Quantum compilation device, quantum compilation method, and program

Abstract

This quantum compilation device obtains, for a set {U1,..., UK} in which unitary matrices representing base gates and / or unitary matrices representing the product of unitary matrices representing base gates are elements U1,...,UK, and for a unitary matrix U representing a quantum circuit to be compiled, a probability p(k) that minimizes the error between a first observed value distribution obtained by observing, using a given observation method, a first quantum state obtained by applying the quantum circuit to be compiled represented by the unitary matrix U to a given input quantum state, and a second observed value distribution obtained by observing, using the aforementioned observation method, a second quantum state obtained by applying quantum circuits respectively expressed by the plurality of elements Uk∈{U1,..., UK} of the set {U1,..., UK} to the aforementioned input quantum state at the probability p(k), and outputs the element Uk at the probability p(k). K is an integer greater than or equal to 2, and k=1,..., K.

Description

[Technical field]

[0001] The present invention relates to a technique for compiling quantum circuits. [Background technology]

[0002] Many quantum circuits are composed of small quantum circuits on a constant number of qubits. Furthermore, many methods have been proposed for decomposing (=compiling) these small quantum circuits into multiple elementary gates (elementary gate elements). Here, the operation of a quantum circuit or elementary gate can be expressed in the form of a unitary matrix acting on a complex vector representing the input quantum state. Hereafter, a unitary matrix that expresses the operation of a quantum circuit will be called a unitary matrix that expresses the operation of an elementary gate, and a unitary matrix that expresses the operation of an elementary gate will be called a unitary matrix that expresses the operation of an elementary gate.

[0003] Non-Patent Document 1 discloses a quantum compilation method that approximates a unitary matrix representing an arbitrary quantum circuit with a finite number of unitary matrices or a product of unitary matrices. A unitary matrix and a product of unitary matrices respectively represent a basic gate and a combination of multiple basic gates. Hereinafter, a basic gate and / or a combination of multiple basic gates is collectively referred to as a basic gate sequence. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Aram W. Harrow, Benjamin Recht, Isaac L. Chuang, "Efficient Discrete Approximations of Quantum Gates," Journal of Mathematical Physics 43, 4445 (2002) Summary of the Invention [Problem to be solved by the invention]

[0005] The compilation method of Non-Patent Document 1 is to deterministically search for one basic gate sequence that most accurately realizes the quantum circuit to be compiled from a number of basic gate sequence candidates. The approximation accuracy is higher as the number of basic gate sequence candidates increases, and the number of basic gate sequence candidates increases as the number of basic gates that can be combined in the basic gate sequence increases. In other words, the longer the basic gate sequence, the higher the approximation accuracy. On the other hand, from the viewpoint of compilation efficiency, it is preferable to use a short basic gate sequence, i.e., a small number of basic gates.

[0006] The present invention has been made in consideration of the above points, and has an object to provide a quantum compiling technique that can improve approximation accuracy without increasing the length of the basic gate sequence. [Means for solving the problem]

[0007] The quantum compilation device generates a unitary matrix representing an elementary gate and / or a unitary matrix representing a product of unitary matrices each representing an elementary gate, with elements U1, ..., U K Let U1,…,U K}, and for a unitary matrix U representing a quantum circuit to be compiled, a distribution of first observation values ​​obtained by observing a first quantum state obtained by acting the quantum circuit to be compiled represented by the unitary matrix U on an arbitrary input quantum state using an arbitrary observation method, and the set {U1, ..., U K} multiple elements of U k ∈{U1,…,U K} is applied to the input quantum state with a probability p(k), and the second quantum state is observed by the observation method to obtain a distribution of second observation values, and the probability p(k) that minimizes the error between the distribution of second observation values ​​and the probability p(k) of the element U k where K is an integer greater than or equal to 2, and k=1,…,K. Effect of the Invention

[0008] In the present invention, since a quantum circuit can be probabilistically compiled into a basic gate sequence, the approximation accuracy can be improved without increasing the length of the basic gate sequence. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a block diagram illustrating a configuration of a quantum compilation system according to an embodiment. [Diagram 2] FIG. 2 is a block diagram illustrating a configuration of a quantum compiling device according to an embodiment. [Diagram 3] FIG. 3 is a diagram for explaining the effect of the embodiment. [Figure 4] FIG. 4 is a diagram for explaining an application example of quantum compilation according to the embodiment. [Diagram 5] FIG. 5 is a block diagram illustrating a hardware configuration of the embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, an embodiment of the present invention will be described. [overview] First, an outline of the embodiment will be described. In this embodiment, a quantum circuit to be compiled is probabilistically decomposed into a sequence of basic gates, as will be described in detail below.

