WO2021177031A1

WO2021177031A1 - Quantum computer, quantum computation method, and program

Info

Publication number: WO2021177031A1
Application number: PCT/JP2021/005889
Authority: WO
Inventors: 雄一郎松下; 小杉　太一; 紘史西
Original assignee: 国立大学法人東京工業大学
Priority date: 2020-03-06
Filing date: 2021-02-17
Publication date: 2021-09-10
Also published as: JPWO2021177031A1

Abstract

[Problem] To provide a technology related to a quantum computer in which the overall number of gate operations is reduced. [Solution] One embodiment of the present invention provides a quantum computer capable of using an imaginary time evolution method to process an optimization problem. This quantum computer is provided with a quantum processor and a storage unit. The quantum processor is configured so as to read a program stored in the storage unit to execute each subsequent step. In a cost function setting step, a prescribed cost function is set as the series sum of a first operator that acts on two quantum bits. The cost function probabilistically has a plurality of levels. In a computation step, an imaginary time evolution computation is executed, in which the existence probability of a desired level among the plurality of levels is increased by means of a quantum gate that includes an imaginary time evolution operator which is dependent on the first operator. With regard to making the imaginary time evolution operator unitary, the first operator is expressed as the series sum of a second operator comprising only a small number of quantum bit operations.

Description

Quantum computer, quantum calculation method and program

The present invention relates to a quantum computer, a quantum calculation method, and a program.

Quantum information processing using quantum mechanics for information processing has been proposed. In addition, many quantum computers based on such quantum information processing have been studied.

For example, Non-Patent Document 1 discloses a quantum calculation algorithm using an imaginary time evolution method.

However, the number of gate operations in NISQ has a strict upper limit that cannot be taken large. If the number of gate operations becomes enormous, not only will it be difficult to realize it as a quantum computer, but it will also be greatly affected by errors that occur during gate operations. Therefore, quantum computers, quantum computing methods, and programs that reduce the number of gate operations as much as possible are important.

In view of the above circumstances, the present invention has decided to provide a technique related to a quantum computer in which the total number of gate operations is reduced.

According to one aspect of the present invention, a quantum computer capable of processing an optimization problem using an imaginary time evolution method is provided. This quantum computer includes a quantum processor and a storage unit. The quantum processor is configured to execute each of the following steps by reading the program stored in the storage unit. In the cost function setting step, a predetermined cost function is set as the series sum of the first operator acting on the two qubits. The cost function stochastically has multiple levels. In the calculation step, a quantum gate including an imaginary time evolution operator that depends on the first operator executes an imaginary time evolution operation that increases the existence probability of a desired level among a plurality of levels. When the imaginary time evolution operator is unitaryized, the first operator is expressed as a series sum of the second operator consisting only of minority qubit operations.

In such a quantum computer, the total number of gate operations is smaller than the number of normal gate operations when the imaginary time evolution method is used, so that it can be realized as realistic NISQ hardware.

It is a block diagram which shows the hardware structure of a quantum computer 1. It is a block diagram which shows the functional structure of the quantum computer 1 (control unit 5). It shows the relationship between the number of gate operations required to execute the imaginary time evolution operator U (Δτ) when it is truncated at a predetermined number of qubits and the size of the problem. This is an example of a schematic diagram of a Max-cut problem in which the number of elements is N = 10. The mode of convergence to the desired level E according to the conventional (comparative example) and the present embodiment when the imaginary time is developed is shown. This is another example of the schematic diagram of the Max-cut problem in which the number of elements is N = 10. The mode of convergence to the desired level E according to the conventional (comparative example) and the present embodiment when the imaginary time is developed is shown. It is a block diagram which shows the gate operation which concerns on this embodiment. The Max-cut problem shown in FIG. 4 is developed by the new quantum calculation method (D = 2) in imaginary time, and the gate operation is bundled in addition to the new quantum calculation method (D = 2). It shows the mode of convergence to the desired level E when the imaginary time evolution is carried out. It is an activity diagram which shows an example of a quantum calculation method.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. The various features shown in the embodiments shown below can be combined with each other.

