can be realized in quantum gates, any quantum computation using a gate-based method can be performed.

[0026] <Quantum annealing method> Quantum annealing is a quantum computation method for finding Hamiltonians (also called Hamiltonian functions), primarily the ground state of the Ising model. By embedding combinatorial optimization problems into the Ising model, it is possible to find optimization problems such as the traveling salesman problem.

[0027] In quantum annealing, first, a Hamiltonian with a trivial ground state and that ground state are prepared as the initial state. Next, the trivial Hamiltonian is gradually changed to the desired Hamiltonian with a nontrivial ground state as time evolves. Finally, the final state is measured to determine the ground state of the desired nontrivial Hamiltonian.

[0028] Specifically, we define the Hamiltonian with a trivial ground state as H D Let the nontrivial Hamiltonian we want to find (also called the "problem Hamiltonian") be H P Then, the time-dependent Hamiltonian H(t) can be expressed as follows:

[0029]

number

[0030] By varying the time t from zero to T over a long enough time, we perform an adiabatic time evolution that traces the ground state over a long enough time. This gives rise to the nontrivial Hamiltonian H P The ground state of can be obtained.

[0031] The quantum annealing method generally has the following advantages: -It uses only the transverse magnetic field Ising model, and in the case of superconducting qubits, microwaves are not required, making it easy to scale experimentally and relatively easy to increase the scale and integrate. In the case of the transverse magnetic field Ising model, D-Wave Systems has realized a real machine with approximately 5,000 qubits using superconducting methods. -Superconducting systems are easier to scale experimentally because they do not require microwave operation or control. It has already been commercialized, with cloud-based services available from D-Wave Systems.

[0032] On the other hand, the quantum annealing method generally has the following drawbacks and problems. - Quantum computing cannot be realized arbitrarily; only specific problems, primarily combinatorial optimization problems, can be solved. · It is unclear whether quantum acceleration exists.

[0033] In contrast to this, the gate type method described above generally has the following advantages. -Algorithms that are guaranteed to be quantum accelerated, such as Shor, Grover, and phase estimation, can be executed. -It is possible to realize arbitrary quantum computation, called universal quantum computation. -It is already commercially available and the service is available on the cloud.

[0034] On the other hand, the gate type method described above generally has the following drawbacks and problems. The largest superconducting quantum bits require microwave operation, making it relatively difficult to scale up and integrate them. · Operations on quantum bits require high precision. Universal quantum computing requires quantum error correction using 100 to 10,000 physical qubits per logical qubit.

[0035] Thus, the realization of gate-based quantum computers, especially those with error-tolerant mechanisms, is expected to enable arbitrary quantum computations and truly guarantee quantum acceleration, making the realization of large-scale devices highly anticipated. In particular, achieving error-tolerant mechanisms requires a huge number of qubits, estimated to be as many as one million, making large-scale implementation and integration extremely important challenges. Currently, with superconducting qubits, which are considered very promising, quantum annealing methods have been able to realize 10 to 100 times more qubits than gate-based methods. This is thought to be due to the difficulty of realizing microwave operation, while quantum annealing devices do not require microwaves. Therefore, achieving microwave-free gate operation is considered one way to resolve the bottleneck in the expansion of gate-based quantum computers.

[0036] <Overall picture> Next, an overview of quantum computing by a quantum computer and a quantum device according to an embodiment will be described with reference to Fig. 3. Fig. 3 is a diagram showing an example of an overview of quantum computing by a quantum computer 100 and a quantum device 110 according to an embodiment.

[0037] The quantum computer 100 and the quantum device 110 employ gate-based quantum computing. As shown in Fig. 3, the quantum computer 100 and the quantum device 110 implement a universal gate set using three quantum gates, for example, an X-axis rotation gate (denoted as "X-rotation" in Fig. 3), a Z-axis rotation gate (denoted as "Z-rotation" in Fig. 3), and a C-NOT gate (denoted as "C-NOT" in Fig. 3). In the idle state, the strength of the transverse magnetic field of the even-numbered quantum bits is changed from the strength of the transverse magnetic field of the odd-numbered quantum bits.

[0038] <Procedure> Next, with reference to Figs. 4 to 7, a procedure for operating the quantum gates of the quantum computer and quantum device according to one embodiment (hereinafter also simply referred to as "gate operation") will be described. Fig. 4 is a diagram for explaining an example of state transitions due to gate operations of the quantum computer 100 and the quantum device 110 in one embodiment. Fig. 5 is a diagram for explaining an example of state transitions due to the first control 310 shown in Fig. 4. Fig. 6 is a diagram for explaining an example of control of the superposition state in the first control 310 shown in Fig. 4. Fig. 7 is a diagram for explaining an example of changes in the Hamiltonian due to gate operations of the quantum computer 100 and the quantum device 110 in one embodiment.

