Classical computer, information processing method, and computer-readable recording medium

Abstract

The result confirmation unit (204) calculates the state space probability, which is the probability that the verification object device (300) does not correctly prepare the state space storing the quantum state, the Pauli measurement probability, which is the probability that the verification object device (300) does not correctly perform the Pauli Z measurement and the Pauli X measurement, and the magic state probability, which is the probability that the verification object device (300) does not generate the magic state of the CCZ. The result confirmation unit (204) then calculates the degree of approximation between the quantum state in the verification object device (300) and the magic state of the CCZ, and the measurement accuracy of the Pauli Z measurement and the Pauli X measurement on the quantum state in the verification object device (300), using the state space probability, the Pauli measurement probability, and the magic state probability.

Description

Technical Field

[0001] The present invention relates to a technology for verifying quantum properties. Background Art

[0002] The verifier's classical computer exchanges only classical information with a device (hereinafter referred to as a black box) whose internal operations are unknown. The verifier verifies whether the black box device has "generated and measured quantum states" as requested by the verifier. This type of testing is called a self-test. By performing this self-test, the verifier's classical computer can characterize the operation of the black box device, which has higher computing power than the classical computer. Self-testing enables various quantum information processing methods, such as quantum encryption.

[0003] In non-patent document 1, a self-testing method for the quantum state of two quantum bits with quantum correlation, namely the "Bell State", is proposed. In the method of non-patent document 1, only classical information is exchanged between the classical computer and the black box device, thereby verifying the generation and measurement of the Bell state. However, in the method of non-patent document 1, the following assumption needs to be made: the "two devices" are provided as black box devices, and these two black box devices are completely unable to exchange classical information during the process of performing self-testing. In the case that this assumption is not true, the self-test of the Bell state cannot be performed in the method of non-patent document 1. The exchange of classical information can be easily carried out through a telephone, etc., so there is a problem that it is unrealistic to give this assumption to an actual black box device.

[0004] To address this issue, Non-Patent Document 2 makes the assumption that a black box device operating in a quantum manner cannot crack quantum-resistant cryptography, known as lattice cryptography. Non-Patent Document 2 demonstrates that by making this assumption, Bell state self-tests can be performed on a "black box device operating in a single quantum manner." Regarding quantum-resistant cryptography, it is believed that even a quantum computer cannot efficiently crack it. Therefore, Non-Patent Document 2 provides a Bell state self-test method for a single black box device under realistic assumptions.

[0005] Prior art literature

[0006] Non-patent literature

[0007] Non-patent document 1: Ben W. Reichardt, Falk Unger, Umesh Vazirani. Classical command of quantum systems. Nature volume 496, pages 456-460 (2013).

[0008] Non-patent literature 2: Tony Metger and Thomas Vidick. Self-testing of a single-quantum device under computational assumptions. arXiv: 2001.09161V2 (2020). Summary of the Invention

[0009] Problems to be solved by the invention

[0010] The "Bell state" is a quantum state that is stable in Pauli Z and Pauli X measurements and belongs to a class known as stable operator states. Whether the black box device being verified generates Bell states can be verified based on the results of stable operator measurements consisting of Pauli Z and Pauli X measurements. Specifically, the self-test method proposed in Non-Patent Document 2 consists of the following two tests.

[0011] (A) Test whether the black box device being verified correctly performs Pauli Z and Pauli X measurements.

[0012] (B) Testing whether the measurement results of the stable operator measurement of the Bell state are correct

[0013] The self-testing method proposed in Non-Patent Document 2 is a test based on the properties of stable operator states. Therefore, by also using the method of Non-Patent Document 2 on other stable operator states, self-testing can be performed. Here, the entire set of quantum states is composed of two mutually exclusive state sets, namely "stable operator states" and "unstable operator states." According to the results of Non-Patent Document 2, it can be self-tested for stable operator states. However, it is unclear whether another state category, namely unstable operator states, can be self-tested using the same mechanism as Non-Patent Document 2.

[0014] The main purpose of the present invention is to address this issue. More specifically, the present invention aims to self-test the "magic state of CCZ (Controlled Controlled-Z)," a representative unstable operator state. Stable operator states are insufficient for quantum computation. On the other hand, the magic state of CCZ is known to be indispensable for quantum computation. Therefore, the present invention provides quantum verification to determine whether a black box device possesses the resource states necessary for quantum computation.

[0015] Means for solving problems

[0016] The classical computer of the present invention comprises: a state space probability calculation unit, which uses a quantum computer to measure a quantum state generated by the quantum computer, namely a first quantum state, and a second measurement result, which is a result obtained by the quantum computer measuring a quantum state after the first quantum state is changed by the measurement of the first quantum state, namely a second quantum state, to calculate the probability that the quantum computer has not correctly prepared a state space storing the first quantum state, namely a state space probability; a Pauli measurement probability calculation unit, which uses the quantum computer to measure a quantum state after the first quantum state is changed by the measurement of the first quantum state, namely a second measurement result, a Pauli measurement probability, which is a probability that the quantum computer has incorrectly performed the Pauli Z measurement and the Pauli X measurement on the fourth quantum state, based on a third measurement result obtained by measuring a third quantum state different from the second quantum state, a fourth measurement result obtained by the quantum computer measuring a fourth quantum state after the third quantum state is changed by the measurement of the third quantum state, and the first measurement result; a magic state probability calculation unit, which calculates the magic state probability, which is a probability that the quantum computer has not correctly generated a magic state of CCZ (Controlled Controlled-Z), using the first measurement result, the third measurement result, and the fourth measurement result; and an approximation accuracy calculation unit, which calculates the approximation between the fourth quantum state and the magic state of CCZ, as well as the measurement accuracy of the Pauli Z measurement and the Pauli X measurement on the fourth quantum state, using the state space probability, the Pauli measurement probability, and the magic state probability.

[0017] Effects of the Invention

[0018] According to the present invention, a self-test can also be performed on the "magic state of CCZ". BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a diagram showing a configuration example of a quantum property verification system according to the first embodiment.

[0020] Figure 2 This is a flowchart showing an example of the operation of the quantum verification system according to the first embodiment.

[0021] Figure 3 This is a flowchart showing an example of the operation of the quantum verification system according to the first embodiment.

[0022] Figure 4 This is a diagram showing a hardware configuration example of the verification device according to the first embodiment. DETAILED DESCRIPTION

[0023] Implementation Method 1

[0024] ***summary***

[0025] In this embodiment, a case is described in which a classical computer uses the same mechanism as in Non-Patent Document 2 to perform a self-test to verify whether a quantum computer, which is a black box device, correctly performs "generation and measurement of quantum states" in the magic state of the CCZ.

[0026] This embodiment is achieved by generalizing the “method of verifying the generation of an unstable operator state using the measurement results of Pauli Z measurement and Pauli X measurement (the results of generalized stable operator measurement)” provided by the following reference.