By the way, the program for realizing the software appearing in the present embodiment may be provided as a non-transitory recording medium (Non-Transity Computer-Readable Medium) that can be read by a computer, or may be downloaded from an external server. It may be provided as possible, or it may be provided so that the program is started by an external computer and the function is realized by the client terminal (so-called cloud computing).

Further, in the present embodiment, the "part" may include, for example, a combination of hardware resources implemented by a circuit in a broad sense and information processing of software that can be concretely realized by these hardware resources. .. In addition, various information is handled in this embodiment, and these information are, for example, physical values of signal values representing voltage and current, and signal values as a binary bit set composed of 0 or 1. It is represented by high-low or quantum superposition (so-called qubit), and communication / operation can be executed on a circuit in a broad sense.

Further, a circuit in a broad sense is a circuit realized by at least appropriately combining a circuit (Circuit), circuits (Circuitry), a processor (Processor), a memory (Memory), and the like. That is, an integrated circuit for a specific application (Application Special Integrated Circuit: ASIC), a programmable logic device (for example, a simple programmable logic device (Simple Programmable Logical Device: SPLD), a composite programmable logic device (Complex Program)) It includes a programmable gate array (Field Programmable Gate Array: FPGA) and the like.

1. 1. Hardware configuration This section describes the hardware configuration of the quantum computer 1 that is configured to be able to process optimization problems using the imaginary time evolution method.

FIG. 1 is a block diagram showing the hardware configuration of the quantum computer 1. As shown in FIG. 1, the quantum computer 1 includes a communication unit 3, a storage unit 4, a control unit 5, a display unit 6, and an input unit 7, and these components are the quantum computer 1. It is internally connected via the communication bus 2. Hereinafter, each component will be further described.

(Communication unit 3)
The communication unit 3 is used for the quantum computer 1 to perform information communication with another information processing device (including a classical computer, a quantum computer, or a computer combining them) or a peripheral device. Although wired communication means such as quantum memory, USB, IEEE1394, Thunderbolt, and wired LAN network communication are preferable, the communication unit 3 is wireless LAN network communication, mobile communication such as 3G / LTE / 5G, and Bluetooth (registered trademark) communication. Etc. may be included as necessary. That is, it is more preferable to carry out as a set of these plurality of communication means.

(Memory unit 4)
The storage unit 4 stores various information defined by the above description. This is, for example, a quantum memory, a storage device such as a solid state drive (SSD), or a quantum memory that stores temporarily necessary information (arguments, arrays, etc.) related to program operations, random access. It can be implemented as a memory such as a memory (Random Access Memory: RAM). Moreover, these combinations may be used.

In particular, the storage unit 4 stores a cost function setting unit program, an initialization program, a quantum gate program, a number determination program, and a specific program that can be read by the control unit 5 described below. Further, the storage unit 4 stores the optimization problem that can be processed by the quantum computer 1 as needed.

(Control unit 5)
The control unit 5 processes and controls the entire operation related to the quantum computer 1. The control unit 5 is, for example, a central processing unit (CPU) (not shown). More preferably, the control unit 5 is a quantum processor. The control unit 5 realizes various functions related to the quantum computer 1 by reading a predetermined program stored in the storage unit 4 or input via the communication unit 3. Specifically, it corresponds to a cost function setting function, an initialization function, a quantum gate function, a number of times determination function, and a specific function. That is, information processing by software (stored in the storage unit 4 or input from another information processing device via the communication unit 3) is specifically realized by the hardware (control unit 5). As shown in FIG. 2, it can be executed as a cost function setting unit 51, an initialization unit 52, a quantum gate 53, a number of times determination unit 54, and a specific unit 55. These will be described in detail in Section 2.

Although it is described as a single control unit 5 in FIG. 1, it is not actually limited to this, and it may be implemented so as to have a plurality of control units 5 for each function. Moreover, it may be a combination thereof.

(Display unit 6)
The display unit 6 may be included in the housing of the quantum computer 1 or may be externally attached, for example. The display unit 6 displays a screen of a graphical user interface (GUI) that can be operated by the user. For example, it is preferable to appropriately implement a display device such as a CRT display, a liquid crystal display, an organic EL display, and a plasma display.

