Quantum network coding method and device based on quantum homomorphic encryption

Abstract

According to the quantum network coding method and device based on quantum homomorphic encryption, quantum state transmission can be achieved through local measurement, only classical measurement results need to be transmitted subsequently, direct transmission of quantum states is avoided, the risks of noise and de-coherence are reduced, quantum operation is simplified through local measurement, the requirement for quantum gates is reduced, and the quantum network coding efficiency is improved. Therefore, the calculation efficiency is improved, and the performance and reliability of the quantum homomorphic encryption scheme are improved. The method comprises the following steps: (1) preprocessing: pre-sharing cluster states among nodes of a butterfly network; (2) encryption and coding: the nodes realize quantum state encryption and transmission through local measurement and classical communication; (3) quantum homomorphic evaluation: operating a quantum gate by using a measurement-based quantum calculation MBQC model on a cluster state, wherein the quantum gate comprises {X, Z, H, S, T, CNOT}; and (4) decryption and decoding: after the receiving node receives the encryption key from the sender and the measurement result of the server, deriving a decryption key, and carrying out Fouli correction operation on the received quantum state.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum information processing, and in particular to a quantum network coding method based on quantum homomorphic encryption, and a quantum network coding device based on quantum homomorphic encryption. Background Art

[0002] Measurement-Based Quantum Computing (MBQC) is a quantum computing model that has attracted much attention. Its earliest prototype was proposed by Raussendorf and Briegel in 2001, namely the one-way quantum computing (1WQC) model. The calculation process of 1WQC mainly includes three steps: first, prepare an entangled resource state with universal computing capability and divide it into a measurement part and an output part; then, perform single-qubit measurements on the qubits in the measurement part step by step, and the measurement results will affect the subsequent operation process; finally, perform Pauli correction on the output part based on the measurement results to obtain the final calculation result. In further research in 2003, Raussendorf et al. proposed a one-way quantum computing scheme based on cluster states, using cluster states, a special entangled state, to realize computing operations through single-qubit measurements. The study proved the universality of this one-way quantum computing model and deeply explored the close connection between quantum algorithms and mathematical graph theory, laying a foundation for theoretical research and application expansion of quantum computing models.

[0003] Unlike the traditional quantum gate circuit model, MBQC completes the calculation by measuring the quantum bits in the entangled state without relying on complex quantum gate operations. Although the two are equivalent in theory, MBQC is easier to implement because it only requires the preparation of entangled states and single-bit measurements. This method is easier to implement on a physical experimental platform and has significant experimental advantages. In addition, the entangled resource state and measurement operations of MBQC can be distributed among multiple nodes, and the measurement results can be coordinated through classical communication, making it particularly suitable for application in quantum networks and distributed quantum computing. In recent years, MBQC has demonstrated its wide application potential and important value in many fields, including the realization of quantum Toffoli gates, the verification and demonstration of quantum algorithms, the design of quantum error correction codes, and quantum network coding. These achievements further highlight the key role and prospects of MBQC in quantum information processing.

[0004] However, current quantum computing cannot realize universal quantum gate operations, the computing efficiency is low, and the calculations of each node in distributed quantum computing are very complicated. Summary of the invention

[0005] In order to overcome the defects of the prior art, the technical problem to be solved by the present invention is to provide a quantum network coding method based on quantum homomorphic encryption, which can realize quantum state transmission through local measurement, and only needs to transmit classical measurement results subsequently, avoiding direct transmission of quantum states, thereby reducing the risk of noise and decoherence, simplifying quantum operations through local measurement, reducing the demand for quantum gates, thereby improving computing efficiency and enhancing the performance and reliability of quantum homomorphic encryption schemes.

[0006] The technical solution of the present invention is: the quantum network coding method based on quantum homomorphic encryption comprises:

[0007] (1) Preprocessing: by pre-sharing the cluster state among the nodes of the butterfly network;

[0008] (2) Encryption and encoding: Nodes encrypt and transmit quantum states through local measurements and classical communications;

[0009] (3) Quantum homomorphic evaluation: quantum gates using measurement-based quantum computation on cluster states

[0010] MBQC model is used for operation, and quantum gates include {X, Z, H, S, T, CNOT};

[0011] (4) Decryption and decoding: After receiving the encryption key from the sender and the measurement result from the server, the receiving node derives the decryption key and performs Pauli correction operation on the received quantum state.

[0012] In the quantum state transmission stage, the present invention can realize quantum state transmission by pre-sharing cluster states and performing local measurements. Subsequently, only the classical measurement results need to be transmitted, avoiding direct transmission of quantum states, thereby reducing the risk of noise and decoherence. In the quantum homomorphic evaluation stage, the MBQC model on the cluster state is used to simplify quantum operations through local measurements, reducing the need for quantum gates, thereby improving computing efficiency. The improved scheme optimizes the quantum state transmission and quantum homomorphic evaluation processes based on the traditional method, and improves the performance and reliability of the quantum homomorphic encryption scheme.

[0013] A quantum network coding device based on quantum homomorphic encryption is also provided, including:

[0014] A preprocessing module configured to pre-share cluster states between nodes of the butterfly network;

[0016] The encryption and encoding module configures nodes to encrypt and transmit quantum states through local measurement and classical communication;

[0017] A quantum homomorphic evaluation module configured to operate quantum gates using a measurement-based quantum computing MBQC model on cluster states, the quantum gates including {X, Z, H, S, T, CNOT};

[0018] The decryption and decoding module is configured to derive a decryption key and perform a Pauli correction operation on the received quantum state after the receiving node receives the encryption key from the sender and the measurement result of the server. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of a quantum network coding method based on quantum homomorphic encryption according to the present invention is shown.

[0020] Figure 2 Measurement-based H-gate crossover quantum homomorphism evaluation on a butterfly network is shown.

[0021] Figure 3 The measurement-based U∈{X,Z,S,T}-gate cross-quantum homomorphic evaluation on a butterfly network is shown.

[0022] Figure 4 The measurement-based CNOT gate crossover quantum homomorphic evaluation on a butterfly network is shown.

[0023] Figure 5 It shows that the sender S 1 Server 1 and the receiver T 2 A 13-particle cluster state pre-shared between them.

[0024] Figure 6 It shows that the sender S 2 Server 2 and the receiver T 1 A 13-particle cluster state pre-shared between them. DETAILED DESCRIPTION

[0025] like Figure 1 As shown, this quantum network coding method based on quantum homomorphic encryption includes:

[0026] (1) Preprocessing: by pre-sharing the cluster state among the nodes of the butterfly network;

[0027] (2) Encryption and encoding: Nodes encrypt and transmit quantum states through local measurements and classical communications;

[0028] (3) Quantum homomorphic evaluation: quantum gates using measurement-based quantum computation on cluster states

[0029] MBQC model is used for operation, and quantum gates include {X, Z, H, S, T, CNOT};

[0030] (4) Decryption and decoding: After receiving the encryption key from the sender and the measurement result from the server, the receiving node derives the decryption key and performs Pauli correction operation on the received quantum state.

[0031] In the quantum state transmission stage, the present invention can realize quantum state transmission by pre-sharing cluster states and performing local measurements. Subsequently, only the classical measurement results need to be transmitted, avoiding direct transmission of quantum states, thereby reducing the risk of noise and decoherence. In the quantum homomorphic evaluation stage, the MBQC model on the cluster state is used to simplify quantum operations through local measurements, reduce the demand for quantum gates, and thus improve computing efficiency. The improved scheme optimizes the quantum state transmission and quantum homomorphic evaluation processes based on the traditional method, and improves the performance and reliability of the quantum homomorphic encryption scheme.