[0027] [Reference] Yuki Takeuchi and Tomoyuki Morimae. Verification of Many-Qubit States. Physical Review X 8, 021060 (2018)

[0028] The verification method described in the reference document can only verify the generation of unstable operator states, assuming that the Pauli Z and Pauli X measurements were performed correctly. Specifically, the verification method described in the reference document does not verify the correct performance of the Pauli Z and Pauli X measurements; it only verifies the correct generation of the quantum state. Self-testing requires verifying the correct performance of both the "generation" and "measurement" of the quantum state. Therefore, the verification method described in the reference document does not implement self-testing.

[0029] In this embodiment, the above-mentioned test (A) provided in Non-Patent Document 2 (discussed again below) is used for the "magic state of CCZ", which is a representative unstable operator state.

[0030] (A) Test whether the black box device being verified correctly performs Pauli Z and Pauli X measurements.

[0031] By performing the aforementioned test (A) provided in Non-Patent Document 2, a classical computer can generalize the verification method described in the reference to a black-box device operating in the magic state of the CCZ. Thus, in this embodiment, a self-test can be implemented that verifies both the generation and measurement of quantum states in the magic state of the CCZ.

[0032] Here, the “magic state of CCZ” is a quantum state in which a “controlled-controlled-phase gate (CCZ gate)” is applied to three quantum bits in an equal superposition of “0” and “1”.

[0033] The quantum states of bits "0" and "1" are represented as "|0>" and "|1>," respectively, and the quantum state in an equal superposition of "|0>" and "|1>" is represented as "|+>." In this case, the "magic state of CCZ" is the quantum state represented as "|+>|+>|+>-2|1>|1>|1>."

[0034] The Pauli Z measurement targets a 2-row, 2-column matrix whose diagonal elements, when expressed using "|0>" and "|1>," are "+1" and "-1," respectively, and whose remaining elements are "0." The Pauli Z measurement yields a measurement result of "+1" or "-1," depending on the eigenspace of the matrix into which the state is projected.

[0035] The Pauli X-measure targets matrices with two rows and two columns, where the two off-diagonal elements are "+1" and the remaining matrix elements are "0" when the matrix is ​​expressed using "|0>" and "|1>." The Pauli X-measure yields a measurement result of "+1" or "-1" depending on the eigenspace of the matrix into which the state is projected.

[0036] ***Description of the structure***

[0037] Figure 1 A configuration example of a quantum property verification system 100 according to this embodiment is shown.

[0038] like Figure 1 As shown, the quantum property verification system 100 includes a verification device 200 and a verification target device 300 .

[0039] Verification device 200 is a classical computer that processes so-called classical information. Verification device 200 is, for example, a PC (Personal Computer). The operation steps of verification device 200 correspond to the information processing method. Furthermore, the program that implements the operation of verification device 200 corresponds to the information processing program.

[0040] The verification target device 300 is a quantum computer that performs quantum calculations and corresponds to a black box device.

[0041] The classic communication path 101 is a communication path connecting the verification device 200 and the verification target device 300. The classic communication path 101 may be any communication path that transmits digital signals, such as a telephone network or the Internet.

[0042] Next, the configuration of the verification device 200 and the configuration of the verification target device 300 will be described in sequence.

[0043] Figure 1The verification device 200 shown includes a data generation unit 201 , a key information generation unit 202 , a random number generation unit 203 , and a result confirmation unit 204 .

[0044] Although not shown in the figure, the verification device 200 includes a verification-side information processing unit that processes classic information used in the verification device 200 .

[0045] The data generation unit 201 randomly selects one 3-bit string from the set of 3-bit strings {000, 001, 010, 100, 111} and transmits the 3-bit string (θ1, θ2, θ3) selected from {000, 001, 010, 100, 111} to the key information generation unit 202 .

[0046] Furthermore, the data generation unit 201 generates a security parameter λ and transmits the security parameter λ to the key information generation unit 202 .

[0047] In addition, the 3-bit string (θ1, θ2, θ3) and the security parameter λ are also referred to as initial data.

[0048] The key information generation unit 202 generates public keys (k1, k2, k3) and trapdoors (tk1, tk2, tk3) using the initial data (3-bit string (θ1, θ2, θ3) and security parameter λ) received from the data generation unit 201.

[0049] Here, the public keys (k1, k2, k3) are data used by the verification target device 300 to prove that the magical state of the CCZ has been generated and the Pauli Z measurement and Pauli X measurement on the magical state of the CCZ have been performed.

[0050] The trapgates (tk1, tk2, tk3) are data used by the verification device 200 to verify that the verification target device 300 has generated the magic state of the CCZ and performed the Pauli Z measurement and the Pauli X measurement on the magic state of the CCZ.

[0051] The key information generation unit 202 calculates the public key (k1, k2, k3) and the trapdoor (tk1, tk2, tk3) using the method described in Non-Patent Document 2.

[0052] The key information generation unit 202 transmits the public key (k1, k2, k3) to the verification target device 300.

[0053] The random number generator 203 generates a randomly selected bit of "0" or "1." The random number generator 203 then transmits the generated bit of "0" or "1" to the result verification unit 204. The result verification unit 204 transmits the bit of "0" or "1" to the verification target device 300. This bit of "0" or "1" is referred to as a probabilistic random number. Details of probabilistic random numbers will be described later.

[0054] Furthermore, the random number generator 203 generates a 3-bit random number (q1, q2, q3) and transmits the generated 3-bit random number (q1, q2, q3) to the verification target device 300 via the classical communication path 101. The random number (q1, q2, q3) is used in the measurement of the fourth quantum state, which will be described later. Hereinafter, this 3-bit random number will be referred to as the measurement random number (q1, q2, q3). The details of the measurement random number (q1, q2, q3) will be described later.

[0055] The result confirmation unit 204 calculates the state space probability, the Pauli measurement probability, and the magic state probability. Details of the state space probability, the Pauli measurement probability, and the magic state probability are described later. Furthermore, the result confirmation unit 204 uses the state space probability, the Pauli measurement probability, and the magic state probability to calculate the degree of similarity between the fourth quantum state and the magic state of the CCZ, as well as the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state.

[0056] The result confirmation unit 204 corresponds to a state space probability calculation unit, a Pauli measurement probability calculation unit, a magic state probability calculation unit, and an approximation accuracy calculation unit.

[0057] The processing performed by the result confirmation unit 204 corresponds to the state space probability calculation processing, the Pauli measurement probability calculation processing, the magic state probability calculation processing, and the approximation accuracy calculation processing.

[0058] The verification target device 300 includes a quantum state generating unit 301 and a quantum state measuring unit 302. Although not shown, the verification target device 300 includes a verification target device-side information processing unit that processes data used in the verification target device 300.

[0059] The quantum state generation unit 301 generates a quantum state.

[0060] The quantum state measurement unit 302 measures the quantum state generated by the quantum state generation unit 301 , thereby outputting a measurement result.

[0061] The verification target device 300 can be any quantum computer. For example, the verification target device 300 can be a quantum computer using superconducting qubits. In this case, the quantum state generation unit 301 generates a quantum state using superconducting qubits and microwaves. Furthermore, the quantum state measurement unit 302 uses microwaves to measure the quantum state of the superconducting qubits, obtaining the measurement result as an electrical signal.