(Input unit 7)
The input unit 7 may be included in the housing of the quantum computer 1 or may be externally attached. For example, the input unit 7 may be implemented as a touch panel integrally with the display unit 6. If it is a touch panel, the user can input a tap operation, a swipe operation, and the like. Of course, instead of the touch panel, a switch button, a mouse, a QWERTY keyboard, or the like may be adopted. The user can input an optimization problem (for example, the Max-cut problem described later) to be processed by the quantum computer 1 via the input unit 7.

2. Functional configuration This section describes the functional configuration of the quantum computer 1 according to this embodiment. FIG. 2 is a block diagram showing a functional configuration of the quantum computer 1 (control unit 5). Regarding the above-mentioned control unit 5, the quantum computer 1 includes a cost function setting unit 51, an initialization unit 52, a quantum gate 53, a number of times determination unit 54, and a specific unit 55. Hereinafter, each component will be further described.

(Cost function setting unit 51)
The cost function setting unit 51 is a predetermined cost function L as a series sum of the first operator L_ij acting on the two qubits for the optimization problem input by the user via the input unit 7 or the communication unit 3. Is configured to set. Here, the cost function L stochastically has a plurality of levels. That is, the cost function L quantum-mechanically holds a plurality of solutions superposed, and one of them is stochastically determined by observation.

(Initialization unit 52)
The initialization unit 52 is configured to initialize the cost function L set by the cost function setting unit 51. For example, the initialization unit 52 can initialize the cost function L by causing the Hadamard gate to act on all the qubits as an initial state. The initialized cost function L will have a plurality of levels with equal probability. In addition to using the initial state having a plurality of levels with equal probability, a state generated by some other method can also be used as the initial state.

(Quantum gate 53)
The quantum gate 53 includes an imaginary time evolution operator U that depends on the first operator L_ij. Further, the quantum gate 53 is composed of a plurality of (for example, X)

quantum gates

531, 532, 533, ..., 53X (see FIG. 2). The quantum gate 53 is configured to perform an imaginary time evolution operation that increases the existence probability of a desired level E among a plurality of levels by the imaginary time evolution operator U. By the way, in the operation by the quantum gate 53, unitaryization of the operator is indispensable. For example, when unitizing the imaginary time evolution operator U, the first operator L_ij can be expressed as a series sum of 2 qubits, 3 qubits, 4 qubits, or more. ..

However, the number of gate operations when the number of qubits is cut off is about 16N using the number of qubits N, and the number of gate operations when the number of qubits is cut off is about 96N. Is about 512N, and the number of gate operations is generally 4 ^ D * D (N-1) / 2 when the process is terminated up to the D qubit operation. The number of gate operations increases exponentially according to the number of qubits. Resulting in. Further, since it is known that at least about 6 qubit operations are usually required to maintain meaningful calculation accuracy, a large number of gate operations are required, and such an imaginary time evolution operator U is used. This does not result in a computational complexity suitable for NISQ. (See Fig. 3)

Therefore, in the present embodiment, when the imaginary time evolution operator U is unitaryized, the first operator L_ij is represented as a series sum of the second operators A_kl, A_klm ,,, which consist only of minority qubit operations. It is ingeniously devised so that it can be done. The minority qubits referred to here are 2,3,4,5 qubits, preferably 2,3,4 qubits, more preferably 2,3 qubits, and most preferably. It is 2 qubits. In other words, the number of gate operations in one quantum gate 53 can be reduced by terminating up to a small number of qubit operations. It should be noted that preferably, the first operator L_ij includes the first subscript set ij independent of each other, and the second operators A_kl, A_klm ,,, are the second independent subscript set ij. Includes subscripts kl, klm ,,,. As a result, in general, the number of gate operations when the process is terminated up to the D qubit operation can be suppressed to the order of 4 ^ D * N ^ {D-1}. For example, when the second operator is terminated by up to 2 qubit operations, the number of gate operations is about 16N, and when it is terminated by up to 3 qubit operations, it is about 64N ^ 2. (However, the number of gate operations can be reduced to order N by capturing only a part of the second operator A_klm even if the operation is terminated up to 3 qubit operations.) For example, the number of nodes in a weighted graph can be reduced to 2. The problem of dividing into two groups (so-called Max-cut problem) is an example of an optimization problem that can be handled without losing generality. For such an optimization problem, as a second operator, it has been confirmed that the accuracy is sufficient even if it is terminated by up to 2 qubit operations, and one quantum gate 53 solves the optimization problem. The number of gate operations on the order of about 16N will be provided. FIG. 4 is a schematic diagram of the Max-cut problem in which the number of elements is N = 10. Of course, this is just an example, and if it includes an optimization problem in which the number of calculations increases exponentially in a classical computer, as well as an optimization problem that appears in electronic state calculation, machine learning, etc., what kind of problem is set. You may.