[0011] The quantum compilation device of the embodiment includes a unitary matrix representing an elementary gate and / or a unitary matrix representing a product of unitary matrices each representing an elementary gate, with elements U1, ..., U K Let U1,…,U K} (i.e., elements U1,…,U K where each of these represents a unitary matrix representing a basic gate sequence) and a unitary matrix U representing a quantum circuit to be compiled are input. The quantum compilation device uses these to calculate a distribution of first observation values ​​obtained by observing a first quantum state obtained by applying an arbitrary observation method to a quantum circuit to be compiled, which is represented by the unitary matrix U, on an arbitrary input quantum state, and a set {U1, ..., U K} multiple elements of U k ∈{U1,…,U K,K, and K is an integer equal to or greater than 2. The quantum compiling device obtains the probability p(k) for a plurality of k. The quantum compiling device may obtain the probability p(k) for all k=1,...,K, or may obtain the probability p(k) for some k=1,...,K. The quantum compiling device obtains the probability p(k) for an element U with probability p(k). k ∈{U1,…,U K For example, the quantum compilation device outputs the set {U1, ..., U K} one element U k Select the selected element U k Output element U k The probability that k is selected is p(k). Alternatively, the quantum compilation device may select the set {U1, ..., U K} to select multiple elements U k Select the selected element U k For each element U k The probability that is selected is p(k). k is the compilation result of the unitary matrix U that represents the quantum circuit to be compiled. That is, the output element U k The unitary matrix U that represents the quantum circuit to be compiled is approximated.

[0012] This improves the approximation accuracy of the unitary matrix U that represents the quantum circuit to be compiled without increasing the length of the basic gate sequence. K} Any one element U selected definitively from k' ∈{U1,…,U K} (for example, Non-Patent Document 1), the unitary matrix U is compiled by the set {U1, ..., U K ,K} with 0≦ε≦1. Then, assume that the set {U1,…,U K} with probability p(k) kBy compiling it by K} gives the approximation accuracy E=ε 2 , or approximately E=ε 2 Here, the smaller E is, the higher the approximation accuracy is. Therefore, when using basic gates of the same length as in the past, a higher approximation accuracy can be achieved. Also, the same approximation accuracy can be achieved with a basic gate sequence of a shorter length than in the past. Note that when a unitary matrix U is a set {U1, ..., U K} can be approximated with approximation accuracy E by the set {U1, ..., U K} an appropriate element U k ∈{U1,…,U K This means that the distribution of observed values ​​x obtained by observing the quantum state obtained by applying a quantum circuit represented by} to an arbitrary input quantum state by an arbitrary observation method differs by at most E in terms of total variation. For example, this is Σ x This means that (1 / 2)|P(x)-Q(x)|≦E is satisfied.

[0013] The quantum compilation device may, for example, compute the set {U1, ..., U K} and a unitary matrix U,

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[0014] [Embodiment] Hereinafter, the present embodiment will be described with reference to the drawings. <Configuration> 1, the quantum compiling system 1 of the present embodiment includes a quantum compiling device 10 and a quantum compiling device 11. The quantum compiling devices 10 and 11 are devices configured, for example, by loading a predetermined program into a known computer. The quantum compiling device 10 and the quantum compiling device 11 may be configured as an integrated device or may be configured separately.

[0015] 2, quantum compiling device 11 of this embodiment has vector generation units 111, 112, matrix generation units 113, 114, probability calculation unit 115, output unit 116, storage unit 117, and control unit 118. Although explanation will be omitted hereafter, quantum compiling device 11 executes each process under the control of control unit 118, and input information and information obtained in each process are stored in storage unit 117. The information stored in storage unit 117 is read and used as necessary, and is utilized in each process.

