Determination device, determination method, and program

Abstract

In the present invention, a predetermined number of quantum bits are individually measured to obtain measurement results, and the quality of the predetermined number of quantum bits is determined on the basis of the measurement result of the final quantum bit, which is a quantum bit measured last among the predetermined number of quantum bits.

Description

Determination device, determination method, and program

[0001] The present invention relates to techniques for determining the quality of a qubit relative to a target state.

[0002] There are known techniques for determining the quality of a predetermined number of qubits relative to a target state (an ideal qubit state, i.e., a target qubit quantum state) based on measurements of each qubit. For example, Non-Patent Documents 1 to 3 disclose techniques for verifying the fidelity of a predetermined number of qubits relative to a target state based on measurements of each qubit called Pauli measurements. Such techniques require the preparation of multiple copies of the predetermined number of qubits to be determined. This is because the measurement results of the qubits are probabilistic, and therefore the same process must be repeated multiple times to determine the quality of the qubits.

[0003] ST Flammia and Y.-K. Liu, "Direct Fidelity Estimation from Few Pauli Measurements," June 8, 2011, Physical Review Letters 106, 230501, (2011).Huangjun Zhu and Masahito Hayashi, "General framework for verifying pure quantum states in the adversarial scenario," December 27, 2019, Physical Review A 100, 062335 (2019). Z. Li, Y.-G. Han, H.-F. Sun, J. Shang, and H. Zhu, "Verification of phased Dicke states," February 3, 2021, Physical Review A 103, 022601 (2021).

[0004] However, conventionally, determining the quality of a predetermined number of qubits for an arbitrary target state based on measurements of each qubit has the problem of requiring many copies of the qubits. For example, the technology of Non-Patent Document 1 can determine the quality of qubits for an arbitrary target state, but the number of qubit copies required for this purpose increases exponentially with the number of qubits to be determined. Furthermore, the technologies of Non-Patent Documents 2 and 3 can only determine the quality of qubits for a limited number of specific target states.

[0005] To solve this problem, a predetermined number of quantum bits are measured quantum bit by quantum bit to obtain measurement results, and the quality of the predetermined number of quantum bits is determined based on the measurement result of the final quantum bit, which is the quantum bit that was measured last among the predetermined number of quantum bits.

[0006] This reduces the number of qubit copies required to determine the quality of a given number of qubits for any target state based on per-qubit measurements.

[0007] FIG. 1 is a diagram illustrating the configuration of a determination system according to an embodiment. FIG. 2 is a block diagram illustrating the configuration of a determination device according to an embodiment. FIG. 3 is a flow diagram illustrating a determination method according to an embodiment. FIGS. 4A and 4B are graphs illustrating the results of numerical experiments. FIGS. 5A and 5B are graphs illustrating the results of numerical experiments. FIG. 6 is a block diagram illustrating the hardware configuration according to an embodiment.

[0008] Hereinafter, embodiments of the present invention will be described. [Notation] First, the notation used in this embodiment will be described. The quantum state of one quantum bit is expressed as shown in the following formula (1) using a complex vector using two complex numbers α, β∈C. C represents a set of complex numbers. The state corresponding to 0 of a classical bit is expressed as follows: The state corresponding to a classical bit of 1 is expressed as follows: Using bracket notation, the states of equations (2) and (3) can be expressed as ket vectors (column vectors) as shown in equations (4) and (5) below. Using these, the state of equation (1) can be expressed as equation (6) below. The probability that the measurement result of the quantum state in equation (6) is 0 (the state corresponding to the classical bit 0) is |α| 2 and the probability that the measurement result is 1 (the state corresponding to the classical bit 1) is |β| 2 Usually, the condition in the following equation (7) is imposed so that the sum of these probabilities becomes 1. Imposing a condition so that the sum of the probabilities becomes 1 is called normalization. |α| 2 +|β| 2 =1 (7)

[0009] The quantum state of N quantum bits (N is a positive integer) can be expressed as the tensor product of the quantum states of each quantum bit, as shown in the following equation (8). where α i represents a complex number, where i = 1,...,N. The quantum state expressed by equation (8) is called the quantum state |Φ>.