(Number of times determination unit 54)
In the present embodiment, when the imaginary time evolution operator U is unitaryized, the first gate operation originally performed in the imaginary time step Δτ unit is combined with the critical number Δk as one new second gate operation. It is more preferable to handle. In such a case, the number of times determination unit 54 determines the number of critical times Δk so that the error of the imaginary time evolution between the case where the first gate operation is performed and the case where the second gate operation is performed is within a predetermined range. Is configured to determine. The number of critical times Δk determined by the number determination unit 54 need not be uniquely determined, and preferably the number determination unit 54 is configured to determine the critical number Δk for each second gate operation. NS. That is, according to the number of times determination unit 54, the number of gate operations can be reduced to about 1 / Δk times.

As a method for determining the critical number Δk, preferably, the number determination unit 54 repeatedly executes an increase process for increasing the critical number by 1, and increases when the energy of the system increases in the increase process in the predetermined order. The processing is interrupted, and the predetermined number of times or a value 1 less than this is set as the critical number of times. In other words, while appropriately performing the increase process of increasing the value of Δk by 1, the first gate operation is sequentially summarized as the second gate operation, and before the increase process of increasing Δk by 1 at a certain timing. Later, when the energy of the system rises when the second operator is operated, the update of the value of Δk may be stopped there. This is because the error of the imaginary time evolution is accumulated by summarizing, and the magnitude of the error becomes larger than the effect of lowering the energy by the imaginary time evolution operator U to the same level.

(Specific part 55)
The identification unit 55 is configured to identify the desired level E of the cost function L developed in imaginary time by the quantum gate 53. As described above, by repeating the quantum gate 53 and the number of times determination unit 54 as many times as necessary, the cost function L is developed in imaginary time, and as a result, the existence probability of the desired level E (low cost or low energy) increases. do. In the case of the Max-cut problem shown in FIG. 4, the value obtained by multiplying the level E specified by the specific unit 55 by -1 can be specified as the solution of the optimization problem, and 11 is specified as the solution. ..

3. 3. Theory This theory supplements the quantum mechanical theory of functional composition described above.

3.1 2 Qubit truncation The cost function L for a given problem is expressed as Equation 1 using the first operator L_i.

On the other hand, the imaginary time evolution operator U (NΔτ) that advances the time in the imaginary time direction by NΔτ is expressed by Equation 2.

Further, the imaginary time evolution operator U (Δτ), which advances the time in the imaginary time direction by Δτ, is expressed as in Equation 3.

Therefore, the imaginary time evolution operator U (NΔτ) is expressed as the product of the imaginary time evolution operator U (Δτ) as shown in Equation 4.

Since each imaginary time evolution operator U (Δτ) has N_pair (order amount of N ^ 2) gate operations, assuming that the number of steps of Δτ is N_step, the total number of gate operations is generally the total number of gate operations. It is expressed as the number 5.

Here, since the first operator L_i is an operator that normally acts on two qubits, it will be written again as the first operator L_ij. In unitizing the imaginary time evolution operator U, in order to realize a good unitization of the imaginary time step, L_ij included in the imaginary time evolution operator U is represented by two or more qubit operations (see Equation 6). ).

FIG. 3 shows the relationship between the number of gate operations required to execute the imaginary time evolution operator U (Δτ) when the number of qubits is cut off and the size of the problem. Comparative Example A is censored by a 4-qubit operation. Comparative Example B is censored by a 3-qubit operation. Comparative Example C is censored by a two-qubit operation. As described above, since the D qubit operation includes 4 ^ D * D (N-1) / 2 gate operations, we do not want to include operations more than multiple qubits as much as possible. On the other hand, the following empirical examples also show that 6 qubit operations or more are required to realize unitaryization that maintains calculation accuracy.