[0062] Figure 4 A hardware configuration example of the verification device 200 according to this embodiment is shown.

[0063] The verification device 200 includes, as hardware, a processor 901 , a main storage device 902 , an auxiliary storage device 903 , and a communication device 904 .

[0064] The auxiliary storage device 903 stores a program for realizing the functions of the data generation unit 201 , the key information generation unit 202 , the random number generation unit 203 , and the result confirmation unit 204 .

[0065] These programs are loaded from the auxiliary storage device 903 to the main storage device 902. Then, the processor 901 executes these programs to perform the operations of the data generation unit 201, the key information generation unit 202, the random number generation unit 203, and the result confirmation unit 204.

[0066] exist Figure 4 , a state in which the processor 901 executes a program that realizes the functions of the data generation unit 201, the key information generation unit 202, the random number generation unit 203, and the result confirmation unit 204 is schematically shown.

[0067] The communication device 904 performs classic communication with the verification target device 300 via the classic communication path 101 .

[0068] ***Description of the action***

[0069] Here, the outline of the operation of the result confirmation unit 204 of this embodiment will be described. In addition, the outline of the operation of the verification target device 300 required to explain the operation of the result confirmation unit 204 will also be described.

[0070] The verification object device 300 uses the public key (k1, k2, k3) sent from the random number generator 203 to generate the public key in step S403 ( Figure 2 ) generates a quantum state. The quantum state generated in step S403 is called the first quantum state.

[0071] The verification target device 300 measures the first quantum state ( S403 ). The measurement result obtained by the verification target device 300 is referred to as the first measurement result ( y1 , y2 , y3 ). The verification target device 300 transmits the first measurement result ( y1 , y2 , y3 ) to the verification device 200 .

[0072] In addition, the steps "S403", "S408" and so on shown below indicate Figure 2 or Figure 3 Steps shown. Figure 2 and Figure 3 The details are described later.

[0073] Furthermore, by measuring the first quantum state ( S403 ), the quantum state changes from the first quantum state.

[0074] When the value of the probability calculation random number generated by the random number generator 203 is “0”, the quantum state that has changed from the first quantum state is referred to as the second quantum state.

[0075] The verification target device 300 measures the second quantum state (S408). The measurement result obtained by the verification target device 300 when measuring the second quantum state (S408) is referred to as the second measurement result (m1, m2, m3). The verification target device 300 transmits the second measurement result (m1, m2, m3) to the verification device 200 (S409).

[0076] On the other hand, the quantum state that changes from the first quantum state when the value of the probability calculation random number is "1" is called the third quantum state. The verification object device 300 measures the third quantum state (S412). The measurement result obtained by the verification object device 300 measuring the third quantum state (S412) is called the third measurement result (d1, d2, d3). The verification object device 300 sends the third measurement result (d1, d2, d3) to the verification device 200 (S413).

[0077] Furthermore, the quantum state resulting from the change in the third quantum state caused by the measurement of the third quantum state (S412) is referred to as the fourth quantum state. The verification object device 300 uses the measurement random number (q1, q2, q3) generated by the random number generator 203 to measure the fourth quantum state (S416). The measurement result obtained by the verification object device 300 from measuring the fourth quantum state (S416) is referred to as the fourth measurement result (v1, v2, v3). The verification object device 300 transmits the fourth measurement result (v1, v2, v3) to the verification device 200 (S417).

[0078] The verification target device 300 performs a quantum state generation and measurement sequence consisting of generation and measurement of a first quantum state, measurement of a second quantum state, or measurement of a third quantum state and measurement of a fourth quantum state multiple times.

[0079] Then, the verification object device 300 generates a measurement sequence for each quantum state and sends the first measurement result (y1, y2, y3) to the verification device 200 (S405), sends the second measurement result (m1, m2, m3) to the verification device 200 (S409), or sends the third measurement result (d1, d2, d3) and the fourth measurement result (v1, v2, v3) to the verification device 200 (S413, S417).

[0080] As described above, the result confirmation unit 204 calculates the state space probability, the Pauli measurement probability, and the magic state probability.

[0081] Furthermore, the result confirmation unit 204 calculates the approximation between the fourth quantum state and the magic state of CCZ and the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state using the state space probability, the Pauli measurement probability, and the magic state probability.

[0082] The state space probability is the probability that the verification target device 300 has not correctly prepared the state space storing the first quantum state. Hereinafter, the state space probability is expressed as state space probability E1 or probability E1.

[0083] The result confirmation unit 204 calculates the state space probability E1 using the public key (k1, k2, k3), the first measurement result (y1, y2, y3) and the second measurement result (m1, m2, m3) of each quantum state generation measurement sequence.

[0084] The Pauli measurement probability is the probability that the verification target device 300 does not correctly perform the Pauli Z measurement and the Pauli X measurement in the fourth quantum state. Hereinafter, the Pauli measurement probability is expressed as the Pauli measurement probability E2 or the probability E2.

[0085] The result confirmation unit 204 uses the public key (k1, k2, k3), the trapdoor (tk1, tk2, tk3), the first measurement result (y1, y2, y3), the third measurement result (d1, d2, d3) and the fourth measurement result (v1, v2, v3) of each quantum state generation measurement sequence to calculate the Pauli measurement probability E2.

[0086] The magic state probability is the probability that the CCZ is not generated in the magic state in the verification target device 300. Hereinafter, the magic state probability is expressed as the magic state probability E3 or the probability E3.

[0087] The result confirmation unit 204 calculates the magic state probability E3 using the public key (k1, k2, k3), the trapdoor (tk1, tk2, tk3), the first measurement result (y1, y2, y3), the third measurement result (d1, d2, d3) and the fourth measurement result (v1, v2, v3) of each quantum state generation measurement sequence.

[0088] Next, the operation of the quantum property verification system 100 according to this embodiment will be described with reference to a flowchart.

[0089] Figure 2 and Figure 3 Is shown using Figure 1 Flowchart of the steps of quantum property verification of the quantum property verification system 100.

[0090] Figure 2 Steps S401 to S402, steps S406 to S407 and S410, Figure 3 Steps S411 , S414 to S415 , and S418 to S420 are processes executed by the verification apparatus 200 . Figure 2 Steps S403 to S405, steps S408 to S409, Figure 3 Steps S412 to S413 and S416 to S417 are processes executed by the verification target device 300 .

[0091] The steps S401 to S418 correspond to a quantum state generation measurement sequence. In this embodiment, the quantum state generation measurement sequence is repeated N times. The method for determining the value of "N" will be described later.

[0092] In step S401 , the data generator 201 randomly selects a 3-bit string from the set of 3-bit strings {000, 001, 010, 100, 111} and sends the selected 3-bit string (θ1, θ2, θ3) to the key information generator 202 .

[0093] Furthermore, the data generation unit 201 generates a security parameter λ and transmits the generated security parameter λ to the key information generation unit 202 .