[0039] The quantum computer 100 and quantum device 110 realize gate operation using the quantum annealing method of the transverse magnetic field Ising model, which has been considered to be relatively easy to scale up. More specifically, the ratio of degenerate states is controlled by adjusting the scheduling in quantum annealing to the degenerate transverse magnetic field Ising model. This realizes gate operation using only the transverse magnetic field Ising model, which does not require microwaves.

[0040] Specifically, as shown in FIG. 4, the gate operations in the quantum computer 100 and the quantum device 110 include a first control 310, a second control 320, and a third control 330.

[0041] The first control 310 controls the ratio of the superposition state of the ground state by quantum annealing to the degenerate Ising model. The first control 310 causes a transition from the ground state (denoted as "Ground state" in FIG. 4) to the adjacent state (the adjacent state to the right in FIG. 4).

[0042] The second control 320 removes the degeneracy without changing the ratio of the superposition state by applying a longitudinal magnetic field. Although the degeneracy of the ground state is removed by the second control 320, the ratio of the superposition state does not change from that by the first control 310.

[0043] The third control 330 performs quantum annealing to a state where only a transverse magnetic field is applied, returning the Hamiltonian to its original state without changing the controlled ratio. The third control 330 changes the ratio between the initial state and the superposition state. In this way, gate operations of the X-axis rotation gate and the C-NOT gate can be realized. Note that the gate operation of the Z-axis rotation gate uses a conventionally known phase difference to realize the rotation operation.

[0044] The first control 310 can be said to be a state manipulation that utilizes the degenerate Ising model and the degeneracy caused by the transverse magnetic field. That is, as shown in Fig. 5, the first control 310 creates a superposition state of degenerate states by performing quantum annealing on the degenerate Ising Hamiltonian. The first control 310 changes the ratio of the superposition state by controlling the strength of the longitudinal magnetic field.

[0045] As shown in Figure 6, the ratio of superposition states is controlled by temporarily applying and then turning off a longitudinal magnetic field during quantum annealing. Note that the vertical axis of the graph in Figure 6 represents intensity, and the value h is a setting given by the user. This method makes it possible to create a variety of superposition states, not just gate operations.

[0046] The Hamiltonians corresponding to the first control 310 to the third control 330 in the gate operation of the quantum computer 100 and the quantum device 110 shown in Fig. 4 change as shown in Fig. 7. In Fig. 7, the longitudinal magnetic field is H C Also, as shown in Figure 7,

number

[0047] In the first control 310 (also referred to as the "Forward part" in FIG. 7), superimposition at any ratio is achieved by transitioning between states, whereas in the third control 330 (also referred to as the "Reverse part" in FIG. 7), there is no transition between states.

[0048] (Example of X-axis rotating gate) Next, an X-axis rotary gate of a quantum computer and quantum device according to an embodiment will be described with reference to FIGS. 8 to 10. FIG. 8 is a graph showing an example of a calculation result of the superposition ratio of the first control 310 shown in FIG. 4 in the example of the X-axis rotary gate. FIG. 9 is a graph showing an example of a calculation result of the superposition ratio of the third control 330 shown in FIG. 4 in the example of the X-axis rotary gate. FIG. 10 is a graph showing an example of a demonstration result performed using a commercial service for the first control 310 shown in FIG. 4 in the example of the X-axis rotary gate. In FIGS. 8 to 10, the vertical axis represents the ratio of the superposition state, which is a value between zero and one, and the horizontal axis represents the strength (Hz) of the longitudinal magnetic field applied along the way.

[0049] The Ising Hamiltonian used to realize the X rotation gate is the Hamiltonian H D Set as follows:

[0050]

number

[0051] Also, the nontrivial Hamiltonian we want to find, that is, the problem Hamiltonian H P Set as follows:

[0052]

number

[0053] Problem Hamiltonian H Pis degenerate between |↓> and |↑>. The superposition state can be controlled by controlling the ratio of these two states with a longitudinal magnetic field.

[0054] 8, the ratio of the superposition state is changed by changing the strength hz of the vertical magnetic field in the first control 310. Note that the initial state is |+>=(|↑>+|↓>) / √2).

[0055] As shown in Figure 9, in the third control 330, the ratio of the superposition state is similarly changed by changing the strength (Hz) of the vertical magnetic field. In this way, by controlling the strength (Hz) of the vertical magnetic field, the ratio of the superposition state can be set arbitrarily. Therefore, rotational operation at any rotation angle can be realized, and gate operation of the X-axis rotary gate can be realized without using microwaves, which were necessary in conventional gate-type systems.