[0032] like Figure 2 As shown, preferably, when the homomorphic evaluation operator U∈{H}, the sender S 1 The quantum state to be encrypted and evaluated is Sender S 2 The quantum state to be encrypted and evaluated is

[0033] The step (1) is:

[0034] S 1 and S 2 Pre-shared two pairs of two-particle cluster states and Among them, particle s 1,1 and 1,2 By node S 1 Hold, particles 2,1 and 2,2 By node S 2 hold,

[0035] Sender S 1 Server 1 and the receiver T 2 Share a three-particle cluster state

[0036]

[0037] Among them, particle p 1 By the sender S 1 Hold, particle p 2 Server 1 Hold, particle p 3 By the receiver T 2 hold,

[0038] Sender S 2 Server 2 and the receiver T1 They also share a three-particle cluster state

[0039]

[0040] Among them, particle q 1 By the sender S 2 Hold, particle q 2 Server 2 Hold, particle q 3 By the receiver T 1 hold;

[0041] The step (2) comprises:

[0042] Sender S 1 Use CZ to manipulate entangled particles 1 and 1,1 , and for particle s 1 and particles 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time key generation. At this time, node S 2 Particles 2,1 The status becomes At the same time, node S 2 Use CZ to manipulate entangled particles 2 and 2,2 , and use the X basis to measure particle s 2 and particles 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state ψ 2 > s2 The encryption key of particle s 1,2 The status becomes Sender S 1 and S 2 The encryption key ek 1 =(a,b) and ek 2 =(c,d) sent to the intermediate node C 1 Encoding is performed to obtain dk = (a⊕c, b⊕d), which is then transmitted through the bottleneck channel C 1 →C 2 Send to receiving node T 1 and T 2 ;

[0043] Node S 1 According to the encryption key (a, b) obtained by measurement, particle s 1,2 Perform unitary operation X b Z a , systems 1,2 The status becomes Xb Z a X d Z c ψ 2 > s2 =X b⊕d Z a⊕c ψ 2 > s2 ; At the same time, node S 2 According to the encryption key (c, d) obtained by measurement, particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S 1 Use CZ to manipulate entangled particles 1,2 and particle p 1 , then for particle s 1,2 and particle p 1 Perform X-based measurement, and the measurement result m 1 and m 2 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and particle q 1 , then use the X basis to measure s 2,1 and particle q 1 , and get the measurement result n 1 and n 2 , sender S 1 and S 2 The measurement results (m 1 ,m 2 )、(n 1 ,n 2 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0044] The step (3) is: Server 1 For particle p 2 Perform X-based measurement and obtain the measurement result m 3 , at this time the receiver T 2 Particle p 3 The status becomes At the same time Server 2 For particle q 2 Perform X-based measurement and obtain the measurement result n 3 , the receiver T 1 Particle q 3 The status becomes

[0045] The step (4) is as follows: the receiver T 2Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (m 1 ,m 2 ,m 3 ), for the particle p held 3 Apply unitary operation Recover the ciphertext state after the H-gate homomorphic evaluation

[0046]

[0047] Receiver T 1 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (n 1 ,n 2 ,n 3 ) after, for particle q 3 Apply unitary operation Recover the ciphertext state after the H-gate homomorphic evaluation

[0048]

[0049]

[0050] ⊕ means modulo 2 addition, Represents a tensor product.

[0051] like Figure 3 As shown, preferably, when evaluating the operator U∈{X,Z,S,T}, it is assumed that the sender S 1 The quantum state to be encrypted and evaluated is Sender S 2 The quantum state to be encrypted and evaluated is

[0052] The step (1) is:

[0053] S 1 and S 2 Pre-shared two pairs of two-particle cluster states and

[0054] Among them, particle s 1,1 and 1,2 By node S 1 Hold, particles 2,1 and 2,2 By node S 2 hold;

[0055] Sender S 1 Server 1 and the receiver T 2 Sharing a four-particle cluster state

[0056]

[0057] Among them, particle p 1 By the sender S 1 Hold, particle p 2 and p 3 By Server 1 Hold, particle p 4 By the receiver T 2 hold;

[0058] Sender S 2 Server 2 and the receiver T 1 They also share a four-particle cluster state

[0059]

[0060] Among them, particle q 1 By the sender S 2 Hold, particle q 2 and q 3 By Server 2 Hold, particle q 4 By the receiver T 1 hold;

[0061] The step (2) is:

[0062] Sender S 1 Use CZ to manipulate entangled particles 1 and 1,1 , and for particle s 1 and particles 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time pad key ek 1 , at this time node S 2 Particles 2,1 The status becomes Node S 2 Use CZ to manipulate entangled particles 2 and 2,2 , and use the X basis to measure particle s 2 and particles 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ 2 > s2 The encryption key ek 2 , then particle s 1,2 The status changes to X d Z c |ψ 2 > s2 ;

[0063] Sender S 1 and S 2 The encryption key ek 1 =(a,b) and ek 2 =(c,d) sent to the intermediate node C 1 Encoding is performed to obtain dk = (a⊕c, b⊕d), and then the bottleneck channel C is used to 1 →C 2 Send to receiving node T 1 and T 2 ;

[0064] Node S 1 According to the key (a, b), particle s 1,2 Perform unitary operation X b Z a , so the system s 1,2 The status becomes X b Z a X d Z c |ψ 2 > s2 =X b⊕d Z a⊕c |ψ 2 > s2 ; At the same time, node S 2 According to the encryption key (c, d), particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes

[0065] Node S 1 Use CZ to manipulate entangled particles 1,2 and particle p 1 , then for particle s 1,2 and particle p 1 Perform X-based measurement, and the measurement result m 1 and m 2 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and particle q 1 , then use the X basis to measure s 2,1 and particle q 1 , and get the measurement result n 1 and n 2 ; Sender S 1 and S 2 The measurement results (m 1 ,m 2 )、(n 1 ,n2 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0066] The step (3) is:

[0067] The server uses different measurement bases to perform single-qubit measurement X-gate operations on the particles it holds according to different evaluation operations: 1 For particle p 2 Perform M(0) basis measurement and obtain the measurement result m 3 , for particle p 3 Perform M(π)-based measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 Perform M(0) basis measurement and obtain the measurement result n 3 , for particle q 3 Perform M(π)-based measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0068] Z-door operation: Server 1 For particle p 2 Perform M(π)-based measurement and obtain the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 Perform M(0) basis measurement and obtain the measurement result n 3 , for particle q 3 Perform M(π)-based measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes S-gate operation: Server 1 For particle p 2 conduct Base measurement, get the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T2 Particle p 4 The status becomes Server 2 For particle q 2 conduct Base measurement, get measurement result n 3 , for particle q 3 Perform M(0) basis measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0069] T-gate operation: Server 1 For particle p 2 conduct Base measurement, get the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 conduct Base measurement, get measurement result n 3 , for particle q 3 Perform M(0) basis measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0070] The step (4) is:

[0071] Receiver T 2 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (m 1 ,m 2 ,m 3 ,m 4 ) after that, for the particle p held 4 Apply unitary operation Recover the ciphertext state after the U-gate homomorphic evaluation

[0072]

[0073] Receiver T 1 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (n 1 ,n 2 ,n 3 ,n4 ) after, for particle q 4 Apply unitary operation Recover the ciphertext state after U homomorphic evaluation

[0074]

[0075] like Figure 4 As shown, preferably, when evaluating the operator U∈{CNOT}, the sender S 1 and S 2 The quantum states that need to be transmitted and evaluated homomorphically are and

[0076] The step (1) is:

[0077] Sender S 1 and S 2 There are 4 pairs of two-particle cluster states pre-shared between them |Φ 1 >,|Φ 2 >,|Φ 3 >,|Φ 4 >

[0078]

[0079] Among them, particle s 1,1 ,s 1,2 ,s 1,3 ,s 1,4 By node S 1 Hold, particles 2,1 ,s 2,2 ,s 2,3 ,s 2,4 By node S 2 hold;

[0080] Sender S 1 Server 1 and the receiver T 2 pre-share a 13-particle cluster state, such as Figure 5 As shown, the particle p 1 , p 2 By the sender S 1 Hold, particle p 3 , p 4 , p 5 , p 6 , p 7 , p 8 , p 9 , p 10 , p 11 By Server 1 Hold, particle p 12, p 13 held by the receiver T 2 ; the sender S 2 , the server Server 2 and the receiver T 1 also share a 13-particle cluster state, as Figure 6 shown, where the particle q 1 , q 2 is held by the sender S 2 , the particle q 3 , q 4 , q 5 , q 6 , q 7 , q 8 , q 9 , q 10 , q 11 is held by the server Server 2 , the particle q 12 , q 13 is held by the receiver T 1 ;

[0081] The step (2) is as follows:

[0082] The sender S 1 uses the CZ operation to entangle the particles s 1 and s 1,1 as well as the particles s 2 and s 1,2 , and performs X-basis measurements on the particles s 1 , s 1,1 , s 2 , s 1,2 to obtain the measurement results a 1 , b 1 , c 1 , d 1 ∈ {0, 1}, and this measurement result is also used as the encryption key ek 1 = (a 1 , b 1 , c 1 , d 1 ) for the one-time pad encryption of the plaintext quantum state. At this time, the states of the particles s 2 and s 2,1 and s 2,2 at node S Node S 2 uses the CZ operation to entangle the particles s 3 and s 2,3 as well as the particles s 4 and s 2,4 , and uses the X-basis to measure the particles s 3 , s 2,3 , s 4,s 2,4 , and obtain the classical bit a corresponding to the measurement result 2 ,b 2 ,c 2 ,d 2 ∈{0,1}, node S 2 The encryption key is ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ), at this time node S 1 Particles 1,3 and 1,4 The status becomes

[0083] Sender S 1 and S 2 The encryption key ek 1 =(a 1 ,b 1 ,c 1 ,d 1 ) and ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ) is sent to middle C 1 Encoding is performed to obtain dk=(a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ), then through the bottleneck channel C 1 →C 2 Send to receiving node T 1 and T 2 ;

[0084] Node S 1 According to the encryption key ek 1 =(a 1 ,b 1 ,c 1 ,d 1 ), for particle s 1,3 and 1,4 Perform unitary operation Systems 1,3 and 1,4 The status becomes

[0085]

[0086]

[0087] At the same time, node S 2 According to the key ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ), for particle s 2,1 and 2,2 Perform unitary operation Therefore, the system 2,1 and 2,2 The status becomes

[0088] Node S 1 Use CZ to manipulate entangled particles 1,3 and p 1 and particles 1,4 and p 2 , then for particle s 1,3 ,s 1,4 and p 2 Perform X-basis measurement on particle p 1 Perform Y-based measurement and obtain the classical measurement results m 1 , m 2 , m 3 , m 4 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and q 1 and particles 2,2 and q 2 , and then use the X basis to measure the particle s 2,1 ,s 2,2 and q 2 , using the Y basis to measure particle q 1 , and obtain the measurement results n 1 , n 2 , n 3 , n 4 ; Next, the sender S 1 and S 2 The measurement results (m 1 ,m 2 ,m 3 ,m 4 )、(n 1 ,n 2 ,n 3 ,n 4 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0089] The step (3) is:

[0090] Server 1 For particle p 3 , p 5 , p 6 , p 7 , p 8 , p 10 Perform Y-based measurement and obtain the classical measurement results m 5 , m 6 , m 7 , m 8 , m 9 , m 10 , for particle p 4 ,p 9 ,p 11 Perform X-based measurement and obtain the measurement result m 11 , m 12 , m 13 , and then send the measurement results to the receiver T through the classical channel 2 , at this time the receiver T 2 Particle p 12 and p 13 The status becomes

[0091] in,

[0092] r 11 =m 4 ⊕m 5 ⊕m 9 ⊕m 10

[0093] r 12 =m 1 ⊕m 2 ⊕m 5 ⊕m 6 ⊕m 7 ⊕m 9 ⊕m 11 ⊕1

[0094] r 13 =m 3 ⊕m 4 ⊕m 5 ⊕m 7 ⊕m 8 ⊕m 13

[0095] r 14 =m 2 ⊕m 11 ⊕m 12 (13)

[0096] Server 2 For particle q3 ,q 5 ,q 6 ,q 7 ,q 8 ,q 10 Perform Y-based measurement and obtain the classical measurement result n 5 ,n 6 ,n 7 ,n 8 ,n 9 ,n 10 , for particle q 4 ,q 9 ,q 11 Perform X-based measurement and obtain the measurement result n 11 ,n 12 ,n 13 , and then send the measurement results to the receiver T through the classical channel 1 , at this time the receiver T 1 Particle q 12 and q 13 The status becomes

[0097]

[0098] in,

[0099] r 21 =n 4 ⊕n 5 ⊕n 9 ⊕n 10

[0100] r 22 =n 1 ⊕n 2 ⊕n 5 ⊕n 6 ⊕n 7 ⊕n 9 ⊕n 11 ⊕1

[0101] r 23 =n 3 ⊕n 4 ⊕n 5 ⊕n 7 ⊕n 8 ⊕n 13

[0102] r 24 =n 2 ⊕n 11 ⊕n 12 (15)

[0103] The step (4) is:

[0104] Receiver T 2Receive the decryption key dk = (a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ) and the measurement result m i (i=1,2,...,13), for the particle p held 12 and p 13 Apply unitary operation

[0105] Recover the quantum state after the CNOT gate homomorphic evaluation

[0106] Receiver T 1 Receive the decryption key dk = (a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ) and measurement results

[0107] n i (i=1,2,...,13), for particle q 12 and q 13 Apply unitary operation

[0108] Recover the quantum state after the CNOT gate homomorphic evaluation

[0109] Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes the steps of the above-mentioned embodiment method, and the storage medium can be: ROM / RAM, magnetic disk, optical disk, memory card, etc. Therefore, corresponding to the method of the present invention, the present invention also includes a quantum network coding device based on quantum homomorphic encryption, which is usually represented in the form of functional modules corresponding to the steps of the method. The device includes:

[0110] A preprocessing module configured to pre-share cluster states between nodes of the butterfly network;

[0112] The encryption and encoding module configures nodes to encrypt and transmit quantum states through local measurement and classical communication;

[0113] A quantum homomorphic evaluation module configured to operate quantum gates using a measurement-based quantum computing MBQC model on cluster states, the quantum gates including {X, Z, H, S, T, CNOT};

[0114] The decryption and decoding module is configured to derive a decryption key and perform a Pauli correction operation on the received quantum state after the receiving node receives the encryption key from the sender and the measurement result of the server.