[0094] In step S402, the key information generation unit 202 generates a public key (k1, k2, k3) and a trapdoor (tk1, tk2, tk3) based on the initial data (the 3-bit string (θ1, θ2, θ3) and the security parameter λ) generated by the data generation unit 201. The key information generation unit 202 then transmits the public key (k1, k2, k3) to the verification target device 300 via the communication device 904 and the standard communication path 101.

[0095] Here, the trapdoor (tk1, tk2, tk3) is secret information and therefore needs to be strictly kept so as not to be leaked outside the verification device 200.

[0096] In step S403, the quantum state generation unit 301 generates a quantum state (first quantum state) based on the public key (k1, k2, k3) transmitted from the verification device 200. Then, the quantum state measurement unit 302 measures the generated quantum state (first quantum state).

[0097] In step S404 , the verification target device 300 stores the first measurement result ( y1 , y2 , y3 ).

[0098] In step S405 , the quantum state measurement unit 302 transmits the first measurement result ( y1 , y2 , y3 ) to the verification device 200 via the classical communication path 101 .

[0099] In the verification device 200, the result confirmation unit 204 receives the first measurement result (y1, y2, y3) via the communication device 904. The result confirmation unit 204 then stores the first measurement result (y1, y2, y3) in the auxiliary storage device 903. The auxiliary storage device 903 stores the first measurement result (y1, y2, y3).

[0100] In step S406 , the random number generator 203 generates a 1-bit random number (probability calculation random number).

[0101] If the random number (probability calculation random number) generated in step S406 is "0", steps S407 to S410 are performed. On the other hand, if the random number (probability calculation random number) generated in step S406 is "1", steps S411 to S418 are performed.

[0102] [When the random number generated in step S406 is 0]

[0103] In step S407, the random number generator 203 of the verification device 200 transmits the probability calculation random number value "0" to the verification target device 300 via the communication device 904 and the classic communication path 101. The random number generator 203 also notifies the result confirmation unit 204 of the probability calculation random number value "0".

[0104] In step S408 , the quantum state measurement unit 302 measures the second quantum state based on the value “0” of the random number calculated by probability, and stores the second measurement result ( m1 , m2 , m3 ).

[0105] In step S409 , the quantum state measurement unit 302 transmits the second measurement result ( m1 , m2 , m3 ) to the verification device 200 via the classical communication path 101 .

[0106] In step S410, the result confirmation unit 204 receives the second measurement result (m1, m2, m3) via the communication device 904. The result confirmation unit 204 then stores the second measurement result (m1, m2, m3) in the auxiliary storage device 903. The auxiliary storage device 903 stores the second measurement result (m1, m2, m3).

[0107] Furthermore, the result confirmation unit 204 uses the public key (k1, k2, k3) generated in step S402 to determine whether the first measurement result (y1, y2, y3) transmitted from the verification target device 300 in step S405 and the second measurement result (m1, m2, m3) transmitted from the verification target device 300 in step S409 are correct. The result confirmation unit 204 then stores the judgment result ("correct" or "incorrect") in the auxiliary storage device 903. The auxiliary storage device 903 stores the judgment result ("correct" or "incorrect"). The details of the judgment method performed by the result confirmation unit 204 will be described later.

[0108] [When the random number generated in step S406 is 1]

[0109] In step S411, the random number generator 203 of the verification device 200 transmits the probability calculation random number value "1" to the verification target device 300 via the communication device 904 and the classic communication path 101. The random number generator 203 also notifies the result confirmation unit 204 of the probability calculation random number value "1".

[0110] In step S412 , the quantum state measurement unit 302 measures the third quantum state based on the value “1” of the probability-calculated random number, and stores the third measurement result ( d1 , d2 , d3 ).

[0111] In step S413 , the quantum state measurement unit 302 transmits the third measurement result ( d1 , d2 , d3 ) to the verification device 200 via the classical communication path 101 .

[0112] In step S414, the result confirmation unit 204 receives the third measurement result (d1, d2, d3) via the communication device 904. The result confirmation unit 204 then stores the third measurement result (d1, d2, d3) in the auxiliary storage device 903. The auxiliary storage device 903 stores the third measurement result (d1, d2, d3).

[0113] Furthermore, the random number generator 203 generates a 3-bit measurement random number (q1, q2, q3).

[0114] In step S415 , the random number generator 203 transmits a 3-bit measurement random number ( q1 , q2 , q3 ) to the verification target device 300 via the classical communication path 101 .

[0115] Furthermore, the random number generation unit 203 notifies the result confirmation unit 204 of the measured random numbers (q1, q2, q3).

[0116] In step S416 , the quantum state measurement unit 302 measures the fourth quantum state based on the 3-bit measurement random number ( q1 , q2 , q3 ) sent from the verification device 200 , and stores the fourth measurement result ( v1 , v2 , v3 ).

[0117] In step S417 , the quantum state measurement unit 302 sends the fourth measurement result ( v1 , v2 , v3 ) to the verification device 200 via the classical communication path 101 .

[0118] In step S418, the result confirmation unit 204 receives the fourth measurement result (v1, v2, v3) via the communication device 904. The result confirmation unit 204 then stores the fourth measurement result (v1, v2, v3) in the auxiliary storage device 903. The auxiliary storage device 903 stores the fourth measurement result (v1, v2, v3).

[0119] Furthermore, the result confirmation unit 204 determines whether the first measurement result (y1, y2, y3) transmitted from the verification target device 300 in step S405, the third measurement result (d1, d2, d3) transmitted from the verification target device 300 in step S413, and the fourth measurement result (v1, v2, v3) transmitted from the verification target device 300 in step S416 are correct, and stores the determination result, "correct" or "incorrect," in the auxiliary storage device 903. The auxiliary storage device 903 stores the determination result, "correct" or "incorrect."

[0120] More specifically, the result confirmation unit 204 uses the 3-bit string (θ1, θ2, θ3) generated in step S401, the public key (k1, k2, k3) and trapdoor (tk1, tk2, tk3) generated in step S402, and the measurement random number (q1, q2, q3) generated in step S414 to determine the correctness of the first measurement result (y1, y2, y3), the third measurement result (d1, d2, d3) and the fourth measurement result (v1, v2, v3).

[0121] After the above quantum state generation measurement sequence is performed N times, in step S419 , the result confirmation unit 204 calculates the probability E1 , the probability E2 , and the probability E3 using the determination results “error” obtained in steps S410 and S418 .

[0122] Finally, in step S420 , the result confirmation unit 204 obtains the result of the self-test based on the probability E1 , probability E2 , and probability E3 calculated in step S419 .

[0123] Next, the details of the operation of the result confirmation unit 204 in step S410 , step S418 , step S419 , and step S420 will be described.

[0124] [When the probability calculated random number notified from the random number generation unit 203 is "0"]

[0125] That is, when the probability calculation random number "0" is notified from the random number generator 203 in step S407, the result confirmation unit 204 determines the correctness of the second measurement result (m1, m2, m3) in step S410 according to the following procedure.

[0126] In addition, step S410 is a process for verifying whether the verification target device 300 has correctly prepared the state space storing the first quantum state.