[0010] Using bracket notation, the complex transpose vector of |Φ> is denoted as <Φ|. The inner product <Φ||Φ> of <Φ| and |Φ> is abbreviated as <Φ|Φ>. When |Φ> is normalized, the following equation (12) holds: <Φ|Φ>=1 (12) Also, when |Φ> is a two-dimensional complex vector, |Φ>∈C 2 and |Φ'>∈C 2 is uniquely determined. The state (quantum state) orthogonal to the quantum state |Φ> means the quantum state expressed as |Φ'> that is orthogonal to |Φ>. In other words, the relationship of the following equation (13) holds: <Φ|Φ'>=0 (13)

[0011] Measurement of one qubit (measurement of each qubit) is called one-qubit measurement (projection). For any normalized one-qubit state |Θ〉∈C 2 For the quantum state |Θ>, the quantum state |Θ'>∈C is orthogonal to the quantum state |Θ>. 2and the quantum state |Θ> with probability 1. Such a measurement is denoted as |Θ>. That is, a measurement using the measurement basis (|Θ>,|Θ'>) is denoted as |Θ>. Similarly, a measurement using the measurement basis (|Θ'>,|Θ>) is denoted as |Θ'>. Note that the measurement bases are assumed to be normalized. Generally, the measurement result of a one-qubit measurement is expressed by a bit value b∈{0,1}. In the following, we assume that the measurement basis |Θ> corresponds to the measurement result 0, and the measurement basis |Θ'> corresponds to the measurement result 1. In this case, the probability that the measurement result is 0 when any one-qubit state (measured state) |ν> is measured with the measurement basis |Θ> is |<ν|Θ>| 2 and the probability that the measurement result is 0 when any one-qubit state |ν> is measured in the measurement basis |Θ'> is |<ν|Θ'>| 2 That is, when a one-qubit state |Θ> is measured in the measurement basis |Θ>, the probability that the measurement result is 0 is |<Θ|Θ>| 2 = 1, and the probability that the measurement result is 0 when measuring a one-qubit state |Θ> in the measurement basis |Θ'> is |<Θ'|Θ>| 2 = 0. In other words, when a measurement |Θ> is performed on a one-qubit state |Θ>, the measurement result is always 0. Also, when a one-qubit state |Θ'> is measured in the measurement basis |Θ>, the probability that the measurement result is 0 is |<Θ|Θ'>| 2 = 0, and the probability that the measurement result is 0 when measuring a one-qubit state |Θ'> in the measurement basis |Θ'> is |<Θ'|Θ'>| 2 = 1. In other words, when a measurement |Θ> is performed on a one-qubit state |Θ'>, the measurement result is always 1. Note that if a one-qubit state |Θ> is measured using a measurement basis that is neither |Θ> nor |Θ'>, the measurement result will be random, and it is not possible to distinguish between the quantum state |Θ'> and the quantum state |Θ> with a probability of 1.

[0012] A Pauli X measurement means measuring a single qubit state using the Pauli X basis as the measurement basis. A Pauli Y measurement means measuring a single qubit state using the Pauli Y basis as the measurement basis. A Pauli Z measurement means measuring a single qubit state using the Pauli Z basis as the measurement basis.

[0013] An operation on the quantum state of one qubit is called a one-qubit operation. A one-qubit operation is a 2×2 complex matrix U∈C 2×2 The quantum state of N qubits is expressed as The one-qubit operation U on is expressed by the matrix of the following equation (14). Here, I represents a 2 × 2 identity matrix. U in equation (14) is the i-th operand of the tensor product (the i-th operand from the left in equation (14)).

