Implementation method of distributed generalized control NOT gate and implementation method of distributed generalized control Z gate

Abstract

The invention relates to the technical field of quantum computing, and discloses an implementation method of a distributed generalized control NOT gate and an implementation method of a distributed generalized control Z gate. Comprising the steps that the local node initializes a flight bit; carrying out Hadamard gate operation on the local target quantum bit; the local quantum bit performs control NOT gate operation on the flight bit; transmitting the flight bit to a central node; the center node performs joint projection measurement on the flight bits; the local node carries out feedforward operation on the local quantum bit according to the joint projection measurement result; and carrying out Hadamard gate operation on the local target quantum bit. According to the invention, two times of Hadamard gate operations on the local target quantum bit are removed, so that a distributed generalized control Z gate can be realized. According to the method, the distribution distance of the distributed quantum logic gate is further increased, and a new effective solution is provided for large-scale distributed quantum calculation.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a method for realizing a distributed generalized controlled NOT gate and a method for realizing a distributed generalized controlled Z gate. Background Art

[0002] Quantum computing uses the superposition of quantum states to perform information processing on quantum systems, which can significantly improve computing speed and efficiency, and its potential far exceeds that of classical computers. In recent years, research on superconducting and photonic quantum processors has made significant progress. These achievements not only demonstrate the advantages of quantum computing in solving classical problems, but also foreshadow its far-reaching impact in the fields of scientific research and technology. However, there are still challenges in building large-scale quantum processors. Inspired by classical distributed computing, scientists proposed distributed quantum computing, which consists of small quantum computers connected by a network. Each node register holds a limited number of quantum bits, and some quantum bits are used for network transmission. Quantum bits within a node can interact freely, while remote interactions must be achieved through teleportation, physical transmission, or non-local operations.

[0003] Distributed quantum computing can be achieved through quantum teleportation or direct exchange of quantum bits, but Eisert et al. proposed a more efficient method in 2000. They used distributed controlled NOT gates to achieve distributed quantum computing by only sharing entangled pairs and communicating between two classical bits. This method is called quantum gate teleportation and has been implemented in systems such as photons, ion traps, and superconducting quantum bits. In complex quantum computing, multi-bit quantum gates have significant advantages. Among them, Toffoli gates, n-bit Toffoli gates, and multi-target bit controlled NOT gates can perform complex logical operations on multiple quantum bits, which is crucial for implementing key algorithms such as quantum Fourier transforms and quantum phase estimation. However, there is currently no implementation solution for distributed generalized controlled NOT gates with multiple control bits and multiple target bits. Summary of the invention

[0004] The purpose of the present invention is to provide a method for implementing a distributed generalized controlled NOT gate and a method for implementing a distributed generalized controlled Z gate in multi-user quantum network or distributed quantum computing research. The present invention aims to solve the problem that the prior art lacks distributed generalized controlled NOT gates and generalized controlled Z gates with multiple control bits and multiple target bits.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] The present invention provides a method for implementing a distributed generalized controlled NOT gate, the method being used to control a central node and multiple local nodes, the multiple local nodes having a total of m+n local quantum bits and m+n flying bits, the local quantum bits including m local control quantum bits and n local target quantum bits, the method comprising:

[0007] The local node initializes the flying bits;

[0008] The local node performs a Hadamard gate operation on the local target quantum bit;

[0009] The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit;

[0010] The local node transmits the flying bit to the central node via the quantum channel;

[0011] The central node receives flying bits transmitted by multiple local nodes via quantum channels, performs joint projection measurement on the flying bits, and transmits the joint projection measurement results to each of the local nodes;

[0012] The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result;

[0013] The local node performs a Hadamard gate operation on the local target quantum bit.

[0014] Furthermore, the local quantum bits include photons, atoms, ions and superconducting quantum bits.

[0015] Furthermore, the performing joint projection measurement on the flying bits specifically comprises adopting a complete orthogonal hypergraph analyzer to perform joint projection measurement on the flying bits.

[0016] Furthermore, the complete orthogonal hypergraph state analyzer includes a Hadamard gate and a generalized controlled Z gate, and the joint projection measurement of the flying bits specifically includes:

[0017] Using the flying bits corresponding to the local control qubits as control bits and the flying bits corresponding to the local target qubits as target bits, executing a generalized control Z gate;

[0018] Performing a Hadamard gate on each of the flying bits;

[0019] A calculation base state measurement is performed on each of the flying bits to obtain the joint projection measurement result.