[0127] The result confirmation unit 204 uses the public key (k1, k2, k3) received from the key information generation unit 202 and the first measurement result (y1, y2, y3) and the second measurement result (m1, m2, m3) received from the verification target device 300 to determine the accuracy of the second measurement result (m1, m2, m3). Furthermore, the result confirmation unit 204 determines the accuracy of the second measurement result (m1, m2, m3) using the method described in Non-Patent Document 2.

[0128] If the verification object device 300 correctly prepares the state space storing the first quantum state, the probability that the second measurement result (m1, m2, m3) is judged to be "erroneous" is zero. However, if the verification object device 300 does not correctly prepare the state space storing the first quantum state, the probability that the second measurement result (m1, m2, m3) is judged to be "erroneous" is greater than zero.

[0129] [When the probability calculated random number notified from the random number generation unit 203 is "1"]

[0130] When the probability calculation random number "1" is notified from the random number generation unit 203 in step S411, in step S418, the result confirmation unit 204 determines the correctness of the first measurement result (y1, y2, y3), the third measurement result (d1, d2, d3) and the fourth measurement result (v1, v2, v3) according to the following steps.

[0131] The process of step S418 is intended to verify whether the verification target device 300 has correctly performed the Pauli Z measurement and the Pauli X measurement in the fourth quantum state, and whether the magical state of the CCZ has been correctly generated.

[0132] Specifically, the result confirmation unit 204 determines whether the result is correct or not according to the following rules (a) to (e).

[0133] Furthermore, rules (a) to (d) are rules used by the result confirmation unit 204 to verify whether the verification target device 300 has correctly performed the Pauli Z measurement and the Pauli X measurement on the fourth quantum state. Rule (e) is a rule used by the result confirmation unit 204 to verify whether the verification target device 300 has correctly generated the magic state of the CCZ for the fourth quantum state.

[0134] Rule (a): Applies to the case where (θ1,θ2,θ3) = (0,0,0)

[0135] The random number generator 203 randomly generates a value from "1, 2, 3" and sends the generated value to the result checker 204. The value sent from the random number generator 203 to the result checker 204 is set to "i". Here, "i" is a value from "1, 2, 3".

[0136] The result confirmation unit 204 obtains the public key ki corresponding to "i" based on the public key (k1, k2, k3) received from the key information generation unit 202. Furthermore, the result confirmation unit 204 obtains the measurement result yi corresponding to "i" based on the first measurement result (y1, y2, y3) received from the verification target device 300. The result confirmation unit 204 then derives the bit bi from the obtained measurement result yi. The result confirmation unit 204 then determines whether both the following (condition 1) and (condition 2) are met.

[0137] If both (condition 1) and (condition 2) are satisfied, the result confirmation unit 204 stores the determination result "error" in the auxiliary storage device 903. If at least one of (condition 1) and (condition 2) is not satisfied, the result confirmation unit 204 stores the determination result "correct" in the auxiliary storage device 903.

[0138] (Condition 1) “bi is different from the measurement result vi received from the verification target device 300”

[0139] (Condition 2) “qi is equal to 0”

[0140] In addition, bit bi is a check bit used to check whether the verification object device 300 has correctly prepared the state of the Z basis in the i-th quantum state in the fourth quantum state and correctly performed the Pauli Z measurement. Therefore, bit bi is called the "i-th Z basis-state generation measurement-check bit". The result confirmation unit 204 calculates the "i-th Z basis-state generation measurement-check bit bi" using the method described in non-patent document 2. The "i-th Z basis-state generation measurement-check bit bi" is equivalent to the Z basis check bit. In addition, the processing based on rule (a) is called Z basis check processing.

[0141] Furthermore, the measurement result vi is the measurement result corresponding to "i" in the fourth measurement result (v1, v2, v3). Furthermore, the bit qi is the bit corresponding to "i" in the measurement random number (q1, q2, q3).

[0142] Rule (b): Applies to the case where (θ1,θ2,θ3) = (1,0,0)

[0143] The result confirmation unit 204 derives bit r1 from the public key (k1, k2, k3) and trapdoor (tk1, tk2, tk3) received from the key information generation unit 202, and the first measurement result (y1, y2, y3) and the third measurement result (d1, d2, d3) received from the verification target device 300. The result confirmation unit 204 then determines whether the following (condition 1) and (condition 2) are both met.

[0144] If both (condition 1) and (condition 2) are satisfied, the result confirmation unit 204 stores the determination result "error" in the auxiliary storage device 903. If at least one of (condition 1) and (condition 2) is not satisfied, the result confirmation unit 204 stores the determination result "correct" in the auxiliary storage device 903.

[0145] (Condition 1) “r1 is different from the measurement result v1 received from the verification target device 300”

[0146] (Condition 2) “q1 is equal to 1”

[0147] Furthermore, bit r1 is a check bit used to verify whether the verification target device 300 correctly prepared the X-basis state in the first quantum state of the fourth quantum state and correctly performed the Pauli X-measurement. Therefore, bit r1 is referred to as the "first X-basis-state generation measurement-check bit." The result confirmation unit 204 calculates the "first X-basis-state generation measurement-check bit r1" using the method described in Non-Patent Document 2. The "first X-basis-state generation measurement-check bit r1" corresponds to the X-basis check bit. Furthermore, the process based on rule (b) is referred to as the X-basis check process.

[0148] Furthermore, the measurement result v1 is the first measurement result v1 in the fourth measurement result (v1, v2, v3). Furthermore, the bit q1 is the first bit q1 in the measurement random number (q1, q2, q3).

[0149] Rule (c): Applies to the case where (θ1,θ2,θ3) = (0,1,0)

[0150] The result confirmation unit 204 derives bit r2 from the public key (k1, k2, k3) received from the key information generation unit 202, the trapdoor (tk1, tk2, tk3), and the second measurement result d2 of the first and third measurement results (d1, d2, d3) received from the verification target device 300. The result confirmation unit 204 then determines whether the following (condition 1) and (condition 2) are both met.

[0151] If both (condition 1) and (condition 2) are satisfied, the result confirmation unit 204 stores the determination result "error" in the auxiliary storage device 903. If at least one of (condition 1) and (condition 2) is not satisfied, the result confirmation unit 204 stores the determination result "correct" in the auxiliary storage device 903.

[0152] (Condition 1) “r2 is different from the measurement result v2 received from the verification target device 300”

[0153] (Condition 2) “q2 is equal to 1”

[0154] Furthermore, bit r2 is a check bit used to verify whether the verification target device 300 correctly prepared the X-basis state in the second quantum state of the fourth quantum state and correctly performed the Pauli X-measurement. Therefore, bit r2 is referred to as the "second X-basis-state generation measurement-check bit." The result confirmation unit 204 calculates the "second X-basis-state generation measurement-check bit r2" using the method described in Non-Patent Document 2. The "second X-basis-state generation measurement-check bit r2" corresponds to the X-basis check bit. Furthermore, the process based on rule (c) is referred to as the X-basis check process.

[0155] Furthermore, the measurement result v2 is the second measurement result v2 in the fourth measurement result (v1, v2, v3). Furthermore, the bit q2 is the second bit q2 in the measurement random number (q1, q2, q3).