[0016] <Processing> The process of this embodiment will be exemplified below. <Processing of the quantum compilation device 10> As shown in FIG. 1, a unitary matrix U representing a quantum circuit to be compiled is input to the quantum compilation device 10. Note that the unitary matrix U is 2 N ×2 N N represents the number of quantum bits on which the quantum circuit represented by the unitary matrix U acts. N is an integer constant equal to or greater than 1. The quantum compiling device 10 calculates a set {U1, ..., U K} and outputs it. Although there is no limitation on the content of this process, for example, the quantum compiling device 10 obtains and outputs the set {U1, ..., U K According to Non-Patent Document 1, the 2 N ×2 NThe unitary matrix U of is a finite set of unitary matrices {g i It is known that it is possible to approximate it with any degree of accuracy using 2 N ×2 N The unitary matrix U of

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[0017] Step S101: The quantum compiling device 10 sets M=1.

[0018] Step S102: The quantum compilation device 10 calculates unitary matrices U1, ..., U2, each of which represents a quantum circuit that can be implemented using M or less basic gates. K The set {U1,…,U K}. That is, the set {U1,…,U K} for each element U k is one 2 N ×2 N It is a unitary matrix or a product of up to M unitary matrices. Each element U k is 2 N ×2 N For example, if the types of basic gates used are three types: Hadamard transform gate, π / 2 phase shift gate, and π / 4 phase shift gate, the unitary matrix g1 representing the Hadamard transform gate is H, the unitary matrix g2 representing the π / 2 phase shift gate is S, the unitary matrix g3 representing the π / 4 phase shift gate is T, the identity matrix (unitary matrix) representing that the gate is not in operation is I, and M=1, then {U1,U2,U3,U4}={I,g1,g2,g3}={I,H,S,T} (U1=I,U2=H,U3=S,U4=T). However, the following is satisfied.

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[0019] Step S103: The quantum compiling device 10 calculates whether the input unitary matrix U is a set {U1, ..., U K}, it is determined whether approximation is possible with an approximation accuracy of E=ε. This determination may be performed using the method described in Non-Patent Document 1, or may be performed using other methods. For example, the quantum compiling device 10 determines whether Σ x If (1 / 2)|P(x)-Q(x)|≦ε, then any unitary matrix U is in the set {U1,…,U K}, it is determined that approximation is possible with approximation accuracy E=ε, and if not, it is determined that approximation is not possible. Here, if it is determined that approximation is possible with approximation accuracy E=ε, the quantum compiling device 10 calculates the set {U1, ..., U KOn the other hand, if it is determined that approximation is not possible with the approximation accuracy E=ε, the quantum compiling device 10 sets M+1 as the new M (increases M by 1) and returns the process to step S102.

[0020] <Processing of the quantum compilation device 11> 2 represents the quantum circuit to be compiled N ×2 N and the set {U1, ..., U K} is input to the quantum compilation device 11 (FIG. 2). That is, the quantum compilation device 11 converts a unitary matrix representing a basic gate and / or a unitary matrix representing a product of unitary matrices each representing a basic gate into elements U1, ..., U K Let U1,…,U K}, and a unitary matrix U that represents the quantum circuit to be compiled.

[0021] The unitary matrix U is input to the vector generation unit 111 of the quantum compiling device 11, and the set {U1, ..., U K} is input to the vector generation unit 112. The vector generation unit 111 uses a unitary matrix U to generate the vector

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[0022] The vector U obtained in step S111 → is input to the matrix generation unit 113, and the vector U obtained in step S112 is k → is input to the matrix generation unit 114. The matrix generation unit 113 generates a vector U → Using the real vector b → =((U → ) + σ1U → ,(U → ) + σU → ,...,(U → ) + σ J U → ) T The matrix generation unit 114 obtains and outputs the vector U k → The real matrix A is obtained and output using the above. However, the k-th column vector from the beginning of the real matrix A is ((U k → ) + σ1U k → ,(U k → ) + σU k → ,...,(U k → ) + σ J U k → ) T and β + represents the adjoint matrix of β, and γ T represents the transpose of γ. Note that {σ1,…,σ J} is 2 2N ×2 2N is an orthonormal basis for Hermitian matrices, where J=2 4N where j = 1,…,J. Here, we consider the set of Hermitian matrices as an inner product space under the Hilbert-Schmidt inner product. In the orthonormal basis {σ1,…,σ J} may be set in advance, or may be generated by a processing unit (not shown) (step S114).