[0115] Preferably, when the homomorphic evaluation operator U∈{H}, the sender S 1 The quantum state to be encrypted and evaluated is Sender S 2 The quantum state to be encrypted and evaluated is

[0116] The preprocessing module is:

[0117] S 1 and S 2 Pre-shared two pairs of two-particle cluster states and Among them, particle s 1,1 and 1,2 By node S 1 Hold, particles 2,1 and 2,2 By node S 2 hold,

[0118] Sender S 1 Server 1 and the receiver T 2 Share a three-particle cluster state

[0119]

[0120] Among them, particle p 1 By the sender S 1 Hold, particle p 2 Server 1 Hold, particle p 3 By the receiver T 2 hold,

[0121] Sender S 2 Server 2 and the receiver T 1 They also share a three-particle cluster state

[0122]

[0123] Among them, particle q 1 By the sender S 2 Hold, particle q2 Server 2 Hold, particle q 3 By the receiver T 1 hold;

[0124] The encryption and encoding module is:

[0125] Sender S 1 Use CZ to manipulate entangled particles 1 and 1,1 , and for particle s 1 and particles 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time key generation. At this time, node S 2 Particles 2,1 The status becomes At the same time, node S 2 Use CZ to manipulate entangled particles 2 and 2,2 , and use the X basis to measure particle s 2 and particles 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ 2 > s2 The encryption key of particle s 1,2 The status becomes Sender S 1 and S 2 The encryption key ek 1 =(a,b) and ek 2 =(c,d) sent to the intermediate node C 1 Encoding is performed to obtain dk = (a⊕c, b⊕d), which is then transmitted through the bottleneck channel C 1 →C 2 Send to receiving node T 1 and T 2 ;

[0126] Node S 1 According to the encryption key (a, b) obtained by measurement, particle s 1,2 Perform unitary operation X b Z a , systems 1,2 The status becomes X b Z a X d Z c |ψ 2 > s2 =X b⊕d Z a⊕c |ψ 2 > s2; At the same time, node S 2 According to the encryption key (c, d) obtained by measurement, particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S 1 Use CZ to manipulate entangled particles 1,2 and particle p 1 , then for particle s 1,2 and particle p 1 Perform X-based measurement, and the measurement result m 1 and m 2 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and particle q 1 , then use the X basis to measure s 2,1 and particle q 1 , and get the measurement result n 1 and n 2 , sender S 1 and S 2 The measurement results (m 1 ,m 2 )、(n 1 ,n 2 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0127] The quantum homomorphic evaluation module is: Server 1 For particle p 2 Perform X-based measurement and obtain the measurement result m 3 , at this time the receiver T 2 Particle p 3 The status becomes At the same time Server 2 For particle q 2 Perform X-based measurement and obtain the measurement result n 3 , the receiver T 1 Particle q 3 The status becomes

[0128] The decryption and decoding module is: 2 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (m 1 ,m 2 ,m 3 ), for the particle p held 3 Apply unitary operation Recover the ciphertext state after the H-gate homomorphic evaluation

[0129]

[0130] Receiver T 1 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (n 1 ,n 2 ,n 3 ) after, for particle q 3 Apply unitary operation Recover the ciphertext state after the H-gate homomorphic evaluation

[0131]

[0132] Preferably, when evaluating the operator U∈{X,Z,S,T}, assume that the sender S 1 The quantum state to be encrypted and evaluated is Sender S 2 The quantum state to be encrypted and evaluated is

[0133] The pre-processing module is:

[0134] S 1 and S 2 Pre-shared two pairs of two-particle cluster states and Among them, particle s 1,1 and 1,2 By node S 1 Hold, particles 2,1 and 2,2 By node S 2 hold;

[0135] Sender S 1 Server 1 and the receiver T 2 Sharing a four-particle cluster state

[0136]

[0137] Among them, particle p 1 By the sender S 1 Hold, particle p 2 and p 3 By Server 1 Hold, particle p 4 By the receiver T 2 hold;

[0138] Sender S 2 Server 2 and the receiver T 1They also share a four-particle cluster state

[0139]

[0140] Among them, particle q 1 By the sender S 2 Hold, particle q 2 and q 3 By Server 2 Hold, particle q 4 By the receiver T 1 hold;

[0141] The encryption and encoding module is:

[0142] Sender S 1 Use CZ to manipulate entangled particles 1 and 1,1 , and for particle s 1 and particles 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time pad key ek 1 , at this time node S 2 Particles 2,1 The status becomes Node S 2 Use CZ to manipulate entangled particles 2 and 2,2 , and use the X basis to measure particle s 2 and particles 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ 2 > s2 The encryption key ek 2 , then particle s 1,2 The status changes to X d Z c |ψ 2 > s2 ;

[0143] Sender S 1 and S 2 The encryption key ek 1 =(a,b) and ek 2 =(c,d) sent to the intermediate node C 1 Encoding is performed to obtain dk = (a⊕c, b⊕d), and then the bottleneck channel C is used to 1 →C 2 Send to receiving node T 1 and T 2 ;

[0144] Node S1 According to the key (a, b), particle s 1,2 Perform unitary operation X b Z a , so the system s 1,2 The status becomes X b Z a X d Z c |ψ 2 > s2 =X b⊕d Z a⊕c |ψ 2 > s2 ; At the same time, node S 2 According to the encryption key (c, d), particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes

[0145] Node S 1 Use CZ to manipulate entangled particles 1,2 and particle p 1 , then for particle s 1,2 and particle p 1 Perform X-based measurement, and the measurement result m 1 and m 2 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and particle q 1 , then use the X basis to measure s 2,1 and particle q 1 , and get the measurement result n 1 and n 2 ; Sender S 1 and S 2 The measurement results (m 1 ,m 2 )、(n 1 ,n 2 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0146] The quantum homomorphic evaluation module is:

[0147] The server uses different measurement bases to perform single-qubit measurement X-gate operations on the particles it holds according to different evaluation operations: 1 For particle p 2 Perform M(0) basis measurement and obtain the measurement result m 3 , for particle p 3Perform M(π)-based measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 Perform M(0) basis measurement and obtain the measurement result n 3 , for particle q 3 Perform M(π)-based measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0148] Z-door operation: Server 1 For particle p 2 Perform M(π)-based measurement and obtain the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 Perform M(0) basis measurement and obtain the measurement result n 3 , for particle q 3 Perform M(π)-based measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes S-gate operation: Server 1 For particle p 2 conduct Base measurement, get the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 conduct Base measurement, get measurement result n 3 , for particle q 3 Perform M(0) basis measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0149] T-gate operation: Server 1 For particle p 2 conduct Base measurement, get the measurement result m 3 , for particle p 3 Perform M(0) basis measurement and obtain the measurement result m 4 , at this time the receiver T 2 Particle p 4 The status becomes Server 2 For particle q 2 conduct Base measurement, get measurement result n 3 , for particle q 3 Perform M(0) basis measurement and obtain the measurement result n 4 , at this time the receiver T 1 Particle q 4 The status becomes

[0150]

[0151] The decryption and decoding modules are:

[0152] Receiver T 2 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (m 1 ,m 2 ,m 3 ,m 4 ) after that, for the particle p held 4 Apply unitary operation Recover the ciphertext state after the U-gate homomorphic evaluation

[0153]

[0154] Receiver T 1 Receive the decryption key dk = (a⊕c, b⊕d) and the measurement result (n 1 ,n 2 ,n 3 ,n 4 ) after, for particle q 4 Apply unitary operation Recover the ciphertext state after U homomorphic evaluation

[0155]

[0156]

[0157] Preferably, when evaluating the operator U∈{CNOT}, the sender S 1 and S 2The quantum states that need to be transmitted and evaluated homomorphically are and

[0158] The pre-processing module is:

[0159] Sender S 1 and S 2 There are 4 pairs of two-particle cluster states pre-shared between them |Φ 1 >,|Φ 2 >,|Φ 3 >,|Φ 4 >

[0160]

[0161] Among them, particle s 1,1 ,s 1,2 ,s 1,3 ,s 1,4 By node S 1 Hold, particles 2,1 ,s 2,2 ,s 2,3 ,s 2,4 By node S 2 hold;