[0156] Rule (d): Applies to the case where (θ1,θ2,θ3) = (0,0,1)

[0157] The result confirmation unit 204 derives bit r3 from the public key (k1, k2, k3) received from the key information generation unit 202, the trapdoor (tk1, tk2, tk3), the first measurement result (y1, y2, y3), and the third measurement result (d1, d2, d3) received from the verification target device 300. The result confirmation unit 204 then determines whether the following (condition 1) and (condition 2) are both met.

[0158] If both (condition 1) and (condition 2) are satisfied, the result confirmation unit 204 stores the determination result "error" in the auxiliary storage device 903. If at least one of (condition 1) and (condition 2) is not satisfied, the result confirmation unit 204 stores the determination result "correct" in the auxiliary storage device 903.

[0159] (Condition 1) “r3 is different from the measurement result v3 received from the verification target device 300”

[0160] (Condition 2) “q3 is equal to 1”

[0161] Furthermore, bit r3 is a check bit used to verify whether the verification target device 300 correctly prepared the X-basis state in the third quantum state of the fourth quantum state and correctly performed the Pauli X-measurement. Therefore, bit r3 is referred to as the "third X-basis-state generation measurement-check bit." The result confirmation unit 204 calculates the "third X-basis-state generation measurement-check bit r3" using the method described in Non-Patent Document 2. The "third X-basis-state generation measurement-check bit r3" corresponds to the X-basis check bit. Furthermore, the process based on rule (d) is referred to as the X-basis check process.

[0162] Furthermore, the measurement result v3 is the third measurement result v3 in the fourth measurement result (v1, v2, v3). Furthermore, the bit q3 is the third bit q3 in the measurement random number (q1, q2, q3).

[0163] Rule (e): Applies to the case where (θ1,θ2,θ3) = (1,1,1)

[0164] The result confirmation unit 204 calculates the following generalized stable operator measurement 1 result, generalized stable operator measurement 2 result, and generalized stable operator measurement 3 result using the fourth measurement result ( v1 , v2 , v3 ) received from the verification target device 300 .

[0165] The result of generalized stable operator measurement 1: v1+δ(v2,1)·v3

[0166] The result of generalized stable operator measurement 2: v2+δ(v1,1)·v3

[0167] The result of generalized stable operator measurement 3: v3+δ(v1,1)·v2

[0168] Here, the symbol "+" represents the exclusive OR of bits. Specifically, 0+0=0, 0+1=1, 1+0=1, and 1+1=0. Furthermore, the symbol "·" represents the product of bits. Specifically, 0·0=0, 0·1=0, 1·0=0, and 1·1=1. Furthermore, "δ(x,1)" is the so-called Kronecker delta function, which outputs "1" if "x" is "1" and "0" if "x" is not "1."

[0169] Furthermore, the result confirmation unit 204 derives bits u1, u2, and u3 from the public key (k1, k2, k3) received from the key information generation unit 202 and the first measurement result (y1, y2, y3) and third measurement result (d1, d2, d3) received from the verification target device 300.

[0170] Here, bit u1 is a legitimacy check bit used to check the legitimacy of the result of the generalized stabilization operator measurement 1. Bit u2 is a legitimacy check bit used to check the legitimacy of the result of the generalized stabilization operator measurement 2. Bit u3 is a legitimacy check bit used to check the legitimacy of the result of the generalized stabilization operator measurement 3. Result confirmation unit 204 calculates legitimacy check bits u1, u2, and u3 using the method described in Non-Patent Document 2.

[0171] The validity check bit u1, the validity check bit u2, and the validity check bit u3 are respectively equivalent to the generalized stable operator measurement result check bits.

[0172] Then, in any of the following (1) to (3), if (condition 1) and (condition 2) are both satisfied, the result confirmation unit 204 stores the judgment result "error" in the auxiliary storage device 903. In all other cases, the result confirmation unit 204 stores the judgment result "correct" in the auxiliary storage device 903.

[0173] (1) (Condition 1) "(q1,q2,q3) = (1,0,0) holds"

[0174] (Condition 2) “u1 differs from the result of the generalized stable operator measurement 1: v1+δ(v2,1)·v3”

[0175] (2) (Condition 1) "(q1,q2,q3)=(0,1,0) holds"

[0176] (Condition 2) “u2 differs from the result of the generalized stable operator measurement 2: v2 + δ(v1,1)·v3”

[0177] (3) (Condition 1) "(q1,q2,q3)=(0,0,1) holds"

[0178] (Condition 2) “u3 differs from the result of the generalized stable operator measurement 3: v3 + δ(v1,1)·v2”

[0179] After the quantum state generation measurement sequence has been performed N times, in step S419, the result confirmation unit 204 uses the "error" judgment result obtained in steps S410 and S418 to calculate the probabilities E1, E2, and E3. The result confirmation unit 204 calculates the probabilities E1, E2, and E3 according to the following steps.

[0180] Probability E1: the probability of obtaining the judgment result "error" in step S410.

[0181] Probability E2: probability of obtaining a determination result of "error" when (θ1, θ2, θ3) is other than (1, 1, 1) in step S418.

[0182] Probability E3: the probability of obtaining a judgment result of "error" when (θ1, θ2, θ3) is (1, 1, 1) in step S418.

[0183] In step S420 , the result confirmation unit 204 obtains the following self-test results.

[0184] [Result 1]

[0185] When (θ1, θ2, θ3) generated in step S401 is (1, 1, 1), the result confirmation unit 204 obtains the result that "the verification target device 300 has generated a quantum state separated from the magical state of the CCZ by a distance H1 (E1, E2, E3)".

[0186] H1(E1, E2, E3) is a function determined by the above-mentioned probability E1, probability E2, and probability E3.

[0187] The proximity of quantum states is measured using a metric called the tracking distance. The distance H1(E1, E2, E3) represents the proximity of the fourth quantum state to the magic state of the CCZ. The result confirmation unit 204 calculates the proximity of the fourth quantum state to the magic state of the CCZ by calculating the function H1(E1, E2, E3).

[0188] [Result 2]

[0189] When (θ1, θ2, θ3) generated in step S401 is (1, 1, 1), the result confirmation unit 204 obtains the result that "[the probability distribution of the measurement results obtained when the quantum state generated by the verification object device 300 is measured according to the measurement random number (q1, q2, q3) generated in step S414] and [the probability distribution of the measurement results obtained when the CCZ magic state is measured according to the measurement random number (q1, q2, q3) generated in step S414] are separated by a distance H2 (E1, E2, E3)".

[0190] Here, H2(E1, E2, E3) is a function determined by the above-mentioned probability E1, probability E2, and probability E3.

[0191] The closeness of probability distributions is measured by a metric called the so-called tracking distance.

[0192] In the measurement of the CCZ magic state based on the measurement random number (q1, q2, q3) generated in step S414, if the value of the bit qi (where "i" is any number from "1, 2, 3") is "0", it refers to the Pauli Z measurement, and if the value of the bit qi is "1", it refers to the Pauli X measurement.