As shown in Equation 7, the inventors have a second operator having a second subscript set kl, klm ,,, which is independent of the first subscript set ij included in the first operator L_ij. By expressing the first operator L_ij as the series sum of A_kl, A_klm ,,,, we newly discovered that sufficient accuracy is maintained even if it is cut off by a small number of qubit operations. In this embodiment, this is newly discovered. It was decided to adopt.

FIG. 5 shows the application result to the Max-cut problem shown in FIG. 4 as a demonstration of the effectiveness of this calculation method. This calculation method, program, and this quantum computer are executed on a quantum computer. Here, in the simulation of a quantum computer using a classical computer, the effectiveness of the above calculation method, program, and this quantum computer. Demonstrated.

FIG. 5 shows a mode of convergence to the desired level E according to the conventional method (for comparison) and the present embodiment when the imaginary time is developed. From FIG. 5, the effectiveness of the new calculation method was demonstrated. In the conventional method, the accuracy is not obtained when censored at D = 2, but it can be seen that the accuracy is sufficient when censored at D = 6. On the other hand, it can be seen that with the new calculation method, the accuracy equivalent to D = 6 (conventional method) has already been obtained at D = 2. On the other hand, it should be noted that the number of gate operations at the new D = 2 is 1/768 of the number of gate operations at D = 6 (conventional method), which is for NISQ. .. Furthermore, when the conventional method and the new calculation method are applied to another Max-cut problem in which the number of elements shown in FIG. 6 is N = 10, a comparison is made. In the conventional method, even at D = 6. While the accuracy is not high, it can be seen that the new calculation method has already achieved good accuracy at D = 2. (See Fig. 7)

FIG. 8 is a block diagram showing a gate operation according to the present embodiment. As shown in FIG. 7, in the case of the present embodiment in which the two qubits are cut off, the number of gate operations (which has been confirmed to have sufficient accuracy even if the two qubits are cut off) is large. It is significantly reduced to the order of N times (N is the number of qubits). It should be noted that by reducing the number of gate operations in this way, the possibility of implementation in NISQ has increased.

3.2 Bundle of gate operations In this embodiment, attention is paid to the approximation shown in Equation 8 in order to further reduce the number of gate operations.

Such an approximation is preferably one in which Δτ is sufficiently small and is acceptable in the first order of Δτ. Since it is only an approximation, it is not preferable to use it as an entire imaginary time evolution, but if it is within a predetermined error range, for example, three gate operations (first gate operation) are combined into one operation (one operation). It can be a second gate operation (see Equation 9). In this way, the number N_critical that combines the first gate operation as the second gate operation corresponds to the above-mentioned critical number Δk.

Therefore, according to such bundling of gate operations, the total number of gate operations is expressed as several tens. It should be noted that by further reducing the number of gate operations in this way, the feasibility of mounting on NISQ has further increased.

FIG. 9 shows the case where the Max-cut problem represented by FIG. 4 is developed in imaginary time by the new quantum calculation method (D = 2), and the gate operation in addition to the new quantum calculation method (D = 2). It shows the mode of convergence to the desired level E when the bundled imaginary time evolution is carried out. By repeating the second gate operation, as shown in FIG. 9, the existence probability of the desired level E can be converged to a value close to 1. It can be seen that this is not inferior to the case where the gate operation is not bundled.

4. Quantum calculation method This section describes the quantum calculation method based on the quantum computer 1. This quantum calculation method includes a cost function setting step and an imaginary time evolution step. In the cost function setting step, a predetermined cost function L is set as the series sum of the first operator L_ij acting on the two qubits. Here, the cost function L stochastically has a plurality of levels. In the imaginary time evolution step, the imaginary time evolution operator U, which depends on the first operator L_ij, performs imaginary time evolution that increases the existence probability of the desired level E among the plurality of levels. Here, when the imaginary time evolution operator U is unitaryized, the first operator L_ij is expressed as a series sum of the second operators A_kl, A_klm ,,, which consist only of minority qubit operations. Preferably, when the imaginary time evolution operator U is unitaryized, the first gate operation originally performed in the imaginary time step Δτ unit is treated as one new second gate operation by collecting the critical number Δk. .. This calculation method is executed on a quantum computer or as a quantum computer simulation on a classical computer.