[0020] Further, performing a feedforward operation on the local quantum bit according to the measurement result specifically includes:

[0021] Determine in turn whether the measurement values ​​corresponding to all flying bits are 1;

[0022] If the measurement value corresponding to the flying bit is 1, a feed-forward Z gate is executed on the local quantum bit corresponding to the flying bit.

[0023] In addition, to achieve the above-mentioned invention object, the present invention also provides a method for implementing a distributed generalized control Z gate, the method is used to control a central node and multiple local nodes, the multiple local nodes hold a total of m+n local quantum bits and m+n flying bits, the local quantum bits include m local control quantum bits and n local target quantum bits, the method includes

[0024] The local node initializes the flying bits;

[0025] The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit;

[0026] Transmitting the flying bits to a central node via a quantum channel;

[0027] The central node receives flying bits transmitted by multiple local nodes via quantum channels, performs joint projection measurement on the flying bits, and transmits the joint projection measurement results to each of the local nodes;

[0028] The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0029] Furthermore, the local quantum bits include photons, atoms, ions and superconducting quantum bits.

[0030] Furthermore, the performing joint projection measurement on the flying bits specifically comprises adopting a complete orthogonal hypergraph analyzer to perform joint projection measurement on the flying bits.

[0031] Furthermore, the complete orthogonal hypergraph state analyzer includes a Hadamard gate and a generalized controlled Z gate, and the joint projection measurement of the flying bits specifically includes:

[0032] Using the flying bits corresponding to the local control qubits as control bits and the flying bits corresponding to the local target qubits as target bits, executing a generalized control Z gate;

[0033] Performing a Hadamard gate on each of the flying bits;

[0034] A calculation base state measurement is performed on each of the flying bits to obtain the joint projection measurement result.

[0035] Further, performing a feedforward operation on the local quantum bit according to the measurement result specifically includes:

[0036] Determine in turn whether the measurement values ​​corresponding to all flying bits are 1;

[0037] If the measurement value corresponding to the flying bit is 1, a feed-forward Z gate is executed on the local quantum bit corresponding to the flying bit.

[0038] The present invention adopts the above technical solution to achieve the following effects:

[0039] The present invention replaces the entanglement distribution in previous schemes by using joint projection measurement of flying bits, transferring the correlation between quantum bits from the quantum entanglement source to quantum measurement, avoiding the preparation of a large number of entangled states, while reducing the number of quantum bits consumed and further improving the distribution distance of distributed quantum logic gates. This provides a new and effective solution for large-scale distributed quantum computing in complex quantum networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is the quantum circuit diagram of the complete orthogonal hypergraph state analyzer in the present invention;

[0041] Figure 2 is a flow chart of the implementation steps of a distributed generalized controlled NOT gate in an embodiment of the present invention;

[0042] Figure 3 is a quantum circuit diagram of a distributed generalized controlled NOT gate in an embodiment of the present invention;

[0043] Figure 4 is a quantum circuit diagram of a distributed generalized controlled Z-gate in an embodiment of the present invention;

[0044] Figure 5 is a quantum circuit diagram of a distributed controlled NOT gate in an embodiment of the present invention;

[0045] Figure 6 It is a schematic diagram of the quantum route of a two-bit complete orthogonal hypergraph state analyzer in an embodiment of the present invention;

[0046] Figure 7 is a quantum circuit diagram of a distributed Toffoli gate in an embodiment of the present invention;

[0047] Figure 8 It is a schematic diagram of the quantum route of a three-bit complete orthogonal hypergraph state analyzer in an embodiment of the present invention;

[0048] Fig. 9 It is a quantum circuit diagram of a distributed multi-bit controlled NOT gate according to an embodiment of the present invention;

[0049] Fig.10 It is a schematic diagram of the quantum route of the n+1-bit complete orthogonal hypergraph analyzer in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0051] This paper first introduces the mathematical representation of commonly used single-bit quantum gates and multi-bit computing ground states. Quantum gates can change the state of quantum bits and implement various logical and arithmetic operations in quantum computing. Quantum gates must be unitary operations, which ensures the reversibility of all quantum gate operations. Commonly used single-bit quantum gates include I gates X-Gate Z-Gate and Hadamard gate The present invention expresses the computational ground state of m+n quantum bits as |x>=|x1x2…x m x m+1 x m+2 …x m+n >, where x1 represents the computational basis state of the first quantum bit, x2 represents the computational basis state of the second quantum bit, and x m represents the computational ground state of the mth quantum bit, x m+1 represents the computational ground state of the m+1th quantum bit, x m+2 represents the computational ground state of the m+2th quantum bit, x m+n represents the computational ground state of the m+nth quantum bit, and defines Compute the decimal representation of the ground state for m+n qubits.