[0193] The result confirmation unit 204 calculates the function H2 ( E1 , E2 , E3 ) to thereby calculate the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state.

[0194] [Basis for Results 1 and 2]

[0195] If the probability E1 of obtaining the determination result of "error" in step S410 is zero, it means that the verification object device 300 has correctly prepared the state space storing the first quantum state.

[0196] If the probability E2 of obtaining the determination result of “error” in step S418 is zero, it means that the verification object device 300 has correctly performed the Pauli Z measurement and the Pauli X measurement on the fourth quantum state.

[0197] If the probability E3 of obtaining “error” in step S418 is zero, it means that the verification target device 300 has correctly generated the magic state of the CCZ.

[0198] Therefore, if the probability E1, the probability E2, and the probability E3 are all zero, the distance H1 and the distance H2 become zero.

[0199] If at least one of probabilities E1, E2, and E3 is non-zero, this means that the verification target device 300 has not performed a correct Pauli Z measurement and / or Pauli X measurement on the fourth quantum state, and / or that the verification target device 300 has not correctly generated the magic state of the CCZ. Therefore, the greater the probabilities E1, E2, and E3, the further the quantum state generated by the verification target device 300 is from the magic state of the CCZ and / or the further it is from an ideal Pauli measurement (the lower the accuracy of the Pauli measurement).

[0200] The explicit relationship (specific functional form) between the probability E1, probability E2 and probability E3 of the judgment result "error" obtained in step S410 and step S418 and the distance H1 (E1, E2, E3) and the distance H2 (E1, E2, E3) is obtained through calculations based on the principles of quantum mechanics.

[0201] [About the value of "N"]

[0202] The number of repetitions "N" for the quantum state generation measurement sequence is determined by the calculation accuracy T of probabilities E1, E2, and E3 calculated in step S419, as well as the probability P of obtaining "Result 1" and "Result 2." Here, probability P represents the probability that the result is correct. Specifically, in the case of "Result 1," probability P represents the probability that the result "that the verification target device 300 generated a quantum state separated from the magic state of the CCZ by a distance H1 (E1, E2, E3)" is correct.

[0203] Below is a formula (Formula 1) for calculating the value of N using calculation accuracy T and probability P. However, Formula 1 is only one example of a method for calculating the value of N, and the value of N can also be calculated using other methods. In other words, the value of N can be calculated based on "calculation accuracy T" and "probability P" and can be calculated using any method.

[0204] N=(1 / 2T 2 )×ln(3 / (1-P)) Formula 1

[0205] In addition, in Formula 1, "ln" represents a natural logarithm.

[0206] The value of N in Formula 1 can be derived by using a probability inequality (Hoeffding inequality) known in statistical mathematics.

[0207] ***Description of the Effects of the Implementation Method***

[0208] According to this embodiment, a self-test can also be performed on the "magic state of CCZ" using the same mechanism as that of Non-Patent Document 2.

[0209] In this embodiment, a classical computer can verify a black-box device whose operation is unknown. Therefore, this embodiment can verify the accuracy of the generation and measurement of the "magic state of the CCZ," a quantum state essential for quantum computing. In other words, this embodiment can verify quantum properties.

[0210] ***Supplementary description of hardware structure***

[0211] Finally, a supplementary description of the hardware structure of the verification device 200 is given.

[0212] Figure 4 The processor 901 shown is an IC (Integrated Circuit) that performs processing.

[0213] The processor 901 is a CPU (Central Processing Unit), a DSP (Digital Signal Processor), or the like.

[0214] Figure 4 The main storage device 902 shown is a RAM (Random Access Memory).

[0215] Figure 4 The auxiliary storage device 903 shown is a ROM (Read Only Memory), a flash memory, an HDD (Hard Disk Drive), or the like.

[0216] Figure 4 The communication device 904 shown is an electronic circuit that performs communication processing of data.

[0217] The communication device 904 is, for example, a communication chip or a NIC (Network Interface Card).

[0218] Furthermore, an OS (Operating System) is also stored in the auxiliary storage device 903 .

[0219] Furthermore, at least a portion of the OS is executed by the processor 901 .

[0220] The processor 901 executes a program that realizes the functions of the data generation unit 201 , the key information generation unit 202 , the random number generation unit 203 , and the result confirmation unit 204 while executing at least a part of the OS.

[0221] The processor 901 executes the OS, thereby performing task management, storage management, file management, communication control, and the like.

[0222] In addition, at least any one of the information, data, signal values ​​and variable values ​​representing the processing results of the data generation unit 201, the key information generation unit 202, the random number generation unit 203 and the result confirmation unit 204 is stored in at least any one of the main storage device 902, the auxiliary storage device 903, the registers within the processor 901 and the cache memory.

[0223] Furthermore, the program that realizes the functions of the data generation unit 201, the key information generation unit 202, the random number generation unit 203, and the result confirmation unit 204 may be stored on a portable recording medium such as a magnetic disk, a floppy disk, an optical disk, a high-density disk, a Blu-ray (registered trademark) disk, or a DVD. Furthermore, a portable recording medium storing the program that realizes the functions of the data generation unit 201, the key information generation unit 202, the random number generation unit 203, and the result confirmation unit 204 may be distributed.

[0224] In addition, the "unit" in the data generation unit 201, the key information generation unit 202, the random number generation unit 203 and the result confirmation unit 204 can also be rewritten as "circuit", "process", "step", "processing" or "line".

[0225] Furthermore, the verification device 200 may also be implemented by a processing circuit, such as a logic IC (Integrated Circuit), a GA (Gate Array), an ASIC (Application Specific Integrated Circuit), or an FPGA (Field Programmable Gate Array).

[0226] In this case, the data generation unit 201 , the key information generation unit 202 , the random number generation unit 203 , and the result confirmation unit 204 are each realized as a part of a processing circuit.

[0227] In this specification, a processor and a processing circuit are collectively referred to as a "processing circuit."

[0228] That is, the processor and the processing circuit are each a specific example of a “processing circuit”.

[0229] Label Description

[0230] 100: Quantum verification system; 101: Classical communication path; 200: Verification device; 201: Data generation unit; 202: Key information generation unit; 203: Random number generation unit; 204: Result confirmation unit; 300: Verification object device; 301: Quantum state generation unit; 302: Quantum state measurement unit.

Claims

1. A classical computer, comprising: a state space probability calculation unit that calculates a probability (i.e., a state space probability) that the quantum computer has not correctly prepared a state space storing the first quantum state, using a first measurement result (i.e., a result obtained by the quantum computer measuring a first quantum state generated by the quantum computer) and a second measurement result (i.e., a result obtained by the quantum computer measuring a second quantum state resulting from a change in the first quantum state caused by the measurement of the first quantum state); a Pauli measurement probability calculation unit configured to calculate a Pauli measurement probability, namely, a probability that the quantum computer has incorrectly performed a Pauli Z measurement and a Pauli X measurement on the fourth quantum state, using a third measurement result (a result obtained by the quantum computer measuring a third quantum state, which is a quantum state different from the second quantum state and is obtained by measuring the first quantum state), a fourth measurement result (a result obtained by the quantum computer measuring a fourth quantum state, which is a quantum state obtained by measuring the third quantum state), and the first measurement result; a magic state probability calculation unit that calculates the probability that the quantum computer does not generate the magic state of CCZ (Controlled-Controlled-Z), using the first measurement result, the third measurement result, and the fourth measurement result; and An approximation accuracy calculation unit calculates the approximation between the fourth quantum state and the magic state of the CCZ and the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state using the state space probability, the Pauli measurement probability, and the magic state probability.