[0162] Sender S 1 Server 1 and the receiver T 2 pre-share a 13-particle cluster state, where particle p 1 , p 2 By the sender S 1 Hold, particle p 3 , p 4 , p 5 , p 6 , p 7 , p 8 , p 9 , p 10 , p 11 By Server 1 Hold, particle p 12 , p 13 By the receiver T 2 Holder; Sender S 2 Server 2 and the receiver T 1 They also share a 13-particle cluster state, in which particle q 1 ,q 2 By the sender S 2 Hold, particle q 3 ,q 4 ,q 5 ,q 6,q 7 ,q 8 ,q 9 ,q 10 ,q 11 By Server 2 Hold, particle q 12 ,q 13 By the receiver T 1 Hold; the encryption and encoding module is:

[0163] Sender S 1 Use CZ to manipulate entangled particles 1 and 1,1 and particles 2 and 1,2 , and for particle s 1 ,s 1,1 ,s 2 ,s 1,2 Perform X-based measurement and obtain the measurement results a 1 ,b 1 ,c 1 ,d 1 ∈{0,1}, the measurement result is also used as the one-time encryption key ek for the plaintext quantum state 1 =(a 1 ,b 1 ,c 1 ,d 1 ), at this time node S 2 Particles 2,1 and 2,2 The status becomes Node S 2 Use CZ to manipulate entangled particles 3 and 2,3 and particles 4 and 2,4 , and use the X basis to measure particle s 3 ,s 2,3 ,s 4 ,s 2,4 , and obtain the classical bit a corresponding to the measurement result 2 ,b 2 ,c 2 ,d 2 ∈{0,1}, node S 2 The encryption key is ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ), at this time node S 1 Particles 1,3 and 1,4 The status becomes

[0164] Sender S 1 and S 2 The encryption key ek 1 =(a 1 ,b 1 ,c 1 ,d 1 ) and ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ) is sent to middle C 1 Encoding is performed to obtain dk=(a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ), then through the bottleneck channel C 1 →C 2 Send to receiving node T 1 and T 2 ;

[0165] Node S 1 According to the encryption key ek 1 =(a 1 ,b 1 ,c 1 ,d 1 ), for particle s 1,3 and 1,4 Perform unitary operation Systems 1,3 and 1,4 The status becomes

[0166]

[0167] At the same time, node S 2 According to the key ek 2 =(a 2 ,b 2 ,c 2 ,d 2 ), for particle s 2,1 and 2,2 Perform unitary operation Therefore, the system 2,1 and 2,2 The status becomes

[0168] Node S 1 Use CZ to manipulate entangled particles 1,3 and p1 and particles 1,4 and p 2 , then for particle s 1,3 ,s 1,4 and p 2 Perform X-basis measurement on particle p 1 Perform Y-based measurement and obtain the classical measurement results m 1 , m 2 , m 3 , m 4 ; At the same time, node S 2 Use CZ to manipulate entangled particles 2,1 and q 1 and particles 2,2 and q 2 , and then use the X basis to measure the particle s 2,1 ,s 2,2 and q 2 , using the Y basis to measure particle q 1 , and obtain the measurement results n 1 , n 2 , n 3 , n 4 ; Next, the sender S 1 and S 2 The measurement results (m 1 ,m 2 ,m 3 ,m 4 )、(n 1 ,n 2 ,n 3 ,n 4 ) is sent to the receiver T through the classical channel 2 and T 1 ;

[0169] The quantum homomorphic evaluation module is:

[0170] Server 1 For particle p 3 , p 5 , p 6 , p 7 , p 8 , p 10 Perform Y-based measurement and obtain the classical measurement results m 5 , m 6 , m 7 , m 8 , m 9 , m 10 , for particle p 4 ,p 9 ,p 11 Perform X-based measurement and obtain the measurement result m 11 , m12 , m 13 , and then send the measurement results to the receiver T through the classical channel 2 , at this time the receiver T 2 Particle p 12 and p 13 The status becomes

[0171] in,

[0172] r 11 =m 4 ⊕m 5 ⊕m 9 ⊕m 10

[0173] r 12 =m 1 ⊕m 2 ⊕m 5 ⊕m 6 ⊕m 7 ⊕m 9 ⊕m 11 ⊕1

[0174] r 13 =m 3 ⊕m 4 ⊕m 5 ⊕m 7 ⊕m 8 ⊕m 13

[0175] r 14 =m 2 ⊕m 11 ⊕m 12 (13)

[0176] Server 2 For particle q 3 ,q 5 ,q 6 ,q 7 ,q 8 ,q 10 Perform Y-based measurement and obtain the classical measurement result n 5 ,n 6 ,n 7 ,n 8 ,n 9 ,n 10 , for particle q 4 ,q 9 ,q 11 Perform X-based measurement and obtain the measurement result n 11 ,n 12 ,n 13, and then send the measurement results to the receiver T through the classical channel 1 , at this time the receiver T 1 Particle q 12 and q 13 The status becomes

[0177]

[0178] in,

[0179] r 21 =n 4 ⊕n 5 ⊕n 9 ⊕n 10

[0180] r 22 =n 1 ⊕n 2 ⊕n 5 ⊕n 6 ⊕n 7 ⊕n 9 ⊕n 11 ⊕1

[0181] r 23 =n 3 ⊕n 4 ⊕n 5 ⊕n 7 ⊕n 8 ⊕n 13

[0182] r 24 =n 2 ⊕n 11 ⊕n 12 (15)

[0183] The decryption and decoding modules are:

[0184] Receiver T 2 Receive the decryption key dk = (a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ) and the measurement result m i (i=1,2,...,13), for the particle p held 12 and p 13 Apply unitary operation

[0185] Recover the quantum state after the CNOT gate homomorphic evaluation

[0186] Receiver T 1 Receive the decryption key dk = (a 1 ⊕a 2 ,b 1 ⊕b 2 ,c 1 ⊕c 2 ,d 1 ⊕d 2 ) and measurement results

[0187] n i (i=1,2,...,13), for particle q 12 and q 13 Apply unitary operation

[0188] Recover the quantum state after the CNOT gate homomorphic evaluation

[0189] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the protection scope of the technical solution of the present invention.

Claims

1. A quantum network coding method based on quantum homomorphic encryption, characterized in that: The method comprises the following steps: (1) Preprocessing: by pre-sharing the cluster state among the nodes of the butterfly network; (2) Encryption and encoding: Nodes encrypt and transmit quantum states through local measurements and classical communications; (3) Quantum homomorphic evaluation: quantum gates are operated using the MBQC model based on measurement quantum computing on cluster states. The quantum gates include {X, Z, H, S, T, CNOT}. (4) Decryption and decoding: After receiving the encryption key from the sender and the measurement result from the server, the receiving node derives the decryption key and performs Pauli correction operation on the received quantum state.