[0023] The real vector b obtained in step S113 → The real matrix A obtained in step S114 is input to the probability calculation unit 115. The probability calculation unit 115 calculates:

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[0024] The probabilities p(1), ..., p(K) obtained in step S115 and the set {U1, ..., U K} is input to the output unit 116. The output unit 116 outputs an element U k and output it (step S115).

[0025] <Why it is possible to improve the approximation accuracy of the unitary matrix U that represents the quantum circuit to be compiled without increasing the number of types of basic gates> As described above, the quantum compiling device 11 calculates the set {U1, ..., U K} and a unitary matrix U,

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[0026] In addition, the method of this embodiment improves the approximation accuracy to E=ε 2 , or approximately E=ε 2 The reason is as follows. The quantum state of one quantum bit can be expressed by points on the surface and inside of a three-dimensional sphere with a diameter of 1, and the distance between two points representing two quantum states corresponds to the maximum value of the total variation of the measurement distribution of these two quantum states. Here, a unitary matrix U representing a quantum circuit acting on an arbitrary one quantum bit is a set {U1, ..., U K In this case, the quantum state σ obtained by applying the quantum circuit represented by the unitary matrix U to the input quantum state ρ of one quantum bit is * and the input quantum state ρ is given by the unitary matrix U k The quantum state σ obtained by applying the quantum circuit represented by k can be considered to be separated by a distance ε on this three-dimensional sphere. * and σ kIn the example of FIG. 3, the quantum state obtained by applying the quantum circuit represented by U1 and the quantum circuit represented by U2 to the input quantum state ρ with a probability p(k)=1 / 2 corresponds to the midpoint σ' between σ1 and σ2. In this case, σ * The distance between and σ' is ε 2 The distance on this three-dimensional sphere represents the maximum value of the total variation of the measurement distribution of the corresponding quantum state. Therefore, by acting on the quantum circuit represented by U1 and the quantum circuit represented by U2 with a probability p(k)=1 / 2, the unitary matrix U can be approximated to an accuracy of E=ε 2 The same can be said for other quantum states σ k and also for probability p(k).

[0027] <Features of the embodiment> As described above, in this embodiment, by probabilistically outputting a basic gate sequence, an arbitrary quantum circuit can be approximated with an approximation accuracy of E=ε 2 That is, the distribution {P(x)} of the observed value x obtained by observing the quantum state obtained by applying the unitary matrix U to the quantum circuit to be compiled to an arbitrary input quantum state using an arbitrary observation method, and the set {U1, ..., U K} an appropriate element U k ∈{U1,…,U K} to an arbitrary input quantum state, the distribution of the observed value x obtained by observing the quantum state by an arbitrary observation method is at most ε 2 Only there is no deviation.

[0028] For example, consider the case where the set of unitary matrices representing basic gates is {I,H,S,T}. The relationship between the number of basic gates Y and the approximation accuracy E when compiling is performed according to Non-Patent Document 1 is shown below. [Table 1] According to this, in conventional compilation, the number of basic gates (the number of types of basic gates) Y and the approximation accuracy E=ε have approximately the following relationship:

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[0029] [Hardware configuration] The quantum compiling device 11 in the embodiment is a device configured by a general-purpose or dedicated computer having a processor (hardware processor) such as a CPU (central processing unit) and a memory such as a RAM (random-access memory) and a ROM (read-only memory) executing a predetermined program. That is, the quantum compiling device 11 in the embodiment has, for example, a processing circuit configured to implement each unit. This computer may have one processor and memory, or may have multiple processors and memories. This program may be installed in the computer, or may be recorded in a ROM or the like in advance. In addition, some or all of the processing units may be configured using electronic circuits that realize processing functions independently, rather than electronic circuits that realize functional configurations by reading a program like a CPU. In addition, an electronic circuit that configures one device may include multiple CPUs.