[0052] The generalized controlled NOT gate is a multi-bit generalization of the controlled NOT gate. A generalized controlled NOT gate with m control bits and n target bits The effect of acting on the multi-bit computational ground state |x> is The subscript 12…m represents m control bits, and (m+1)(m+2)…(m+n) represents n target bits. is the direct product of m identity matrices I, It is the direct product of n X gates. is the product of m control bits. When all are in the |1> state, the product is 1, and in other cases it is 0. Therefore, when all control bits are in the |1> state, the target bit is acted on Otherwise the target bit remains unchanged.

[0053] The generalized controlled Z-gate is a multi-bit generalization of the controlled Z-gate. The generalized controlled Z-gate with m control bits and n target bits The effect of acting on the multi-bit computational ground state |x> is The subscript 12…m represents m control bits, and (m+1)(m+2)…(m+n) represents n target bits. is the direct product of m identity matrices I, It is the direct product of n Z gates. is the product of m control bits. When all are in the |1> state, the product is 1, and in other cases it is 0. Therefore, when all control bits are in the |1> state, the target bit is acted on Otherwise the target bit remains unchanged.

[0054] Definition of the invention is a complete orthogonal hypergraph state, h is the decimal representation of the computational basis state of m+n flying bits, |h> is the computational basis state of m+n flying bits, |g h > is the corresponding hypergraph state of m+n flying bits. The quantum circuit of a complete orthogonal hypergraph state analyzer can be found in Figure 1 , which in turn includes a generalized controlled Z gate and m+n single-bit Hadamard gates and m+n single-bit computational ground state measurements. The analyzer can distinguish 2 m+n A complete orthogonal hypergraph |g h >, input quantum state |g h >, where |g h > represents the h+1th hypergraph state, according to the relationship between the hypergraph state and the computational ground state The m+n single-bit computational ground state measurement results are h1h2…h m h m+1 h m+2 …h m+n .

[0055] In the present invention, five embodiments are used for explanation, including a distributed generalized controlled NOT gate, a distributed generalized controlled Z gate, a distributed controlled NOT gate, a distributed Toffoli gate, and a distributed multi-bit controlled NOT gate.

[0056] Embodiment 1

[0057] Specifically, see Figure 2 and Figure 3, Embodiment 1 of the present application is a method for implementing a distributed generalized controlled NOT gate, which is used to control a central node and multiple local nodes.

[0058] Multiple local nodes hold a total of m+n local qubits {s1,s2,…,s m ,s m+1 ,s m+2 ,…,s m+n} and m+n flying bits {f1,f2,…,f m ,f m+1 ,f m+2 ,…,f m+n}, where s1 represents the first local quantum bit, s2 represents the second local quantum bit, and s m represents the mth local qubit, s m+1 represents the m+1th local quantum bit, s m+2 represents the m+2th local quantum bit, s m+n represents the m+nth local quantum bit, h1 represents the first flying bit, h2 represents the second flying bit, and h m represents the mth flying bit, f m+1 represents the m+1th flying bit, f m+2 represents the m+2th flying bit, f m+n represents the m+nth flying bit. In this embodiment, the first m local qubits are called local control qubits, and the last n local qubits are called local target qubits. The m+n local qubits can be in any quantum state, that is, Among them, |ψ> s represents the quantum state of the local qubit, and the computational basis state of m+n local qubits is represented by |x> s , x is the decimal representation of the computational basis state of m+n local qubits, a x is the quantum state |ψ> s In the computational ground state |x> s The probability amplitude, coefficient {a x}Satisfy the probability conservation law Quantum state |ψ> s In |x> s The probability of |a x | 2 Each local node contains an unlimited number of local quantum bits and an equal number of flying bits, and the central node completes the joint projection measurement of the flying bits, which is the complete orthogonal hypergraph analyzer.

[0059] Among them, flying bit refers to a quantum bit in transmission, which moves between different physical locations, or propagates in a quantum channel (such as optical fiber or free space), from one quantum node (such as quantum processor, quantum storage or quantum transmission device) to another. Flying bit is one of the key elements to realize long-distance quantum communication, build quantum networks and realize large-scale quantum computing. Photons are the most mature flying bits that people can control at present because of their easy control, non-decoherence and easy detection.