[0014] [(ε,δ,M)-Quantum State Verification Protocol] The (ε,δ,M)-quantum state verification protocol is a protocol for determining the quality of a given number of quantum bits. That is, the (ε,δ,M)-quantum state verification protocol takes as input a classical description (hereinafter referred to as "quantum state information") representing the target state of N quantum bits (the ideal quantum bit state, i.e., the quantum state of the target quantum bit) |Φ> (Equation (8)) and M quantum states ρ obtained by copying the quantum state ρ of the N quantum bits to be judged (verified), and satisfies the following properties (1) and (2): (1) When ρ and |Φ><Φ| are equal, the protocol outputs "accept" with probability 1. (2) If the fidelity between ρ and |Φ><Φ|, F(ρ,|Φ><Φ|) = <Φ|ρ|Φ>, satisfies 1-F(ρ,|Φ><Φ|) ≥ ε (ρ and |Φ><Φ| deviate by more than ε in terms of fidelity), then "reject" is output with probability p ≥ 1-δ. Because the measurement results of quantum bits are probabilistic, the same process must be repeated to ensure property (2) with a small δ. Because quantum states change with observation, a quantum state ρ is required for each iteration of the process. If M quantum states ρ are input, M iterations of the process are possible. The smaller the number M (number of copies) of quantum states ρ required to satisfy property (2), the more efficient the protocol, i.e., the higher its performance. In this study, we focus on quantum state verification protocols that can be implemented by measuring each quantum bit and propose a method that can reduce the number of copies M required for any target state.

[0015] [Overview] An overview of an embodiment will be described. In an embodiment, a measurement unit measures a predetermined number of quantum bits quantum bit by quantum bit to obtain a measurement result, and a determination unit determines the quality of the predetermined number of quantum bits based on the measurement result of a final quantum bit, which is the quantum bit measured last among the predetermined number of quantum bits. Here, when the predetermined number of quantum bits to be determined are measured quantum bit by quantum bit, the quantum states of the other quantum bits also change each time a quantum bit is measured. Therefore, the quality of the predetermined number of quantum bits can be determined based on the measurement result of the final quantum bit. Furthermore, because the quality of the predetermined number of quantum bits is determined based only on the measurement result of the final quantum bit, the variance in the determination result is small. Therefore, the number of repetitions of processing required to obtain a final determination result can be reduced, and as a result, the number of copies of quantum bits can be reduced.

[0016] Preferably, the measurement unit measures the final quantum bit based on a measurement basis obtained by updating quantum state information |Ψ> representing the quantum state |Φ> (target state) of the target quantum bit in accordance with measurement results of quantum bits other than the final quantum bit to obtain a measurement result of the final quantum bit. Here, when the quantum state of the quantum bit is measured, the quantum state of the measured quantum bit is determined (contracted) to the measurement result. If the quantum state ρ of the predetermined number of quantum bits to be determined is the target state |Φ> (i.e., if ρ = |Φ><Φ|), the state represented by the final quantum state information |Ψ> obtained by updating the quantum state information |Ψ> representing the target state |Φ> in accordance with measurement results of quantum bits other than the final quantum bit should represent the quantum state of the unmeasured final quantum bit itself. Therefore, when the quantum state ρ is the target state |Φ>, if a measurement |Ψ> is performed on the final quantum bit using the one-qubit state |Ψ> represented by the final quantum state information and the one-qubit state |Ψ'> orthogonal to the state represented by the final quantum state information |Ψ> as the measurement basis (|Ψ>, |Ψ'>), the measurement result will be 0 with probability 1. Therefore, the above-mentioned property (1) of the (ε,δ,M)-quantum state verification protocol is satisfied. Furthermore, because the quality of the specified number of quantum bits is determined based only on the measurement result of the final quantum bit, the number of copies M required to satisfy property (2) of the (ε,δ,M)-quantum state verification protocol can be reduced.

[0017] Preferably, the measurement unit measures qubits other than the final qubit using a measurement basis selected according to a set probability. More preferably, the measurement unit measures qubits other than the final qubit selected according to a set probability using a measurement basis selected according to the probability. By appropriately setting this probability, the copy number M can be further reduced.

