A semi-blind quantum computing method based on quantum circuit computing model

Abstract

The present invention proposes a semi-blind quantum computing method based on a quantum circuit computing model, comprising the following steps: S1 server n indivual Bell The state of particle 1 is sent to the client in sequence; the S2 client immediately measures particle 1 after receiving it, so that the state of each particle 2 evolves into the real computation input state with a one-time pad operator; the S3 server measures the state of particle 2 according to the state sent by the client. H,T,CX The circuit diagram composed of gates executes logic gates in sequence. In the calculation phase, additional quantum measurement interactions with the client are performed to ensure the correctness and confidentiality of the calculation results. S4 The server returns the particles carrying the calculation results to the client. S5. The client executes the corresponding Pauli X,Z The gate can restore the correct calculation result. In the present invention, the client only needs to perform single-particle rotation measurement to achieve the purpose of keeping the calculation result confidential, making semi-blind quantum computing easier to implement experimentally.

Description

Technical Field

[0001] The present invention relates to the field of entrusted quantum computing, and in particular to a semi-blind quantum computing method based on a quantum circuit computing model. Background Art

[0002] Since Feynman proposed the quantum circuit computing model in 1976, the construction of a universal quantum computer has received widespread attention. Its importance stems from the fact that some quantum algorithms implemented on quantum computers are much less complex than classical algorithms that achieve the same purpose. For example, in the factorization problem, Shor's algorithm can be exponentially faster than the best known classical algorithm. In recent years, some countries have invested a lot of resources in the research and development of quantum computers to compete for "quantum supremacy", such as the 72-bit quantum processor Bristlecone released by Google in 2018 and the Osprey chip containing 433 quantum bits released by IBM in 2022. These research results make it possible to successfully develop universal quantum computers in the future. Due to the high cost of constructing and maintaining quantum computers, when they are successfully developed, they will only be in the hands of a few institutions or companies. For some clients who want to achieve universal quantum computing but have only a small amount of quantum capabilities or are completely classical, quantum cloud computing provides a way for them. However, this approach has caused possible problems such as information leakage. How to keep the client's calculation results confidential from the quantum computer (server) during cloud computing is a problem that semi-blind quantum computing is committed to solving.

[0003] Now consider the following question: A client (Alice) with a small amount of quantum power intends to entrust a remote quantum server (Bob) to complete the quantum computation of an arbitrary quantum algorithm. How can Alice keep her computational results confidential from Bob while obtaining the correct computational results? In the scheme proposed by the general semi-blind quantum computation protocol [Tan, Annals of Telecommunications 72, 589–595 (2017)], Alice has the quantum power to prepare any single quantum bit and perform Pauli X and Z operations. Specifically, Alice first prepares a single quantum bit with a one-time pad key and a circuit diagram consisting of several H, S, CX, and Toffoli gates. She then sends both to Bob at the same time, with the former serving as the input particle of the circuit diagram and the latter representing the real algorithm. Next, Bob executes each logic gate on the input particle according to the circuit diagram. Note that the H, S, and CX gates are Clifford gates, and Bob can directly execute these three gates on the input particle with the one-time pad. When Bob executes the Toffoli gate, since this gate does not belong to the Clifford gate, he should return the three particles to be executed before executing it. Alice then performs random X, Z operations on the particle to update the one-time pad key. Finally, Bob performs Toffoli gates on the three particles after the key is updated and eliminates the possible additional SWAP and CZ gates through classical interaction with Alice on the updated key. Repeat the above steps until all logic gates in the circuit diagram are executed. Unfortunately, there is a security vulnerability in this scheme, that is, a dishonest server can obtain the real calculation results without being noticed by the client. Specifically, the server can reproduce the random Pauli X, Z operations performed by the client on the particle through subsequent Bell measurements by replacing the single particle originally sent to the client with a particle in the Bell state. Then, based on the classical interaction with Alice on the updated key, the original one-time pad information on the output state can be restored. On the other hand, the semi-blind quantum computing protocol requires the client to prepare any single quantum bit, which also requires high quantum capabilities of the client. Summary of the invention

[0004] The technical problems to be solved by the present invention are:

[0005] Design a semi-blind quantum computing protocol that can both fill the security loopholes of general semi-blind quantum computing and reduce the quantum capabilities of the client and server.

[0006] The technical solution adopted by the present invention is:

[0007] S1. Bob prepares n pairs of Bell states |φ> 12 =(|00>+|11>) / √2, and send n 1 particles to Alice in sequence;

[0008] S2. Alice performs measurement immediately after receiving each particle, so that the state of the corresponding two particles evolves into the real computation input state with the one-time pad operator, denoted as state X i Z j |ψ>, where i and j are one-time pad keys, |ψ> is the real input state and the coefficients are real numbers;

[0009] S3. Alice sends a circuit diagram consisting of H, T, and CX gates and representing the real algorithm to Bob. Bob then executes the logic gates on n 2-particles in sequence according to the diagram. For the H and CX gates on the circuit diagram, Bob can execute them directly. For the T gate on the circuit diagram, Bob executes according to the following steps A1-A4.

[0010] A1. Bob first executes the T gate on the particle and records it as particle 1;

[0011] A2. Bob prepares two particles with state |+> and executes CZ on these two particles. 12 The door then distributes 1 particle to Alice;

[0012] A3. Alice executes the following on particle 1: is the measurement of the basis, where δ=(r-3i / 2)π, r is a random number of 0 or 1, and the measurement result is recorded as k;

[0013] A4.Bob executes the H gate on particle 2. The state of the particle is Where i, j is the one-time key of particle 1 before executing gate T.