[0060] In this embodiment, each local node contains an unlimited number of local qubits, which may have local control bits or local target bits, wherein the local control bits are used as control bits in the distributed generalized controlled NOT gate. Since the local qubits are distributed in different local nodes, it is necessary to implement a distributed generalized controlled NOT gate.

[0061] Specifically, the implementation method of the distributed generalized controlled NOT gate includes the following steps:

[0062] S1. The local node initializes the flying bits.

[0063] Specifically, all flying bits are initialized to |0>, and the quantum state of the flying bits is

[0064] S2. The local node performs a Hadamard gate operation on the local target quantum bit.

[0065] After the operation, the quantum state of the local quantum bit |ψ> s becomes x is the decimal representation of the computational basis state of m+n local qubits, b x is the quantum state |ψ′> s In the computational ground state |x> s Since the single-bit operation does not introduce correlation, the present invention uses a new set of coefficients {b x} indicates that the coefficient {b x}Satisfy the probability conservation law At this time, the overall quantum state of m+n local quantum bits and m+n flying bits can be written as the quantum state of the local quantum bit |ψ′> s and the quantum state of the flying bit |ψ> f The direct product form

[0066] S3. Perform a control NOT gate operation on the flying bit according to the local quantum bit.

[0067] Specifically, the local control bit or local target bit of each node performs a two-bit control NOT gate with the flying bit of the node. Among them, s i represents the i-th local quantum bit, f i represents the i-th flying bit, where all flying bits are the target bits in the two-bit controlled NOT gate, and the overall quantum state evolves as Among them, |x> f is the computational ground state of all flying bits, is a control NOT gate with s1 as the control bit and f1 as the target bit, is the control NOT gate with s2 as the control bit and f2 as the target bit, Yes m+n As a control bit, f m+n Acts as a control NOT gate for the target bit.

[0068] S4. Transmitting the flying bits to a central node via a quantum channel.

[0069] S5. The central node receives flying bits transmitted by multiple local nodes via the quantum channel, performs joint projection measurement on the flying bits, and transmits the joint projection measurement result to each of the local nodes.

[0070] The joint projection measurement is performed by a complete orthogonal hypergraph analyzer, and the corresponding eigenstate is 2 m+n mutually orthogonal (inner product is 0) complete orthogonal hypergraphs. The orthogonal hypergraph analyzer includes the generalized controlled Z gate Hadamard Door Operation m+n single-bit computational ground state measurements, the overall quantum state |ψ> sf Before reaching m+n single-bit computing ground state measurements, it evolves to:

[0071]

[0072]

[0073] The present invention uses |h> f is the computational ground state of the m+n flying bits during the computational ground state measurement, h i represents the computational ground state of the ith flying bit. Since the ith local qubit corresponds to the ith flying bit, the same subscript is used here, and the definition is the same as |x> s Similarly. In addition, yes Specifically, Z 0 =I, Z 1 = Z. The calculated ground state in the above formula |h>f The result of performing the computational ground state measurement on the flying bit is h1h2…h m h m+1 h m+2 …h m+n , where h1 represents the computational basis state of the first flying bit, h2 represents the computational basis state of the second flying bit, and h m represents the computational ground state of the mth flying bit, h m+1 represents the computational ground state of the m+1th flying bit, h m+2 represents the computational ground state of the m+2th flying bit, h m+n represents the computational ground state of the m+nth flying bit, which is equivalent to the input quantum state of the complete orthogonal hypergraph state analyzer: At this time, the quantum state of the local quantum bit is

[0074] S6. The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0075] Specifically, the local node receives the joint projection measurement result transmitted by the central node via the classical channel. When the measurement result of the i-th flying bit is "1", the Z gate is performed on the i-th local quantum bit. After the feedforward operation, the quantum state of the local quantum bit becomes

[0076]

[0077] For example, when the flying bit is projected by the hypergraph analyzer to the first orthogonal hypergraph state |g0>, the measurement result h1h2…h m h m+1 h m+2 …h m+n are all 0, just for the quantum state |ψ′> s The generalized control Z gate is realized; when the flying bit is projected to the second orthogonal hypergraph state |g1>, h m+n is 1, and the rest are h i are all 0, then there will be an extra Z transformation on the m+nth local quantum bit, so it is necessary to perform another Z-gate unitary operation on the m+nth bit to offset the previous Z transformation, that is, ZZ=I, thereby realizing the quantum state |ψ′> s The generalized control Z gate; and so on, the flying bit performs a joint projection measurement projected to the second m+n Orthogonal Hypergraph At this time, all local control bits and local target bits have a redundant Z transformation, and a unitary operation of a Z gate needs to be performed on all local control bits and local target bits to offset the aforementioned Z transformation.