[0018] [Embodiment] Next, this embodiment will be described in detail with reference to the drawings. <Configuration> As illustrated in Fig. 1, a determination system 1 of this embodiment includes a quantum bit providing device 11 and a determination device 13. As illustrated in Fig. 2, the determination device 13 includes a memory 130, storage units 131a, 131b, and 131c, an input unit 132, a control unit 133, an update unit 134, a measurement control unit 135, a measurement unit 136, a determination unit 137, and an output unit 138. Although detailed explanations will be omitted below, information obtained in each process of the determination device 13 is stored in the memory 130 one by one, and is read out as needed and used in other processes. Furthermore, each process of the determination device 13 is performed under the control of the control unit 133.

[0019] <Pre-processing> As a pre-processing, the measurement |Θ of the quantum bits other than the final quantum bit is stored in the storage unit 131a of the determination device 13 (FIG. 2). j > the measurement basis (|Θ j >,|Θ j '>) (j=1,...,J) where the measurement |Θ j > is the measurement per qubit. J is an integer, e.g., J ≥ 2. The measurement basis (|Θ j >,|Θ j Examples of the quantum state information |Φ> representing the target state of N quantum bits are input to the input unit 132 and stored in the storage unit 131b. s (i, j) is input and stored in the storage unit 131c. Here, the probability p s (i,j) is the quantum bit Q shown below in the loop processing corresponding to the integer index s shown below. i Measured against |Θ j > represents the probability that

[0020] <Determination Process> The quantum bit provider 11 (FIG. 1) generates N quantum bits Q1, . . . , Q N A string of qubits (e.g., N qubits Q1,...,Q NA quantum bit sequence (quantum bit sequence by Q) is generated M times to obtain M quantum bit sequences 102-1, ..., 102-M. N is 1 or more, for example, N≧2. n=1,...,N, and each quantum bit is Q n and the qubits Q1,...,Q N are collectively referred to as quantum bit Q. M is an integer equal to or greater than 1, for example, M≧2. m=1,...,M, and each quantum bit string is referred to as quantum bit string 102-m, and quantum bit strings 102-1,...,102-M are collectively referred to as quantum bit string 102. The same applies to other notations hereinafter. Each quantum bit string 102-m is made up of quantum bits Q1,...,Q N and the quantum state of each quantum bit string 102-m is ρ. For example, quantum bit Q is a photon, and the quantum state of quantum bit Q is the polarization direction of the photon. However, this is not a limitation of the present invention, and quantum bit Q may be implemented in any physical system. The M quantum bit strings 102-1, ... 102-M are provided (output) to a decision device 13.

[0021] The decision device 13 uses the quantum bit strings 102-1, . . . , 102-M to determine N quantum bits Q1, . . . , Q N The process of the determination device 13 will be described below with reference to FIG.

[0022] The control unit 133 of the determination device 13 (FIG. 2) sets the integer index m to m=1 (step S101).

[0023] The control unit 133 selects an unmeasured quantum bit string 102-m from the quantum bit strings 102-1, ..., 102-M (step S102). The control unit 133 sets the integer index s to s = 1 (step S103). The update unit 134 extracts quantum state information |Φ> representing the target state from the storage unit 131b and sets it as the initial information of the quantum state information |Ψ>. That is, the quantum state information |Ψ> is set so that |Ψ> = |Φ> (step S104).

[0024] The measurement control unit 135 receives the probability p s Extract (i,j) with probability p s(i, j) is the measurement basis (|Θ j >,|Θ j Measurements at '>) |Θ j > is the unmeasured quantum bit Q included in the quantum bit string 102-m. i In response to this, the measurement unit 136 instructs the measurement unit 136 to perform the measurement with the probability p s (i,j) is the quantum bit Q i Measurement of |Θ j > (one quantum bit measurement) to obtain a measurement result b∈{0,1}. That is, the measurement unit 136 measures a predetermined number of quantum bits for each quantum bit to obtain a measurement result. At this time, the measurement unit 136 measures a predetermined probability p s The measurement basis (|Θ j >,|Θ j '>) to find the qubits Q other than the final qubit i The measurement result b is sent to the update unit 134 (step S105).