[0056] Here, we compare the calculation results shown in Figures 8 and 9 with the results of a demonstration using a commercial service provided on the cloud. The commercial service on the cloud uses a device from D-Wave Systems (hereinafter referred to as the "D-Wave device"). The D-Wave device allows only |+> to be prepared as the initial state. Furthermore, the D-Wave device is only capable of measuring the Ising model. This corresponds to the final state in Figure 5 (the superposition state in Figure 5).

[0057] As shown in Figure 10, in the D-Wave device, the ratio of the superposition state changes by changing the strength (Hz) of the vertical magnetic field, just as in the calculation results shown in Figure 8. Therefore, it can be said that the actual device also achieves gate operation equivalent to the X-axis rotary gate.

[0058] (Example of a C-NOT gate) Next, referring to FIGS. 11 to 14, the C-NOT gate of the quantum computer and the quantum device according to an embodiment will be described. FIG. 11 is a diagram for explaining the energy levels of the first control 310 shown in FIG. 4 in an example of the C-NOT gate. FIG. 12 is a diagram for explaining the energy levels of the third control 330 shown in FIG. 4 in an example of the C-NOT gate. FIG. 13 is a graph showing an example of the calculation result of the superposition ratio of the first control 310 shown in FIG. 4 in an example of the C-NOT gate. FIG. 14 is a graph showing an example of the demonstration result obtained by using a commercial service for the first control 310 shown in FIG. 4 in an example of the C-NOT gate. In FIGS. 13 to 14, the vertical axis represents the ratio of the superposition state, which is a numerical value between zero and one, and the horizontal axis is the intensity hz of the longitudinal magnetic field applied in the middle.

[0059] The Ising Hamiltonian used when realizing the C-NOT gate has a Hamiltonian H with a trivial ground state D set as follows. [[ID=۸]]

[0060] [Number]

[0061] Also, the non-trivial Hamiltonian to be obtained, that is, the problem Hamiltonian H P is set as follows.

[0062] [Number]

[0063] The problem Hamiltonian H P has |↓↑> and |↓↓> degenerate in the range of 0 < a < 1. By controlling the ratio of these two states with the longitudinal magnetic field in the middle, the superposition state is controlled.

[0064] Since the C-NOT gate is a gate operation for two qubits, there are four states. In the first control 310 shown in FIG. 4, the energy levels of each state are as shown in FIG. 11. As shown in the lower part of FIG. 11, when the first qubit is |↓>, the second qubit remains unchanged. The ratio of the superposition states can be controlled between the degenerate states in the lower part. On the other hand, as shown in the middle and upper parts of FIG. 11, when the first qubit is |↑>, a rotation operation is applied to the second qubit.

[0065] In the third control 330, the Hamiltonian with degeneracy removed is set as follows.

[0066] [Number]

[0067] At this time, when a < b and 0 < b < 1, the energy levels of each state are as shown in FIG. 12. As can be seen from FIG. 12, the degeneracy of all levels is removed. Also, when corresponding to the energy levels of the transverse magnetic field, |↓> corresponds to |+> and |↑> corresponds to |->. This corresponds to the Hadamard gate.

[0068] As shown in FIG. 13, in the first control 310, by changing the intensity hz of the longitudinal magnetic field, the ratio of the superposition states changes. In FIG. 13, the calculation results for each of the four initial states, namely, (a) |++>, (b) |+->, (c) |-+>, and (d) |--> are shown. As can be seen from FIG. 13, when the first qubit is +, a rotation operation is applied to the second qubit. Also, when the first qubit is -, the second qubit remains unchanged. In this way, the gate operation of the C-NOT gate can be realized without using microwaves that were necessary in the conventional gate-type method.

[0069] Here, we compare the calculation results shown in Figure 13 with the results of a demonstration using a commercial service provided on the cloud. The commercial service on the cloud uses a D-Wave device. With the D-Wave device, it is possible to prepare only |++> as the initial state. Furthermore, with the D-Wave device, it is only possible to measure the Ising model. This corresponds to the final state in Figure 5 (the superposition state in Figure 5).

[0070] As shown in Figure 14, in the D-Wave device, as with the calculation results shown in Figure 13, when the first qubit is ↓, the second qubit is rotated, and when the first qubit is ↑, the second qubit remains unchanged. Therefore, it can be said that a gate operation equivalent to a C-NOT gate can be realized in the actual device.