FIG. 10 is an activity diagram showing an example of the quantum calculation method. Hereinafter, this quantum calculation method will be described along with each activity in FIG.

(Activity A1)
The cost function setting unit 51 sets the cost function L for the optimization problem input in advance by the input unit 7 or the communication unit 3. In other words, the quantum processor, which is an example of the control unit 5, executes the cost function setting step by reading the program stored in the storage unit 4.

(Activities A2 and A3)
The initialization unit 52 initializes the qubit of the cost function L. The first operator L_ij, which is terminated by the above-mentioned minority qubit operation (operation of about 2 qubits or 3 qubits), is set.

(Activities A4 to A6)
Activities A4 to A6 are repeatedly executed as a process of imaginary time evolution. First, the number of times determination unit 54 determines the critical number of times Δk in which a plurality of first gate operations are bundled as a second gate operation within a range in which an error can be tolerated. In other words, the quantum processor, which is an example of the control unit 5, executes the critical number determination step by reading the program stored in the storage unit 4. Then, the quantum gate 53 collectively executes these as a second gate operation. After that, k is advanced by Δk and the process is repeated. As a result, imaginary time evolution progresses. In other words, the quantum processor, which is an example of the control unit 5, executes the calculation step by reading the program stored in the storage unit 4.

(Activity A7)
When the imaginary time evolution is made, the identification unit 55 identifies the desired level E whose existence probability has converged to 1. In other words, the quantum processor, which is an example of the control unit 5, executes a specific step by reading the program stored in the storage unit 4.

5. Modification example This section describes a modification example of the quantum computer 1. That is, the quantum computer 1 according to the present embodiment may be further creatively devised according to the following aspects.

(1) Since the effect of censoring a small number of qubits and the effect of bundling gate operations occur independently, only one of them may be implemented.
(2) A program that causes a computer to execute each step in the quantum computer 1 may be executed. This program may be in a form that can be downloaded from a server, may be executed or distributed on a cloud computer, or may be stored in a non-volatile or volatile storage medium, and such a program may be stored. May be distributed.

6. Conclusion As described above, according to the present embodiment, it is possible to implement a quantum computer, a quantum calculation method, and a program in which the total number of gate operations is reduced.