[0025] The update unit 134 performs an operation on |Ψ> expressed by the matrix of the following equation (15), and normalizes the state obtained thereby to obtain a new |Ψ>. where |Θ j 0 >=|Θ j > and |Θ j 1 >=|Θ j '>. As mentioned above, |Θ j '> is |Θ j >. Also, in equation (15), j b |(b∈{0,1}) is the i-th operand of the tensor product. That is, the update unit 134 updates |Ψ〉 to the following equation (16) by normalizing it. The updated |Ψ〉 represents the measurement results of the measured s qubits and the unmeasured (Ns) qubit states, where the measured s qubit states have been contracted to the states corresponding to the measurement results (step S106).

[0026] The control unit 133 determines whether s < N - 1 is satisfied (step S107). Here, if it is determined that s < N - 1 is satisfied, the control unit 133 sets s + 1 as the new s and returns the process to step S105. That is, the control unit 133 increments s by 1 (increments) and returns the process to step S105 (step S108). On the other hand, if it is determined that s < N - 1 is not satisfied (in the case of s = N - 1), the control unit 133 advances the process to step S109.

[0027] In step S109, the update unit 134 sends the latest |Ψ〉 to the measurement control unit 135. The measurement control unit 135 sends an instruction to the measurement unit 136 to perform a measurement of |Ψ〉 on the last remaining unmeasured qubit Q end (the final qubit) (Q end ∈ {Q1,..., Q N}). In accordance with this, the measurement unit 136 performs a measurement of |Ψ〉 on the qubit Q end (the final qubit) to obtain a measurement result b ∈ {0, 1}. That is, the measurement unit 136 measures the qubit Q end using the measurement basis (|Ψ〉, |Ψ’〉) to obtain a measurement result b ∈ {0, 1}. In other words, the measurement unit 136 measures the final qubit Q end based on the measurement basis (|Ψ〉, |Ψ’〉) obtained by updating the quantum state information representing the quantum state of the target qubit according to the measurement results of the qubits other than the final qubit, and obtains the measurement result b of the final qubit Q end . Here, at the stage before the measurement in step S109, |Ψ〉 is a two-dimensional vector. Therefore, when the quantum state of the qubit Q end is |Ψ〉, b = 0 with probability 1. The measurement result b is sent to the determination unit 137 (step S110).

[0028] The determination unit 137 is the qubit Q s endIt is determined whether the measurement result b of (the final quantum bit) is 0 (step S110). Here, if b = 0, the determination unit 137 sends information indicating rejection to the output unit 138, and the output unit 138 outputs the information indicating rejection (step S111), and the process ends. On the other hand, if b = 0, the control unit 133 determines whether m = M (step S112). Here, if m = M is not, m + 1 is set as a new m, and the process returns to step S102. That is, the control unit 133 increments m by 1, and the process returns to step S102 (step S113). On the other hand, if m = M, the determination unit 137 sends information indicating acceptance to the output unit 138, and the output unit 138 outputs information indicating acceptance (step S114), and the process ends. That is, the above-described process is performed for all quantum bit strings 102-1, . . . 102-M, and if it is determined that b=0 in step S110 for all of them, information indicating acceptance is output.

[0029] <Performance Evaluation> The performance of the (ε, δ, M)-quantum state verification protocol according to the method of this embodiment will be described. Regarding property (1): If ρ = |Φ><Φ|, the quantum state of the unmeasured (Ns) qubits remaining after the measurement in step S105 of each loop process is the unmeasured (Ns) qubit state represented by |Ψ〉 updated in step S106. Therefore, if ρ = |Φ><Φ|, the quantum state of the one qubit Q remaining in step S109 end The measurement result obtained by performing measurement |Ψ〉 on (the final quantum bit) is always b=0 (yes in step S110), satisfying performance (1) of the (ε, δ, M)-quantum state verification protocol described above (step S114).