2. The classical computer according to claim 1, wherein The classical computer further comprises a key information generating unit, which generates a public key and a trapdoor according to initial data. The quantum computer generates the first quantum state according to the public key, The state space probability calculation unit calculates the state space probability using the first measurement result, the second measurement result, and the public key. The Pauli measurement probability calculation unit calculates the Pauli measurement probability using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor. The magic state probability calculation unit calculates the magic state probability using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor.

3. The classical computer according to claim 2, wherein: The Pauli measurement probability calculation unit performs the following processing: a Z-basis check process, using the first measurement result and the public key to generate a Z-basis check bit for checking whether the quantum computer has correctly prepared a Z-basis state for the fourth quantum state and correctly performed the Pauli Z measurement, and determining whether the Z-basis check bit is consistent with the fourth measurement result; as well as X-basis check processing, using the first measurement result, the third measurement result, the public key, and the trapdoor, to generate an X-basis check bit for checking whether the quantum computer has correctly prepared an X-basis state in the fourth quantum state and correctly performed the Pauli X-measurement, and determining whether the X-basis check bit is consistent with the fourth measurement result. The Pauli measurement probability calculation unit calculates the Pauli measurement probability.

4. The classical computer according to claim 2, wherein: The magic state probability calculation unit uses the fourth measurement result and Kronecker delta to calculate the generalized stable operator measurement result, uses the first measurement result, the third measurement result, the public key and the trapdoor to generate a generalized stable operator measurement result check bit for checking the legitimacy of the generalized stable operator measurement result, determines whether the generalized stable operator measurement result and the generalized stable operator measurement result check bit are consistent, and calculates the magic state probability.

5. The classical computer according to claim 1, wherein: The classical computer further includes a random number generator that generates a random number, namely, a probability calculation random number, for determining which of the state space probability calculation, the Pauli measurement probability calculation, and the magic state probability calculation is to be performed. The classical computer calculates the value of the random number according to the probability, and performs any of the calculation of the state space probability by the state space probability calculation unit, the calculation of the Pauli measurement probability by the Pauli measurement probability calculation unit, and the calculation of the magic state probability by the magic state probability calculation unit.

6. The classical computer according to claim 1, wherein: The quantum computer repeatedly performs a quantum state generation and measurement sequence consisting of generation of the first quantum state and measurement of the first quantum state, and measurement of the second quantum state or measurement of the third quantum state and measurement of the fourth quantum state. The state space probability calculation unit calculates the state space probability using the first measurement result and the second measurement result of each of the quantum state generation measurement sequences. The Pauli measurement probability calculation unit calculates the Pauli measurement probability using the first measurement result, the third measurement result, and the fourth measurement result of each of the quantum state generation measurement sequences. The magic state probability calculation unit calculates the magic state probability using a first measurement result, a third measurement result, and a fourth measurement result of each of the quantum state generation measurement sequences.

7. The classical computer according to claim 3, wherein: The classical computer further includes a random number generator that generates a random number used in the measurement of the fourth quantum state by the quantum computer, that is, a measurement random number. The quantum computer uses the measurement random number to measure the fourth quantum state, The Pauli measurement probability calculation unit determines whether the Z-basis check bit and the fourth measurement result are consistent with each other in the Z-basis check process, and determines whether the measurement random number is a predetermined value. The Pauli measurement probability calculation unit determines whether the X-basis check bit and the fourth measurement result match in the X-basis check process, and determines whether the measurement random number is a value other than the predetermined value.

8. The classical computer according to claim 4, wherein: The classical computer further includes a random number generator that generates a random number used in the measurement of the fourth quantum state by the quantum computer, that is, a measurement random number. The quantum computer uses the measurement random number to measure the fourth quantum state, The magic state probability calculation unit determines whether the generalized stable operator measurement result and the generalized stable operator measurement result check bit are consistent, determines whether the measurement random number is a specified value, and calculates the magic state probability.

9. An information processing method, wherein: A classical computer uses a quantum computer to measure a first quantum state generated by the quantum computer, that is, a first measurement result, and a second measurement result, that is, a result obtained by the quantum computer measuring a second quantum state, that is, a quantum state after the first quantum state is changed by the measurement of the first quantum state, to calculate a probability, that is, a state space probability, that the quantum computer has not correctly prepared a state space storing the first quantum state. The classical computer uses a third measurement result obtained by the quantum computer measuring a third quantum state, which is a quantum state different from the second quantum state and is obtained by measuring the first quantum state with the quantum computer, a fourth measurement result obtained by the quantum computer measuring a fourth quantum state, which is a quantum state obtained by measuring the third quantum state with the quantum computer, and the first measurement result to calculate a Pauli measurement probability, that is, a probability that the quantum computer has incorrectly performed a Pauli Z measurement and a Pauli X measurement on the fourth quantum state. The classical computer uses the first measurement result, the third measurement result, and the fourth measurement result to calculate the probability that the quantum computer does not generate the magic state of CCZ, i.e., the magic state probability. The classical computer calculates the approximation between the fourth quantum state and the magic state of the CCZ and the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state using the state space probability, the Pauli measurement probability and the magic state probability.

10. A computer-readable recording medium having recorded thereon an information processing program, the information processing program causing a classical computer to execute the following processing: a state space probability calculation process, using a first measurement result obtained by a quantum computer measuring a first quantum state generated by the quantum computer, and a second measurement result obtained by the quantum computer measuring a second quantum state resulting from a change in the first quantum state caused by the measurement of the first quantum state, to calculate a probability that the quantum computer has not correctly prepared a state space storing the first quantum state, namely, a state space probability; a Pauli measurement probability calculation process, using a third measurement result obtained by the quantum computer measuring a third quantum state, which is a quantum state different from the second quantum state and is obtained by measuring the first quantum state; a fourth measurement result obtained by the quantum computer measuring a fourth quantum state, which is a quantum state obtained by measuring the third quantum state; and the first measurement result, to calculate a Pauli measurement probability, which is a probability that the quantum computer has incorrectly performed a Pauli Z measurement and a Pauli X measurement on the fourth quantum state; a magic state probability calculation process, using the first measurement result, the third measurement result, and the fourth measurement result to calculate the probability that the quantum computer does not generate the magic state of CCZ (controlled-controlled-Z), that is, the magic state probability; and The approximation accuracy calculation process uses the state space probability, the Pauli measurement probability and the magic state probability to calculate the approximation between the fourth quantum state and the magic state of the CCZ and the measurement accuracy of the Pauli Z measurement and the Pauli X measurement for the fourth quantum state.

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