[0071] <How to achieve this> A quantum computer and a quantum device according to an embodiment can be basically realized using adiabatic time evolution if the transverse magnetic field Ising model can be realized. Currently, the following quantum devices are known that can realize the transverse magnetic field Ising model. Superconducting qubits Transmon qubits Flux qubits KPO type qubit Neutral atomic quantum bits NMR quantum bits -Ion trap quantum computer Optical quantum bits ·semiconductor ·diamond

[0072] Among the quantum devices that can realize the above-mentioned transverse magnetic field Ising model, we will explain the specific realization method by taking the superconducting flux bit used in D-Wave devices and other superconducting devices as an example, focusing in particular on a method called rf-SQUID.

[0073] In this method, first consider a superconducting circuit, and as shown in Figure 15, two states, |↑> (up) and |↓> (down), are expressed by the direction of the current flowing through the circuit. A magnetic field controls the direction of the current, with a rightward direction representing up and a leftward direction representing down. Since there is zero resistance in a superconducting circuit, the state can be maintained stably.

[0074] The circuit of a superconducting flux qubit, such as a D-Wave device, looks like Figure 16, and the potential of this system is controlled by controlling the strength of the magnetic field (magnetic flux Φin, Φout) that penetrates the two rings.

[0075] The quantum annealing mechanism can be explained by a time-varying energy diagram, as shown in Figure 17. Initially, there is a single valley (a) with a minimum, but as the quantum annealing process runs, the barrier rises and transforms into a double-well potential (b). Here, the left valley corresponds to the 0 state (equivalent to up) and the right valley corresponds to the 1 state (equivalent to down). The qubit will end up in one of these valleys at the end of quantum annealing.

[0076] In this case, the probability of the qubit ending up in either the 0 or 1 state is equal, but this probability can be controlled by applying an external magnetic field to the qubit, as shown in (c). This field tilts the double-well potential, increasing the probability that the qubit will end up in the lower well. Here, controlling the magnetic flux Φin corresponds to the transverse magnetic field, and controlling the magnetic flux Φout corresponds to the local longitudinal magnetic field, so the following term can be realized:

[0077]

number

[0078] Furthermore, by creating a coupling circuit between the two flux qubits shown in Figure 16 as shown in Figure 18 and adjusting Φco in particular, we can control the interaction (Jij) between the two qubits. This allows us to realize the following terms:

[0079]

number

[0080] Therefore, by controlling the longitudinal magnetic field and transverse magnetic field and realizing the interaction, it is possible to realize the following transverse magnetic field Ising model, which is required for the quantum computer and quantum device according to one embodiment.

[0081]

number

[0082] <Embodiment> A quantum device according to one embodiment basically realizes quantum gates, which are the basic elements of quantum computers, and can therefore be applied to all algorithms expected of quantum computers, such as speeding up quantum chemical calculations, speeding up financial calculations, speeding up machine learning on quantum data, and speeding up the solution of differential equations.

[0083] As a specific algorithm, we will explain the Grover search algorithm. The search problem is to search for M correct labels from a database consisting of N elements.

[0084] Step 1: Prepare a superposition of all states. A Hadamard gate is applied to all quantum bits to prepare a superposition of all states as follows:

[0085]

number

[0086] Step 2: Apply Oracle U. The operator Uw that inverts only the correct labels is given as follows:

[0087]

number

[0088] At this time, the oracle U acts on the state |x> of a certain Z basis (computational basis), and the sign of only the correct data is inverted as follows:

[0089]

number

[0090] Step 3: Apply the inversion operation Us with |s> as the axis of symmetry. The operator Us that inverts only the correct labels is given as follows:

[0091]

number

[0092] At this time, it acts on |ψ> as follows, and the phase (sign) of only the term related to |s⊥> is inverted.

number

[0093] Step 4: Repeat steps 2 and 3 k times. By repeatedly applying the operator Uw in step 2 and the operator Us in step 3 O(√((N / M))) times, the correct answer can be obtained with a sufficiently high probability in the measurement in the next step 5.

[0094] Step 5: Take measurements. Current state: (UwUs) k By measuring |s> in the z-base, the correct answer can be found with a high probability.

[0095] The quantum device gate operation method, quantum device, quantum computer, and quantum computing system of the present application have at least one of the following advantages and effects in addition to or in addition to the above-described embodiments.

[0096] By utilizing quantum annealing of the transverse magnetic field Ising model, which is generally easy to create experimentally on large-scale quantum devices, it is possible to realize gate operations that do not require microwaves, thereby solving the bottleneck in increasing the scale of gate-type quantum computers.