[0030] Regarding property (2): Positive semidefinite matrix Ω s (|Ψ>) is recursively defined as in the following equations (17) and (18). Ω N (|Ψ>)=|Ψ><Ψ| / <Ψ|Ψ> (18) where i=1,...,N, j=1,...,J, s=1,...,N-1. i is the quantum bit Q to be measured in step S105 of the loop corresponding to the integer index s. i(Qbit Q selected from the (N-s+1) unmeasured qubits i ) and j corresponds to the implementable measurement basis (|Θ j >,|Θ j '>) (e.g., Pauli X measurement, Pauli Y measurement, Pauli Z measurement). Here, |Θ j 0 >=|Θ j > and |Θ j 1 >=|Θ j '>. Also, |Θ in equation (17) j b ><Θ j b |(b∈{0,1}) is the ith qubit Q i When the argument |Ψ> in equation (18) is a zero vector, Ω N (|Ψ>) is a zero matrix. This positive semidefinite matrix Ω s Using (|Ψ>), when ρ and |Φ><Φ| are misaligned by more than ε in the sense of fidelity (when F(ρ,|Φ><Φ|) = <Φ|ρ|Φ> satisfies 1-F(ρ,|Φ><Φ|) ≧ ε), it can be said that in step S110, the answer is yes with probability p≦1-(1-λ2(Ω1(|Φ>)))ε. Here, λ2(Ω1(|Φ>)) represents the second eigenvalue (the second largest eigenvalue) of Ω1(|Φ>). Therefore, to satisfy property (2) of the (ε,δ,M)-quantum state verification protocol, it is sufficient to have M copies of the quantum state ρ (the number of copies), approximated by the following equation (19). That is, the smaller the second eigenvalue of Ω1(|Φ>), the smaller the number of copies M required for verification. In this embodiment, the second eigenvalue λ2(Ω1(|Φ>)) can be made smaller than in the past, and therefore the number of copies M required for verification can be reduced compared to the past.

[0031] <Numerical Experiments> Next, we will show the results of numerical experiments in this embodiment. N This shows the relationship between the number N of eigenvalues ​​and 1 / (λ2(Ω1(|Φ>))) in equation (19). As shown in equation (17), the second eigenvalue λ2(Ω1(|Φ>)) has a probability p sDepending on (i,j), we minimize the second eigenvalue λ2(Ω1(|Φ>)) by performing a full loop (Fig. 3) corresponding to integer indices s=1,...,N-1. s It is computationally difficult to calculate (i,j). Therefore, in the numerical experiment, we used Ω in equation (17) for s=N-1. s+1 =Ω N Ω defined by equation (18) N Ω obtained by substituting (|Ψ>) N-1 (|Φ>) corresponding to λ2(Ω N-1 (|Φ>)) to minimize p N-1 (i,j) was found. Then, s-1 was set as the new s, and the already obtained Ω s (|Φ>)) corresponding to λ2(Ω s (|Φ>))) that minimizes p s (i,j). This gives p1(i,j), ..., p N-1 (i, j) was obtained. The results of this numerical experiment are shown in Figures 4A, 4B, 5A, and 5B. Figure 4A shows the results of the following N-qubit state (RANDOM STATE) when equation (20) is used as the target state |Φ>. where: are two independent Gaussian sampled N+1 4B shows the result of the N-qubit state (RANDOM PRODUCT STATE) when the target state |Φ> is the equation (21). FIG. 5A shows the result of the following N-qubit state (GHZ STATE) when equation (22) is set as the target state |Φ>. Here, the tensor product spans N |0> or |1>. That is, the tensor product has N |0> or |1> operands. Figure 5B shows the result when the following N-qubit state is expressed by Equation (23) as the target state |Φ> (W STATE). Here, the tensor product spans N |0> or |1>. That is, the tensor product has N |0> or |1> operands. The horizontal axes of Figures 4A, 4B, 5A, and 5B represent the qubits Q1,...,Q NThe vertical axis represents the number N of quantum bits, and the vertical axis represents the value of 1 / (λ2(Ω1(|Φ>))). As illustrated in these results, in this embodiment, the linearity of 1 / (λ2(Ω1(|Φ>))) with respect to the number N of quantum bits can be confirmed. That is, in this embodiment, it can be confirmed that the number of copies M required is linear with the number N of quantum bits. In contrast, in Non-Patent Document 1, when RANDOM STATE is set as the target state, the number of copies M required increases exponentially with the number N of quantum bits (M=Ω(2 N )) From this point of view, the superiority of this format can be seen.