[0030] FIG. 5 is a block diagram illustrating a hardware configuration of the quantum compiling device 11 in the embodiment. As illustrated in FIG. 5, the quantum compiling device 11 in this example has a CPU (Central Processing Unit) 11a, an input unit 11b, an output unit 11c, a RAM (Random Access Memory) 11d, a ROM (Read Only Memory) 11e, an auxiliary storage device 11f, a communication unit 11h, and a bus 11g. The CPU 11a in this example has a control unit 11aa, a calculation unit 11ab, and a register 11ac, and executes various calculation processes according to various programs loaded into the register 11ac. The input unit 11b is an input terminal, a keyboard, a mouse, a touch panel, etc., to which data is input. The output unit 11c is an output terminal, a display, etc., to which data is output. The communication unit 11h is a LAN card, etc., controlled by the CPU 11a that has loaded a predetermined program. The RAM 11d is a static random access memory (SRAM), a dynamic random access memory (DRAM), or the like, and has a program area 11da in which a predetermined program is stored, and a data area 11db in which various data is stored. The auxiliary storage device 11f is, for example, a hard disk, a magneto-optical disc (MO), a semiconductor memory, or the like, and has a program area 11fa in which a predetermined program is stored, and a data area 11fb in which various data is stored. The bus 11g connects the CPU 11a, the input unit 11b, the output unit 11c, the RAM 11d, the ROM 11e, the communication unit 11h, and the auxiliary storage device 11f so that information can be exchanged. The CPU 11a writes the program stored in the program area 11fa of the auxiliary storage device 11f to the program area 11da of the RAM 11d according to the loaded OS (Operating System) program. Similarly, the CPU 11a writes various data stored in the data area 11fb of the auxiliary storage device 11f to the data area 11db of the RAM 11d. The address on the RAM 11d where this program or data is written is stored in the register 11ac of the CPU 11a.The control unit 11aa of the CPU 11a sequentially reads out these addresses stored in the register 11ac, reads out programs and data from the areas on the RAM 11d indicated by the read addresses, causes the calculation unit 11ab to sequentially execute the calculations indicated by the programs, and stores the calculation results in the register 11ac. With this configuration, the functional configuration of the quantum compiling device 11 is realized.

[0031] The above-mentioned program can be recorded in a computer-readable recording medium. An example of a computer-readable recording medium is a non-transitory recording medium. Examples of such a recording medium include a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, and the like.

[0032] The distribution of this program is performed, for example, by selling, transferring, lending, etc., a portable recording medium such as a DVD or CD-ROM on which the program is recorded. Furthermore, the program may be stored in a storage device of a server computer, and the program may be distributed by transferring the program from the server computer to another computer via a network. As described above, a computer that executes such a program, for example, first temporarily stores in its own storage device the program recorded in the portable recording medium or the program transferred from the server computer. Then, when executing the process, the computer reads the program stored in its own storage device and executes the process according to the read program. As another execution form of the program, the computer may directly read the program from the portable recording medium and execute the process according to the program, and further, each time the program is transferred from the server computer to the computer, the computer may execute the process according to the received program. Furthermore, the server computer may not transfer the program to the computer, and the above-mentioned process may be executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by issuing an execution instruction and obtaining the result. In addition, the program in this embodiment includes information used for processing by an electronic computer and equivalent to a program (such as data that is not a direct instruction to a computer but has the nature of defining computer processing).

[0033] In the embodiment, the present device is configured by executing a predetermined program on a computer, but at least a part of the processing contents may be realized by hardware.

[0034] [Other variations] It should be noted that the present invention is not limited to the above-described embodiment. For example, in the above-described embodiment, the quantum compiling device 10 derives a set {U1, ..., U K However, this does not limit the present invention, and the quantum compiling device 10 may obtain and output a set {U1, ..., U K For example, the quantum compiling device 10 may randomly select a set {U1, ..., U K} and the set {U1,…,U K The approximation accuracy E that can be realized by} may be set as ε.

[0035] In addition, the various processes described above may not only be executed in chronological order as described, but may also be executed in parallel or individually depending on the processing capacity of the device that executes the processes or on the need of the device. Needless to say, other appropriate modifications are possible without departing from the spirit of the present invention. [Explanation of symbols]

[0036] 1. Quantum Compilation System 10,11 Quantum Compilation Device 111, 112 Vector generation unit 113,114 Matrix generator 115 Probability Calculation Unit 116 Output section