[0097] Due to the characteristics of this technique, it has the properties of both gate-type quantum computers and quantum annealing (analog quantum computing), so operations that would require many quantum gates in normal gate operations can be achieved with a small number of gate operations.

[0098] Since quantum annealing of a small number of systems is performed, a technique called adiabatic shortcut can be used, allowing gate operations to be performed very quickly.

[0099] Among the components called universal gate sets that are the minimum necessary to realize any gate operation, the X-axis rotation gate and the C-NOT gate can be realized by performing quantum annealing on a degenerate Hamiltonian for these gate operations, and then controlling the ratio of the two superposition states in the final state by applying a longitudinal magnetic field during this quantum annealing.

[0100] Furthermore, numerical calculations were performed on the X-axis rotation gate and the C-NOT gate, as well as experiments using actual D-Wave devices on the cloud. As a result, the operation of these two gates was realized through numerical calculations, and the theory was also reproduced in demonstrations using actual devices.

[0101] By using quantum annealing on a degenerate Hamiltonian, various superposition states can be created adiabatically. In addition to its application to gate-based quantum computing, it can also be used as a method for efficiently creating various superposition states, including entangled states.

[0102] It is not limited to specific experimental systems such as superconducting qubits, but can be realized in various systems such as cold atom systems.

[0103] Furthermore, the specification, claims, and drawings of the present application encompass at least the following inventions together with or in addition to the description of the above embodiments.

[0104] -Methods for realizing superposition states using degeneracy and gate operations. - A method for realizing quantum superposition states and gate operations using quantum annealing with a degenerate Hamiltonian as the problem Hamiltonian.

[0105] A method that allows smooth operation of many gates by idling the transverse magnetic field. A method that uses the analog quantum computing properties of quantum annealing to perform a large number of gate operations with a small number of operations. A method to speed up gate operations using adiabatic shortcuts in gate operations using degeneracy.

[0106] A method for realizing gate operation using only the transverse magnetic field Ising model, which is considered relatively easy to scale up, and controlling the ratio of degenerate states by adjusting the scheduling in quantum annealing to the degenerate transverse magnetic field Ising model, without the need for microwaves. A method for realizing a gate-type quantum computer using the above-mentioned method for realizing gate operations.

[0107] The techniques described in this specification are not limited to superconducting systems, but can also be used in many other systems, such as neutral atoms, ions, semiconductors, light, nanomechanical machines, nuclear magnetic resonance (NMR), diamonds, etc.

[0108] The above-described embodiments are intended to facilitate understanding of the present invention and are not intended to limit the scope of the present invention. The present invention may be modified or improved without departing from its spirit, and equivalents are also encompassed within the scope of the present invention. In other words, designs modified by those skilled in the art as appropriate are also encompassed within the scope of the present invention as long as they incorporate the characteristics of the present invention. For example, the elements of the embodiments, their arrangement, materials, conditions, shapes, sizes, etc., are not limited to those illustrated and can be modified as appropriate. Furthermore, the embodiments are merely examples, and partial substitution or combination of the configurations shown in different embodiments is, of course, possible. These are also encompassed within the scope of the present invention as long as they incorporate the characteristics of the present invention.

Claims

1. A first control that controls the ratio of the superposition state of the ground state by quantum annealing to a degenerate transverse magnetic field Ising Hamiltonian; A second control that removes degeneracy without changing the ratio of the superposition state by applying a longitudinal magnetic field; A third control is performed to return the Hamiltonian to the original state without changing the ratio of the controlled superposition state by performing quantum annealing to a state in which only a transverse magnetic field is applied. A gate operation method for a gate-type quantum device, comprising:

2. 2. The method for operating a gate in a quantum device according to claim 1, wherein the ratio of the superposition states is controlled by controlling the strength of a longitudinal magnetic field applied during the quantum annealing in the first control.

3. 3. The method for operating a gate on a quantum device according to claim 1, wherein the quantum device is an X-axis rotation gate and / or a C-NOT gate.

4. A first control that controls the ratio of the superposition state of the ground state by quantum annealing to a degenerate transverse magnetic field Ising Hamiltonian; A second control that removes degeneracy without changing the ratio of the superposition state by applying a longitudinal magnetic field; A third control that returns the controlled superposition state to the original Hamiltonian without changing the ratio of the controlled superposition state by performing quantum annealing in a transverse magnetic field; A gate-type quantum device in which gate operations are performed by

5. 5. The quantum device according to claim 4, which is an X-axis rotation gate and / or a C-NOT gate.

6. A quantum computer comprising the quantum device according to claim 4 or 5.

7. A quantum computing system comprising the quantum computer according to claim 6 and a computer.

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