[0032] [Hardware Configuration] The functions performed by the components described herein may be implemented in circuitry or processing circuitry, including general-purpose processors, application-specific processors, integrated circuits, quantum computers, ASICs (Application Specific Integrated Circuits), a CPU (Central Processing Unit), conventional circuits, and / or combinations thereof, programmed to perform the described functions. A processor includes transistors and other circuits and is considered to be circuitry or processing circuitry. A processor may also be a programmed processor that executes a program stored in a memory.

[0033] In this specification, a circuitry, unit, or means is hardware that is programmed to realize or performs the described functions, which may be any hardware disclosed herein or any hardware known to be programmed to realize or perform the described functions.

[0034] If the hardware is a processor considered to be a type of circuitry, the circuitry, means, or unit is a combination of the hardware and software used to configure the hardware and / or processor.

[0035] For example, the determination device 13 in each embodiment is a device configured by a general-purpose or dedicated computer including, for example, a processor (hardware processor) such as a central processing unit (CPU), memories such as random-access memory (RAM) and read-only memory (ROM), a quantum computer, or the like, executing a predetermined program. That is, the determination device 13 in each embodiment has, for example, a processing circuit configured to implement each of the components. This computer may include one processor and memory, or multiple processors and memories. This program may be installed on the computer or may be pre-recorded in a ROM or the like. Furthermore, some or all of the processing units may be configured using electronic circuits that independently realize processing functions, rather than electronic circuits that realize functional configurations by loading programs like a CPU. Furthermore, the electronic circuits constituting one device may include multiple CPUs.

[0036] FIG. 6 is a block diagram illustrating a hardware configuration of a determination device 13 according to an embodiment. As illustrated in FIG. 6, the determination device 13 of this example includes a central processing unit (CPU) 10a, an input unit 10b, an output unit 10c, a random access memory (RAM) 10d, a read-only memory (ROM) 10e, an auxiliary storage device 10f, a measurement unit 10h, and a bus 10g. The CPU 10a of this example includes a control unit 10aa, a calculation unit 10ab, and a register 10ac, and executes various calculation processes according to various programs loaded into the register 10ac. The input unit 10b is an input terminal, keyboard, mouse, touch panel, or the like, through which data is input. The output unit 10c is an output terminal, display, or the like, through which data is output. The measurement unit 10h is a device that measures the quantum state of each quantum bit. The RAM 10d is a static random access memory (SRAM), dynamic random access memory (DRAM), or the like, and has a program area 10da where predetermined programs are stored and a data area 10db where various data are stored. The auxiliary storage device 10f is a hard disk, magneto-optical disc (MO), semiconductor memory, or the like, and has a program area 10fa where predetermined programs are stored and a data area 10fb where various data are stored. The bus 10g connects the CPU 10a, input unit 10b, output unit 10c, RAM 10d, ROM 10e, measurement unit 10h, and auxiliary storage device 10f so that information can be exchanged. The CPU 10a writes the program stored in the program area 10fa of the auxiliary storage device 10f to the program area 10da of RAM 10d in accordance with the loaded OS (Operating System) program. Similarly, the CPU 10a writes various data stored in the data area 10fb of the auxiliary storage device 10f to the data area 10db of the RAM 10d. The addresses in the RAM 10d where the programs and data are written are then stored in the register 10ac of the CPU 10a.The control unit 10aa of the CPU 10a sequentially reads out these addresses stored in the register 10ac, reads out programs and data from the areas on the RAM 10d indicated by the read addresses, causes the calculation unit 10ab to sequentially execute the calculations indicated by the programs, and stores the calculation results in the register 10ac. With this configuration, the functional configuration of the determination device 13 is realized.