It may be provided in each of the following aspects.
In the quantum computer, the first operator includes a first subscript set that is independent of each other, and the second operator includes a second subscript set that is independent of the first subscript set. thing.
In the quantum computer, the quantum processor is configured to further execute a specific step by reading a program stored in the storage unit, and in the specific step, the imaginary time is developed by the quantum gate. A cost function that identifies the desired level.
In the quantum computer, one quantum gate has a number of gates on the order of the number of qubits included in the cost function in solving the optimization problem.
In the quantum computer, the optimization problem includes a problem in which the number of calculations increases exponentially in a classical computer, a problem appearing in electronic state calculation, or an optimization problem appearing in machine learning.
A quantum computer capable of processing an optimization problem using an imaginary time evolution method, the quantum processor includes a quantum processor, and the quantum processor executes each of the following steps by reading a program stored in the storage unit. In the cost function setting step, a predetermined cost function is set as the sum of the series of the first operator acting on the two qubits, where the cost function has a plurality of levels probabilistically. Then, in the calculation step, the imaginary time evolution calculation that increases the existence probability of the desired level among the plurality of levels is executed by the quantum gate including the imaginary time evolution operator that depends on the first operator. Then, when the imaginary time evolution operator is unified, the first gate operation originally performed in the imaginary time step unit is treated as one new second gate operation by collecting the critical times, and the calculation is performed. Things to do.
In the quantum computer, the quantum processor is configured to further execute the number-of-times determination step by reading a program stored in the storage unit, and in the number-of-times determination step, the first gate operation is performed. The number of critical times is determined so that the error of imaginary time evolution between the case and the case where the second gate operation is performed is within a predetermined range.
In the quantum computer, in the number-of-times determination step, the critical number of times is determined for each of the second gate operations.
In the quantum computer, in the number-of-times determination step, an increase process for increasing the critical number of times by 1 is repeatedly executed, and when the energy of the system increases in the increase process in a predetermined order, the increase process is interrupted. , The predetermined number of times or a value one less than this is set as the critical number of times.
It is a quantum calculation method capable of processing an optimization problem using an imaginary time evolution method, and includes a cost function setting step and a calculation step. In the cost function setting step, a first calculation acting on two qubits. A predetermined cost function is set as the sum of the qubits of the children, where the cost function has a plurality of levels probabilistically, and in the calculation step, an imaginary time evolution operator that depends on the first operator. The qubit gate containing the above executes an operation of imaginary time evolution that increases the existence probability of a desired level among the plurality of levels, and here, when the imaginary time evolution operator is unitized, the first A method in which one operator is represented as a sum of functions of a second operator consisting only of minority qubit operations.
In the quantum calculation method, the first operator includes a first subscript set that is independent of each other, and the second operator includes a second subscript set that is independent of the first subscript set. ,Method.
A method of the quantum calculation method further comprising a specific step, in which the desired level of the cost function developed by the quantum gate in the imaginary time is specified.
In the quantum calculation method, one quantum gate has a number of gates on the order of the number of qubits included in the cost function in solving the optimization problem.
In the quantum calculation method, the optimization problem includes a problem in which the number of calculations increases exponentially in a classical computer, a problem appearing in electronic state calculation, or an optimization problem appearing in machine learning.
It is a quantum calculation method capable of processing an optimization problem using an imaginary time evolution method, and includes a cost function setting step and a calculation step. In the cost function setting step, a first calculation acting on two qubits. A predetermined cost function is set as the sum of the qubits of the children, where the cost function has a plurality of levels probabilistically, and in the calculation step, an imaginary time evolution operator that depends on the first operator. By a qubit gate containing A method of performing an operation by treating the first gate operation to be performed as one new second gate operation collectively for the number of critical times.
The quantum calculation method further includes a number-of-times determination step, and in the number-of-times determination step, an error in imaginary time evolution between the case where the first gate operation is performed and the case where the second gate operation is performed is within a predetermined range. A method of determining the number of critical times so as to be within.
In the quantum calculation method, in the number-of-times determination step, the critical number of times is determined for each of the second gate operations.
In the quantum calculation method, in the number-of-times determination step, an increase process for increasing the critical number of times by 1 is repeatedly executed, and when the energy of the system increases in the increase process in a predetermined order, the increase process is interrupted. Then, the method of setting the critical number of times to the predetermined number of times or a value one less than this.
A program that causes a computer to perform each step of the quantum calculation method.
Of course, this is not the case.

Finally, various embodiments according to the present invention have been described, but these are presented as examples and are not intended to limit the scope of the invention. The novel embodiment can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the gist of the invention. The embodiment and its modifications are included in the scope and gist of the invention, and are included in the scope of the invention described in the claims and the equivalent scope thereof.

1: Quantum computer 2: Communication bus 3: Communication unit 4: Storage unit 5: Control unit 51: Cost function setting unit 52: Initialization unit 53: Quantum gate 531: Quantum gate 532: Quantum gate 533: Quantum gate 53X: Quantum Gate 54: Number of times determination unit 55: Specific unit 6: Display unit 7: Input unit