2. The quantum network coding method based on quantum homomorphic encryption according to claim 1 is characterized in that: When the homomorphic evaluation operator U∈{H}, the quantum state to be encrypted and evaluated by the sender S1 is The quantum state that the sender S2 wants to encrypt and evaluate is The step (1) is: Two pairs of two-particle cluster states are pre-shared between S1 and S2 and Among them, particle s 1,1 and 1,2 Held by node S1, particle s 2,1 and 2,2 Held by node S2, The sender S1, the server Server1 and the receiver T2 share a three-particle cluster state Among them, particle p1 is held by the sender S1, particle p2 is held by server Server1, and particle p3 is held by the receiver T2. The sender S2, the server Server2 and the receiver T1 also share a three-particle cluster state Among them, particle q1 is held by the sender S2, particle q2 is held by server Server2, and particle q3 is held by the receiver T1; The step (2) comprises: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 , and for particles s1 and s 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time key, at this time, particle s at node S2 2,1 The status becomes At the same time, node S2 uses CZ operation to entangle particles s2 and s 2,2 , and use the X basis to measure particles s2 and s 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ2> s2 The encryption key of particle s 1,2 The status becomes The senders S1 and S2 send the encryption keys ek1 = (a, b) and ek2 = (c, d) to the intermediate node C1 for encoding. It is then sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the encryption key (a, b) obtained from the measurement to encrypt particle s 1,2 Perform unitary operation X b Z a , systems 1,2 The status becomes At the same time, node S2 uses the encryption key (c, d) obtained by measurement to 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S1 uses CZ operation to entangle particle s 1,2 and particle p1, then particle s 1,2 Perform X-based measurement with particle p1, and measure the results m1 and m2; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and particle q1, and then use the X basis to measure s 2,1 and particle q1, and obtain the measurement results n1 and n2. The senders S1 and S2 send the measurement results (m1, m2) and (n1, n2) to the receivers T2 and T1 through the classical channel respectively; The step (3) is: Server1 performs X-based measurement on particle p2 and obtains measurement result m3. At this time, the state of particle p3 at the receiving end T2 becomes At the same time, Server2 performs X-based measurement on particle q2 and obtains the measurement result n3. The state of particle q3 at the receiver T1 becomes The step (4) is as follows: the receiver T2 receives the decryption key And the measurement results (m1,m2,m3), apply the unitary operation to the particle p3 held Recover the ciphertext state after the H-gate homomorphic evaluation Receiver T1 receives the decryption key After the measurement results (n1, n2, n3), the unitary operation is applied to particle q3 Recover the ciphertext state after the H-gate homomorphic evaluation It represents modulo 2 addition. Represents a tensor product.

3. The quantum network coding method based on quantum homomorphic encryption according to claim 1 is characterized in that: When evaluating the operator U∈{X,Z,S,T}, it is assumed that the quantum state to be encrypted and evaluated by the sender S1 is The quantum state that the sender S2 wants to encrypt and evaluate is The step (1) is: Two pairs of two-particle cluster states are pre-shared between S1 and S2 and Among them, particle s 1,1 and 1,2 Held by node S1, particle s 2,1 and 2,2 Held by node S2; The sender S1, the server Server1 and the receiver T2 share a four-particle cluster state Among them, particle p1 is held by the sender S1, particles p2 and p3 are held by server Server1, and particle p4 is held by the receiver T2; The sender S2, the server Server2 and the receiver T1 also share a four-particle cluster state Among them, particle q1 is held by the sender S2, particles q2 and q3 are held by server Server2, and particle q4 is held by the receiver T1; The step (2) is: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 , and for particles s1 and s 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state The quantum one-time key ek1 is used. At this time, the particle s at node S2 2,1 The status becomes Node S2 uses CZ operation to entangle particles s2 and s 2,2 , and use the X basis to measure particles s2 and s 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ2> s2 The encryption key ek2, at this time particle s 1,2 The status changes to X d Z c |ψ2> s2 ; The senders S1 and S2 send the encryption keys ek1 = (a, b) and ek2 = (c, d) to the intermediate node C1 for encoding. Then it is sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the key (a, b) to generate particle s 1,2 Perform unitary operation X b Z a , so the system s 1,2 The status becomes At the same time, node S2 uses the encryption key (c, d) to encrypt particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S1 uses CZ operation to entangle particle s 1,2 and particle p1, then particle s 1,2 Perform X-based measurement with particle p1, and measure the results m1 and m2; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and particle q1, and then use the X basis to measure s 2,1 and particle q1, and obtain the measurement results n1 and n2; senders S1 and S2 send the measurement results (m1, m2) and (n1, n2) to receivers T2 and T1 through the classical channel respectively; The step (3) is: According to different evaluation operations, the server uses different measurement bases to perform single-qubit measurement X-gate operations on the particles it holds: Server1 performs M(0) basis measurement on particle p2 and obtains measurement result m3, and performs M(π) basis measurement on particle p3 and obtains measurement result m4. At this time, the state of particle p4 at the receiver T2 becomes Server2 performs M(0)-based measurement on particle q2 and obtains measurement result n3. It performs M(π)-based measurement on particle q3 and obtains measurement result n4. At this time, the state of particle q4 at the receiver T1 becomes Z-gate operation: Server1 performs M(π)-based measurement on particle p2 and obtains measurement result m3. It performs M(0)-based measurement on particle p3 and obtains measurement result m4. At this time, the state of particle p4 at the receiver T2 becomes Server2 performs M(0)-based measurement on particle q2 and obtains measurement result n3. It performs M(π)-based measurement on particle q3 and obtains measurement result n4. At this time, the state of particle q4 at the receiver T1 becomes S-gate operation: Server1 performs S-gate operation on particle p2. The measurement result m3 is obtained by performing M(0) basis measurement on particle p3, and the measurement result m4 is obtained. At this time, the state of particle p4 at the receiving end T2 becomes Server2 performs the following operations on particle q2: The measurement result n3 is obtained by performing M(0) basis measurement on particle q3, and the measurement result n4 is obtained. At this time, the state of particle q4 at the receiving end T1 becomes T-gate operation: Server1 performs a The measurement result m3 is obtained by performing M(0) basis measurement on particle p3, and the measurement result m4 is obtained. At this time, the state of particle p4 at the receiving end T2 becomes Server2 performs the following operations on particle q2: The measurement result n3 is obtained by performing M(0) basis measurement on particle q3, and the measurement result n4 is obtained. At this time, the state of particle q4 at the receiving end T1 becomes The step (4) is: Receiver T2 receives the decryption key After the measurement results (m1, m2, m3, m4), the unitary operation is applied to the particle p4 held Recover the ciphertext state after the U-gate homomorphic evaluation Receiver T1 receives the decryption key After summing the measurement results (n1, n2, n3, n4), the unitary operation is applied to particle q4 Recover the ciphertext state after U homomorphic evaluation 4. The quantum network coding method based on quantum homomorphic encryption according to claim 1 is characterized in that: When evaluating the operator U∈{CNOT}, the quantum states that the senders S1 and S2 need to transmit and homomorphically evaluate are and The step (1) is: The senders S1 and S2 pre-share 4 pairs of two-particle cluster states |Φ1>,|Φ2>,|Φ3>,|Φ4> Among them, particle s 1,1 ,s 1,2 ,s 1,3 ,s 1,4 Held by node S1, particle s 2,1 ,s 2,2 ,s 2,3 ,s 2,4 Held by node S2; The sender S1, the server Server1 and the receiver T2 pre-share a 13-particle cluster state, where particles p1 and p2 are held by the sender S1, and particles p3, p4, p5, p6, p7, p8, p9, p 10 , p 11 Held by server Server1, particle p 12 , p 13 The sender S2, the server Server2 and the receiver T1 also share a 13-particle cluster state, where particles q1 and q2 are held by the sender S2, and particles q3, q4, q5, q6, q7, q8, q9, q 10 ,q 11 Held by server Server2, particle q 12 ,q 13 Held by the receiver T1; The step (2) is: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 and particles s2 and s 1,2 , and for particles s1, s 1,1 , s2, s 1,2 Perform X-basis measurement and obtain the measurement results a1, b1, c1, d1∈{0,1} respectively. The measurement results are also used as the one-time encryption key ek1=(a1, b1, c1, d1) for the plaintext quantum state. At this time, the particle s at node S2 2,1 and 2,2 The status becomes Node S2 uses CZ operation to entangle particles s3 and s 2,3 and particles s4 and s 2,4 , and use the X basis to measure particles s3, s 2,3 ,s4,s 2,4 , and obtain the classical bits a2, b2, c2, d2∈{0,1} corresponding to the measurement results. The encryption key of node S2 is ek2=(a2, b2, c2, d2). At this time, the particle s at node S1 1,3 and 1,4 The status becomes The senders S1 and S2 send the encryption keys ek1 = (a1, b1, c1, d1) and ek2 = (a2, b2, c2, d2) to the middle C1 for encoding. It is then sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the encryption key ek1 = (a1, b1, c1, d1) to encrypt particle s 1,3 and 1,4 Perform unitary operation Systems 1,3 and 1,4 The status becomes At the same time, node S2 uses the key ek2 = (a2, b2, c2, d2) to generate particle s 2,1 and 2,2 Perform unitary operation Therefore, the system 2,1 and 2,2 The status becomes Node S1 uses CZ operation to entangle particle s 1,3 and p1 and particle s 1,4 and p2, then for particle s 1,3 ,s 1,4 Perform X-basis measurement on p2 and Y-basis measurement on particle p1, and obtain classical measurement results m1, m2, m3, and m4 respectively; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and q1 and particle s 2,2 and q2, and then use the X basis to measure particle s 2,1 ,s 2,2 and q2, use the Y basis to measure particle q1, and obtain measurement results n1, n2, n3, n4 respectively; next, senders S1 and S2 send the measurement results (m1, m2, m3, m4) and (n1, n2, n3, n4) to receivers T2 and T1 through the classical channel respectively; The step (3) is: Server1 has particles p3, p5, p6, p7, p8, p 10 Perform Y-based measurement and obtain the classical measurement results m5, m6, m7, m8, m9, m 10 , for particles p4, p9, p 11 Perform X-based measurement and obtain the measurement result m 11 , m 12 , m 13 , and then send the measurement result to the receiver T2 through the classical channel. At this time, the particle p at the receiver T2 12 and p 13 The status becomes in, Server2 has particles q3,q5,q6,q7,q8,q 10 Perform Y-based measurement and obtain the classic measurement results n5, n6, n7, n8, n9, n 10 , for particles q4,q9,q 11 Perform X-based measurement and obtain the measurement result n 11 ,n 12 ,n 13 Then the measurement result is sent to the receiver T1 through the classical channel. At this time, the particle q 12 and q 13 The status becomes in, The step (4) is: Receiver T2 receives the decryption key And the measurement result m i (i=1,2,...,13), for the particle p held 12 and p 13 Apply unitary operation Recover the quantum state after the CNOT gate homomorphic evaluation Receiver T1 receives the decryption key And the measurement result n i (i=1,2,...,13), for particle q 12 and q 13 Apply unitary operation Recover the quantum state after the CNOT gate homomorphic evaluation 5. A quantum network coding device based on quantum homomorphic encryption, characterized in that: include: A preprocessing module configured to pre-share cluster states between nodes of the butterfly network; The encryption and encoding module configures nodes to encrypt and transmit quantum states through local measurement and classical communication; A quantum homomorphic evaluation module configured to operate quantum gates using a measurement-based quantum computing MBQC model on cluster states, the quantum gates including {X, Z, H, S, T, CNOT}; The decryption and decoding module is configured to derive a decryption key and perform a Pauli correction operation on the received quantum state after the receiving node receives the encryption key from the sender and the measurement result of the server.