[0037] The program describing this processing can be recorded on a computer-readable recording medium. Examples of computer-readable recording media are non-transitory recording media. Examples of such recording media include magnetic recording devices, optical disks, magneto-optical recording media, and semiconductor memories.

[0038] The program may be distributed by, for example, selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded. Furthermore, the program may be stored in a storage device of a server computer, and then transferred from the server computer to other computers via a network, thereby distributing the program.

[0039] A computer that executes such a program may first temporarily store the program recorded on a portable recording medium or transferred from a server computer in its own storage device. Then, when executing a process, the computer reads the program stored on its own recording medium and executes the process in accordance with the read program. Alternatively, the computer may read the program directly from a portable recording medium and execute the process in accordance with the program. Furthermore, the computer may execute the process in accordance with the program each time a program is transferred from a server computer to the computer. Alternatively, the server computer may not transfer the program to the computer, but may instead execute the process through a so-called ASP (Application Service Provider) service, which realizes the processing function by issuing an execution instruction and obtaining the results. Furthermore, the server computer may execute the process at the terminal using a so-called SaaS (Software as a Service) service, which allows users to use part of a server computer along with the program. In this embodiment, the program includes information used for processing by an electronic computer that is equivalent to a program (such as data that is not a direct instruction to a computer but has properties that dictate computer processing).

[0040] The computer that performs classical processing may be a classical computer or a quantum computer. In this embodiment, the device is configured by running a predetermined program on the computer, but at least a part of the processing may be realized by hardware.

[0041] [Other Modifications] The present invention is not limited to the above-described embodiment. For example, in this embodiment, N quantum bits Q1, ..., Q2 generated by the quantum bit provider 11 are N The quantum state ρ of the quantum bit string 102-m including N quantum bits Q1,...,Q NThe quantum state ρ of the quantum bit string 102-m including N The quantum state ρ of the quantum bit string 102-m including N quantum bits Q1,...,Q obtained by other methods may be used as the object of determination. N The quantum state ρ of the quantum state ρ may be the object of determination. Furthermore, 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 executing the processes or as needed. Needless to say, other modifications are possible within the scope of the present invention.

[0042] The present invention can be used, for example, to evaluate the function of generating a desired quantum state in a quantum computer, to evaluate the function of performing a desired quantum calculation, and to evaluate a quantum state transmitted by quantum communication.

[0043] REFERENCE SIGNS LIST 1 Determination system 11 Quantum bit providing device 13 Determination device 134 Update unit 135 Measurement control unit 136 Measurement unit 137 Determination unit

Claims

1. A determination device having: a measurement unit that measures a predetermined number of quantum bits for each quantum bit to obtain a measurement result; and a determination unit that determines the quality of the predetermined number of quantum bits based on the measurement result of a final quantum bit that is the quantum bit that was last measured among the predetermined number of quantum bits.

2. A determination device according to claim 1, wherein the measurement unit measures the final quantum bit based on a measurement basis obtained by updating quantum state information representing the quantum state of a target quantum bit in accordance with the measurement results of quantum bits other than the final quantum bit, to obtain a measurement result of the final quantum bit.

3. A determination device according to claim 2, wherein the measurement unit measures quantum bits other than the final quantum bit using a measurement basis selected according to a set probability.

4. A determination method using a determination device, comprising: a measurement step of measuring a predetermined number of quantum bits for each quantum bit to obtain a measurement result; and a determination step of determining the quality of the predetermined number of quantum bits based on the measurement result of a final quantum bit that is the quantum bit that was last measured among the predetermined number of quantum bits.

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

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