Claims

A quantum computer that can handle optimization problems using the imaginary time evolution method.
Equipped with a quantum processor and a storage unit
The quantum processor is configured to execute each of the following steps by reading a program stored in the storage unit.
In the cost function setting step, a predetermined cost function is set as the series sum of the first operator acting on the two qubits, where the cost function stochastically has a plurality of levels.
In the calculation step, a qubit that includes an imaginary time evolution operator that depends on the first operator executes an imaginary time evolution operation that increases the existence probability of a desired level among the plurality of levels. Here, when the imaginary time evolution operator is unitized, the first operator is represented as the sum of the series of the second operator consisting only of minority qubit operations.
In the quantum computer according to claim 1,
The first operator includes a first subscript set that is independent of each other.
The second operator includes a second subscript set that is independent of the first subscript set.
In the quantum computer according to claim 1 or 2.
The quantum processor is configured to further execute a specific step by reading a program stored in the storage unit.
In the specific step, the desired level of the cost function developed by the quantum gate in the imaginary time is specified.
In the quantum computer according to any one of claims 1 to 3.
One of the quantum gates has a number of gates on the order of the number of qubits included in the cost function in solving the optimization problem.
In the quantum computer according to claim 4,
The optimization problem includes a problem in which the number of calculations increases exponentially in a classical computer, a problem appearing in electronic state calculation, or an optimization problem appearing in machine learning.
A quantum computer that can handle optimization problems using the imaginary time evolution method.
Equipped with a quantum processor and a storage unit
The quantum processor is configured to execute each of the following steps by reading a program stored in the storage unit.
In the cost function setting step, a predetermined cost function is set as the series sum of the first operator acting on the two qubits, where the cost function stochastically has a plurality of levels.
In the calculation step
A quantum gate containing an imaginary time evolution operator that depends on the first operator executes an imaginary time evolution operation that increases the existence probability of a desired level among the plurality of levels.
When the imaginary time evolution operator is unitaryized, the first gate operation originally performed in the imaginary time step unit is treated as one new second gate operation by collecting the critical times, and the operation is executed. ,thing.
In the quantum computer according to claim 6,
The quantum processor is configured to further execute the number determination step by reading the program stored in the storage unit.
In the number-of-times determination step, the critical number of times is determined so that the error of imaginary time evolution between the case where the first gate operation is performed and the case where the second gate operation is performed is within a predetermined range. thing.
In the quantum computer according to claim 7,
In the number-of-times determination step, the critical number of times is determined for each of the second gate operations.
In the quantum computer according to claim 8,
In the number-of-times determination step,
The increasing process of increasing the number of critical times by 1 is repeatedly executed.
In the increase process in the predetermined order, when the energy of the system rises, the increase process is interrupted and the predetermined order or a value one less than this is set as the critical number.
It is a quantum calculation method that can process optimization problems using the imaginary time evolution method.
It has a cost function setting step and a calculation step.
In the cost function setting step, a predetermined cost function is set as the series sum of the first operator acting on the two qubits, where the cost function stochastically has a plurality of levels.
In the calculation step, a qubit evolution operation that increases the existence probability of a desired level among the plurality of levels is executed by a qubit gate including an imaginary time evolution operator that depends on the first operator. Here, when the imaginary time evolution operator is unitized, the first operator is represented as the sum of the series of the second operator consisting only of minority qubit operations.
In the quantum calculation method according to claim 10,
The first operator includes a first subscript set that is independent of each other.
The method comprising the second operator a second subscript set independent of the first subscript set.
In the quantum calculation method according to claim 10 or 11.
With more specific steps
In the specific step, a method of identifying the desired level of the cost function developed by the quantum gate in the imaginary time.
In the quantum calculation method according to any one of claims 10 to 12,
One of the quantum gates has a number of gates on the order of the number of qubits included in the cost function in solving the optimization problem.
In the quantum calculation method according to claim 13,
The optimization problem is a method including a problem in which the number of calculations increases exponentially in a classical computer, a problem appearing in electronic state calculation, or an optimization problem appearing in machine learning.
It is a quantum calculation method that can process optimization problems using the imaginary time evolution method.
It has a cost function setting step and a calculation step.
In the cost function setting step, a predetermined cost function is set as the series sum of the first operator acting on the two qubits, where the cost function stochastically has a plurality of levels.
In the calculation step,
An imaginary time evolution that increases the existence probability of a desired level among the plurality of levels is performed by a quantum gate including an imaginary time evolution operator that depends on the first operator.
When the imaginary time evolution operator is unitaryized, the first gate operation originally performed in the imaginary time step unit is treated as one new second gate operation by collecting the critical times, and the operation is executed. ,Method.
In the quantum calculation method according to claim 15,
With more steps to determine the number of times
In the number-of-times determination step, the critical number of times is determined so that the error of imaginary time evolution between the case where the first gate operation is performed and the case where the second gate operation is performed is within a predetermined range. Method.
In the quantum calculation method according to claim 16,
In the number-of-times determination step, the critical number of times is determined for each of the second gate operations.
In the quantum calculation method according to claim 17,
In the number-of-times determination step,
The increasing process of increasing the number of critical times by 1 is repeatedly executed.
A method in which, when the energy of the system rises in the increase process in the predetermined order, the increase process is interrupted and the predetermined order or a value one less than this is set as the critical number.
It ’s a program
A computer that causes a computer to perform each step of the quantum calculation method according to any one of claims 10 to 18.