Claims

1. K is an integer equal to or greater than 2, k=1,…,K, Let us denote by element U a unitary matrix representing a basic gate and / or a unitary matrix representing a product of unitary matrices each of which represents a basic gate. 1 ,…,U K Let U be the set 1 ,…,U K } and the unitary matrix U representing the quantum circuit to be compiled, A distribution of first observation values ​​obtained by observing a first quantum state obtained by applying the quantum circuit to be compiled, which is represented by the unitary matrix U, to an arbitrary input quantum state using an arbitrary observation method; The set {U 1 ,…,U K } multiple elements of U k ∈{U 1 ,…,U K A distribution of second observation values ​​obtained by observing a second quantum state obtained by applying a quantum circuit represented by each of the above formulas to the input quantum state with a probability p(k) using the observation method; a probability calculation unit for obtaining the probability p(k) that minimizes the error of With the probability p(k), the element U k an output unit that outputs A quantum compilation device having:

2. 2. The quantum compiling device of claim 1, The set {U 1 ,…,U K } Any one element U selected definitively from k' ∈{U 1 ,…,U K }, the unitary matrix U is the set {U 1 ,…,U K } with approximation accuracy E = ε, k'∈{1,…,K}, The set {U 1 ,…,U K }, the element U is probabilistically selected with the probability p(k). k If the unitary matrix U is compiled by 1 ,…,U K } gives the approximation accuracy E=ε 2 It can be approximated by, or approximately E=ε 2 A quantum compilation device that can be approximated by

3. 3. The quantum compiling device of claim 1, The unitary matrix U is 2 N ×2 N where N is an integer greater than or equal to 1, {σ 1 ,…,σ J } is 2 2N ×2 2N is an orthonormal basis for Hermitian matrices, where J=2 4N for j=1,…,J, e L → 2 N represents a vertical vector of dimension e L → The Lth element from the beginning of is 1, and the other two N -1 element is 0, L=1,...,2 N and [0022] and [0023] and [0024] is α 1 and α 2 represents the Kronecker product with A represents a real matrix, and the k-th column vector from the beginning of the real matrix A is ((U k → ) + σ 1 U k → ,(U k → ) + σ 2 U k → ,...,(U k → ) + σ J U k → ) T and β + represents the adjoint matrix of β, and γ T represents the transpose of γ, b → represents a real vector, and b → =((U → ) + σ 1 U → ,(U → ) + σ 2 U → ,...,(U → ) + σ J U → ) T and Let Δ denote the set of real vectors, Δ={(p(1),p(2),...,p(K)) T |Σ k=1,...,K p(k)=1, p(k)≧0}, Let R denote the set of real vectors, and R={(tr[σ 1 Φ], tr[σ 2 Φ],...,tr[σ J Φ]) T : ∃ ρ≧0,(tr[ρ]=1)∧(0≦Φ≦ρ(×)I)}, tr[κ] denotes the trace of κ, and I is 2 N ×2 N represents the identity matrix of N ×2 N The matrix γ, where γ ≥ 0 and 0 ≤ γ , means that γ is a positive semidefinite matrix, i.e., a Hermitian matrix with nonnegative eigenvalues. The matrix γ of η × η 1 and γ 2 In 1 ≦γ 2 is γ 2 -γ 1 ≧0, i.e., γ 2 -γ 1 represents a positive semidefinite matrix, η is an integer equal to or greater than 1, μ is an integer equal to or greater than 1, and Φ represents a positive semidefinite matrix, The probability calculation unit [0025] Achieve → = {p(1), …, p(K)}∈Δ. Quantum Compilation Device.

4. A quantum compilation method using a quantum compilation device, K is an integer equal to or greater than 2, k=1,…,K, In the probability calculation unit, Let us denote by element U a unitary matrix representing a basic gate and / or a unitary matrix representing a product of unitary matrices each of which represents a basic gate. 1 ,…,U K Let U be the set 1 ,…,U K } and the unitary matrix U representing the quantum circuit to be compiled, A distribution of first observation values ​​obtained by observing a first quantum state obtained by applying the quantum circuit to be compiled, which is represented by the unitary matrix U, to an arbitrary input quantum state using an arbitrary observation method; The set {U 1 ,…,U K } multiple elements of U k ∈{U 1 ,…,U K A distribution of second observation values ​​obtained by observing a second quantum state obtained by applying a quantum circuit represented by each of the above formulas to the input quantum state with a probability p(k) using the observation method; a probability calculation step of obtaining the probability p(k) that minimizes the error of At the output, the element U k an output step for outputting A quantum compilation method having the following construction.

5. A program for causing a computer to function as the quantum compiling device according to any one of claims 1 to 3.

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