6. The quantum network coding device based on quantum homomorphic encryption according to claim 5 is characterized in that: When the homomorphic evaluation operator U∈{H}, the quantum state to be encrypted and evaluated by the sender S1 is The quantum state that the sender S2 wants to encrypt and evaluate is The preprocessing module is: Two pairs of two-particle cluster states are pre-shared between S1 and S2 and Among them, particle s 1,1 and 1,2 Held by node S1, particle s 2,1 and 2,2 Held by node S2, The sender S1, the server Server1 and the receiver T2 share a three-particle cluster state Among them, particle p1 is held by the sender S1, particle p2 is held by server Server1, and particle p3 is held by the receiver T2. The sender S2, the server Server2 and the receiver T1 also share a three-particle cluster state Among them, particle q1 is held by the sender S2, particle q2 is held by server Server2, and particle q3 is held by the receiver T1; The encryption and encoding module is: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 , and for particles s1 and s 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state Perform quantum one-time key, at this time, particle s at node S2 2,1 The status becomes At the same time, node S2 uses CZ operation to entangle particles s2 and s 2,2 , and use the X basis to measure particles s2 and s 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ2> s2 The encryption key of particle s 1,2 The status becomes The senders S1 and S2 send the encryption keys ek1 = (a, b) and ek2 = (c, d) to the intermediate node C1 for encoding. It is then sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the encryption key (a, b) obtained from the measurement to encrypt particle s 1,2 Perform unitary operation X b Z a , systems 1,2 The status becomes At the same time, node S2 uses the encryption key (c, d) obtained by measurement to 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S1 uses CZ operation to entangle particle s 1,2 and particle p1, then particle s 1,2 Perform X-based measurement with particle p1, and measure the results m1 and m2; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and particle q1, and then use the X basis to measure s 2,1 and particle q1, and obtain the measurement results n1 and n2. The senders S1 and S2 send the measurement results (m1, m2) and (n1, n2) to the receivers T2 and T1 through the classical channel respectively; The quantum homomorphic evaluation module is as follows: Server1 performs X-basis measurement on particle p2 and obtains the measurement result m3. At this time, the state of particle p3 at the receiving end T2 becomes At the same time, Server2 performs X-based measurement on particle q2 and obtains the measurement result n3. The state of particle q3 at the receiver T1 becomes The decryption and decoding module is: the receiver T2 receives the decryption key And the measurement results (m1,m2,m3), apply the unitary operation to the particle p3 held Recover the ciphertext state after the H-gate homomorphic evaluation Receiver T1 receives the decryption key After the measurement results (n1, n2, n3), the unitary operation is applied to particle q3 Recover the ciphertext state after the H-gate homomorphic evaluation 7. The quantum network coding device based on quantum homomorphic encryption according to claim 5 is characterized in that: When evaluating the operator U∈{X,Z,S,T}, it is assumed that the quantum state to be encrypted and evaluated by the sender S1 is The quantum state that the sender S2 wants to encrypt and evaluate is The pre-processing module is: Two pairs of two-particle cluster states are pre-shared between S1 and S2 and Among them, particle s 1,1 and 1,2 Held by node S1, particle s 2,1 and 2,2 Held by node S2; The sender S1, the server Server1 and the receiver T2 share a four-particle cluster state Among them, particle p1 is held by the sender S1, particles p2 and p3 are held by server Server1, and particle p4 is held by the receiver T2; The sender S2, the server Server2 and the receiver T1 also share a four-particle cluster state Among them, particle q1 is held by the sender S2, particles q2 and q3 are held by server Server2, and particle q4 is held by the receiver T1; The encryption and encoding module is: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 , and for particles s1 and s 1,1 Perform X-based measurement and obtain the measurement results a, b∈{0,1} as the state The quantum one-time key ek1 is used. At this time, the particle s at node S2 2,1 The status becomes Node S2 uses CZ operation to entangle particles s2 and s 2,2 , and use the X basis to measure particles s2 and s 2,2 , and the classical bit c,d∈{0,1} corresponding to the measurement result is the quantum state |ψ2> s2 The encryption key ek2, at this time particle s 1,2 The status changes to X d Z c |ψ2> s2 ; The senders S1 and S2 send the encryption keys ek1 = (a, b) and ek2 = (c, d) to the intermediate node C1 for encoding. Then it is sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the key (a, b) to generate particle s 1,2 Perform unitary operation X b Z a , so the system s 1,2 The status becomes At the same time, node S2 uses the encryption key (c, d) to encrypt particle s 2,1 Perform unitary operation X d Z c , systems 2,1 The status becomes Node S1 uses CZ operation to entangle particle s 1,2 and particle p1, then particle s 1,2 Perform X-based measurement with particle p1, and measure the results m1 and m2; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and particle q1, and then use the X basis to measure s 2,1 and particle q1, and obtain the measurement results n1 and n2; senders S1 and S2 send the measurement results (m1, m2) and (n1, n2) to receivers T2 and T1 through the classical channel respectively; The quantum homomorphic evaluation module is: According to different evaluation operations, the server uses different measurement bases to perform single-qubit measurement X-gate operations on the particles it holds: Server1 performs M(0) basis measurement on particle p2 and obtains measurement result m3, and performs M(π) basis measurement on particle p3 and obtains measurement result m4. At this time, the state of particle p4 at the receiver T2 becomes Server2 performs M(0)-based measurement on particle q2 and obtains measurement result n3. It performs M(π)-based measurement on particle q3 and obtains measurement result n4. At this time, the state of particle q4 at the