[0014] S4. Bob repeats S3 until all logic gates H, T, CX in the circuit diagram are executed. Finally, he returns the calculation result to Alice;

[0015] S5.Alice can recover the correct calculation results by executing the corresponding Pauli X, Z gates on each particle.

[0016] Beneficial effects of the present invention:

[0017] 1. The present invention makes up for the security loopholes of general semi-blind quantum computing. Specifically, due to the no-signaling principle, Alice's measurement results in the above S2 and A3 processes are kept secret from Bob. Therefore, the latter will not know the state of the corresponding particle after collapse. Therefore, Bob cannot obtain the client's calculation results through cheating methods similar to those in semi-blind quantum computing. The proposed protocol is confidential.

[0018] 2. The present invention makes semi-blind quantum computing easier to implement experimentally. Specifically, the present invention reduces the quantum capability of the client from preparing any single particle in the general semi-blind quantum computing to performing single particle rotation measurement, thereby reducing the quantum capability of the client. On the other hand, the server in the present invention implements quantum computing through a general logic gate set {H, T, CX}, so that it does not need to simultaneously manipulate the three-particle Toffoli gate in the general semi-blind quantum computing protocol, thereby also reducing the quantum capability of the server. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The protocol flow chart is

[0020] Figure 2 Execute S for the client and server 3i Door diagram DETAILED DESCRIPTION

[0021] Consider the following situation: A client (Alice) with the ability to measure quantum bits intends to entrust a remote quantum server (Bob) to complete the quantum computation of any quantum algorithm. How can Alice obtain the correct computation result while keeping her computation result confidential from Bob? To accomplish this task, the specific steps of the protocol are as follows.

[0022] Phase 1. Prepare individual encrypted inputs.

[0023] S1. Bob prepares Bell state And send 1 particle to Alice.

[0024] S2. Alice prepares each input particle X with a one-time pad i Z j When |ψ>=(x|0>+y|1>), where i,j∈{0,1}, x,y are real numbers, and |ψ> is a single quantum bit of real input, she first designs the measurement operator according to the state of the particle.

[0025] M0=U|0><0|U + ,M1=U|1><1|U + ,U=x|0><0|+y|0><1|+y|1><0|-x|1><1|.

[0026] Alice then executes M on the received particle 1. s (s=0,1) is used as the basis for the measurement, and the measurement result is expressed as s. At this time, the state of the two particles is

[0027]

[0028] Repeat the above steps until all input particles with one-time density are prepared.

[0029] Stage 2. Execute logic gates according to the circuit diagram.

[0030] S3. Alice sends a circuit diagram consisting of H, T, and CX gates, which represents the real algorithm. Bob then executes the logic gates in sequence according to the diagram. For the H and CX gates on the circuit diagram, Bob can directly execute them because

[0031] H.X i Z j |ψ>=X j Z i ·H|ψ>,

[0032]

[0033] where i,j,k,l∈{0,1},|ψ>, is an arbitrary single quantum bit, and the matrix subscript indicates the position of the quantum bit it acts on. For the T gate on the circuit diagram, Bob will generate an additional S gate after direct execution, because after ignoring a global phase factor, the following relationship holds:

[0034]

[0035] Note that S i ·S 3i =I, so Alice can perform an additional S 3i The specific steps are as described in A1-A4. Figure 2 .

[0036] A1. After Bob executes the T gate, the state of the particle is S i X i Z j ·T|ψ>1=(α|0>+β|1>)1.

[0037] A2. Then Bob prepares particles with state |+>2 and executes CZ on these two particles. 12 Gate. At this time, the state of the two particles can be expressed as (α|0>|+>+β|1>|->) 12 , then Bob distributes 1 particle to Alice.

[0038] A3. Alice executes the following on the particle: The measurement is based on δ = (r-3i / 2)π, where r is a random number of 0 or 1, and the measurement result is recorded as k. At this time, the state of the two particles is

[0039]

[0040]

[0041] A4.Bob executes the H gate on particle 2 to make the state evolve to The measurement result k and the random number r are only known to Alice.

[0042] S4. Bob repeats S3 until all logic gates H, T, CX in the circuit diagram are executed. Finally, he returns the calculation result to Alice.

[0043] S5.Alice only needs to execute the corresponding Pauli X, Z gates on each particle to recover the true calculation results.

[0044] Note: The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A semi-blind quantum computing based on a quantum circuit computing model, characterized in that: The steps include: S1. Bob prepares n pairs of Bell states and sends the 1 particles of the n Bell states to Alice in sequence. Alice is the client and Bob is the quantum server. S2. Alice measures particle 1 immediately after receiving it, so that the states of each particle 2 evolve into the real input state with the one-time secret operator; Bob uses these n particles as input particles; S3. Alice sends a circuit diagram consisting of H, T, CX gates and representing the real algorithm to Bob; Bob executes logic gates H, T, CX on the n input particles in sequence according to the circuit diagram, and after each T gate is executed, the following steps A1-A4 need to be additionally executed; A1.Bob counts the particle that executes the T gate as particle 1 A2. Bob prepares another 2-particle with state |+>; then performs CZ on these two particles 12 The door distributes 1 particle to Alice; A3.Alice performs a single-particle rotation measurement on particle 1 and records the measurement result; A4.Bob performs H gate on particle 2; S4. When all H, T, and CX gates in the circuit diagram are executed, the input consisting of n particles will evolve into the target output with a one-time pad operator; S5.Bob returns these output particles to Alice; Alice executes the corresponding Pauli X, Z gates on each output particle to restore the correct calculation output.

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