receiver T1 becomes Z-gate operation: Server1 performs M(π)-based measurement on particle p2 and obtains measurement result m3. It performs M(0)-based measurement on particle p3 and obtains measurement result m4. At this time, the state of particle p4 at the receiver T2 becomes Server2 performs M(0)-based measurement on particle q2 and obtains measurement result n3. It performs M(π)-based measurement on particle q3 and obtains measurement result n4. At this time, the state of particle q4 at the receiver T1 becomes S-gate operation: Server1 performs S-gate operation on particle p2. The measurement result m3 is obtained by performing M(0) basis measurement on particle p3, and the measurement result m4 is obtained. At this time, the state of particle p4 at the receiving end T2 becomes Server2 performs the following operations on particle q2: The measurement result n3 is obtained by performing M(0) basis measurement on particle q3, and the measurement result n4 is obtained. At this time, the state of particle q4 at the receiving end T1 becomes T-gate operation: Server1 performs a The measurement result m3 is obtained by performing M(0) basis measurement on particle p3, and the measurement result m4 is obtained. At this time, the state of particle p4 at the receiving end T2 becomes Server2 performs the following operations on particle q2: The measurement result n3 is obtained by performing M(0) basis measurement on particle q3, and the measurement result n4 is obtained. At this time, the state of particle q4 at the receiving end T1 becomes The decryption and decoding modules are: Receiver T2 receives the decryption key After the measurement results (m1, m2, m3, m4), the unitary operation is applied to the particle p4 held Recover the ciphertext state after the U-gate homomorphic evaluation Receiver T1 receives the decryption key After summing the measurement results (n1, n2, n3, n4), the unitary operation is applied to particle q4 Recover the ciphertext state after U homomorphic evaluation 8. The quantum network coding device based on quantum homomorphic encryption according to claim 5 is characterized in that: When evaluating the operator U∈{CNOT}, the quantum states that the senders S1 and S2 need to transmit and homomorphically evaluate are and The pre-processing module is: The senders S1 and S2 pre-share 4 pairs of two-particle cluster states |Φ1>,|Φ2>,|Φ3>,|Φ4> Among them, particle s 1,1 ,s 1,2 ,s 1,3 ,s 1,4 Held by node S1, particle s 2,1 ,s 2,2 ,s 2,3 ,s 2,4 Held by node S2; The sender S1, the server Server1 and the receiver T2 pre-share a 13-particle cluster state, where particles p1 and p2 are held by the sender S1, and particles p3, p4, p5, p6, p7, p8, p9, p 10 , p 11 Held by server Server1, particle p 12 , p 13 The sender S2, the server Server2 and the receiver T1 also share a 13-particle cluster state, where particles q1 and q2 are held by the sender S2, and particles q3, q4, q5, q6, q7, q8, q9, q 10 ,q 11 Held by server Server2, particle q 12 ,q 13 Held by the receiver T1; the encryption and encoding module is: Sender S1 uses CZ operation to entangle particles s1 and s 1,1 and particles s2 and s 1,2 , and for particles s1, s 1,1 , s2, s 1,2 Perform X-basis measurement and obtain the measurement results a1, b1, c1, d1∈{0,1} respectively. The measurement results are also used as the one-time encryption key ek1=(a1, b1, c1, d1) for the plaintext quantum state. At this time, the particle s at node S2 2,1 and 2,2 The status becomes Node S2 uses CZ operation to entangle particles s3 and s 2,3 and particles s4 and s 2,4 , and use the X basis to measure particles s3, s 2,3 ,s4,s 2,4 , and obtain the classical bits a2, b2, c2, d2∈{0,1} corresponding to the measurement results. The encryption key of node S2 is ek2=(a2, b2, c2, d2). At this time, the particle s at node S1 1,3 and 1,4 The status becomes The senders S1 and S2 send the encryption keys ek1 = (a1, b1, c1, d1) and ek2 = (a2, b2, c2, d2) to the middle C1 for encoding. It is then sent to receiving nodes T1 and T2 through the bottleneck channel C1→C2; Node S1 uses the encryption key ek1 = (a1, b1, c1, d1) to encrypt particle s 1,3 and 1,4 Perform unitary operation Systems 1,3 and 1,4 The status becomes At the same time, node S2 uses the key ek2 = (a2, b2, c2, d2) to generate particle s 2,1 and 2,2 Perform unitary operation Therefore, the system 2,1 and 2,2 The status becomes Node S1 uses CZ operation to entangle particle s 1,3 and p1 and particle s 1,4 and p2, then for particle s 1,3 ,s 1,4 Perform X-basis measurement on p2 and Y-basis measurement on particle p1, and obtain classical measurement results m1, m2, m3, and m4 respectively; at the same time, node S2 uses CZ operation to entangle particle s 2,1 and q1 and particle s 2,2 and q2, and then use the X basis to measure particle s 2,1 ,s 2,2 and q2, use the Y basis to measure particle q1, and obtain measurement results n1, n2, n3, n4 respectively; next, senders S1 and S2 send the measurement results (m1, m2, m3, m4) and (n1, n2, n3, n4) to receivers T2 and T1 through the classical channel respectively; The quantum homomorphic evaluation module is: Server1 has particles p3, p5, p6, p7, p8, p 10 Perform Y-based measurement and obtain the classical measurement results m5, m6, m7, m8, m9, m 10 , for particles p4, p9, p 11 Perform X-based measurement and obtain the measurement result m 11 , m 12 , m 13 , and then send the measurement result to the receiver T2 through the classical channel. At this time, the particle p at the receiver T2 12 and p 13 The status becomes in, Server2 has particles q3,q5,q6,q7,q8,q 10 Perform Y-based measurement and obtain the classic measurement results n5, n6, n7, n8, n9, n 10 , for particles q4,q9,q 11 Perform X-based measurement and obtain the measurement result n 11 ,n 12 ,n 13 Then the measurement result is sent to the receiver T1 through the classical channel. At this time, the particle q 12 and q 13 The status becomes in, The decryption and decoding modules are: Receiver T2 receives the decryption key And the measurement result m i (i=1,2,...,13), for the particle p held 12 and p 13 Apply unitary operation Recover the quantum state after the CNOT gate homomorphic evaluation Receiver T1 receives the decryption key And the measurement result n i (i=1,2,...,13), for particle q 12 and q 13 Apply unitary operation Recover the quantum state after the CNOT gate homomorphic evaluation

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