[0078] In the process of communicating measurement results through classical channels, it is necessary to use quantum storage technology to temporarily store local quantum bits, or other technologies to increase time delays until the corresponding feedforward unitary operation is applied.

[0079] S7. The local node performs a Hadamard gate operation on the local target quantum bit.

[0080] After the operation, the quantum state of the local quantum bit |ψ″> s The changes are:

[0081]

[0082] So far, this embodiment has used the above seven steps to utilize the flying bit joint projection measurement and feedforward unitary operation to measure the m+n local quantum bits |ψ> s Generalized controlled NOT gate The first m local qubits serve as control bits, and the last n local qubits serve as target bits.

[0083] Embodiment 2

[0084] Specifically, see Figure 4 , Embodiment 2 of the present application is a method for implementing a distributed generalized control Z-gate, which is used to control a central node and multiple local nodes.

[0085] Multiple local nodes hold a total of m+n local qubits {s1,s2,…,s m ,s m+1 ,s m+2 ,…,s m+n} and m+n flying bits {f1,f2,…,f m ,f m+1 ,f m+2 ,…,f m+n}, s1 represents the first local quantum bit, s2 represents the second local quantum bit, s m represents the mth local qubit, s m+1 represents the m+1th local quantum bit, s m+2 represents the m+2th local quantum bit, s m+n represents the m+nth local quantum bit, f1 represents the first flying bit, f2 represents the second flying bit, and f m represents the mth flying bit, f m+1represents the m+1th flying bit, f m+2 represents the m+2th flying bit, f m+n represents the m+nth flying bit. In this embodiment, m of them are called local control qubits and n are called local target qubits. The m+n local qubits can be in any quantum state, that is, The computational ground state of m+n local qubits is represented by |x> s , a x is the quantum state |ψ> s In |x> s The probability amplitude, coefficient {a x}Satisfy the probability conservation law Quantum state |ψ> s In |x> s The probability of |a x | 2 Each local node contains an unlimited number of local quantum bits and an equal number of flying bits, and the central node completes the joint projection measurement of the flying bits, which is the complete orthogonal hypergraph analyzer.

[0086] The implementation method of the distributed generalized control Z gate includes the following steps:

[0087] S1. The local node initializes the flying bits.

[0088] In this embodiment, all flying bits are initialized to |0>, and the quantum state of the flying bits is At this time, the quantum states of m+n local quantum bits and m+n flying bits can be written as the direct product form

[0089] S2. The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit.

[0090] Specifically, the local control bit or local target bit of each node performs a two-bit control NOT gate with the flying bit of the node. All flying bits are target bits in the two-bit controlled NOT gate, and the overall quantum state evolves as follows:

[0091] is a control NOT gate with s1 as the control bit and f1 as the target bit, is the control NOT gate with s2 as the control bit and f2 as the target bit, Yes m+n As a control bit, f m+n Acts as a control NOT gate for the target bit.

[0092] S3. Transmit the flying bits to a central node via a quantum channel.

[0093] S4. The central node receives flying bits transmitted by multiple local nodes via the quantum channel, performs joint projection measurement on the flying bits, and transmits the joint projection measurement result to each of the local nodes.

[0094] That is, the joint projection measurement is performed by a complete orthogonal hypergraph analyzer, and the corresponding eigenstate is 2 m+n mutually orthogonal (inner product is 0) complete orthogonal hypergraph states. The analyzer contains generalized controlled Z gates Hadamard Door Operation m+n single-bit computational ground state measurements, the overall quantum state |ψ> sf Before reaching m+n single-bit computing ground state measurements, it evolves to:

[0095]

[0096] The present invention uses |h> f is the computational ground state of m+n flying bits, defined similarly to |x> s Similarly. In addition, yes Specifically, Z 0 =I, Z 1 = Z. The calculated ground state in the above formula |h> f The result of performing the computational ground state measurement on the flying bit is h1h2…h m h m+1 h m+2 …h m+n , which is equivalent to the input quantum state of a complete orthogonal hypergraph state analyzer is At this time, the quantum state of the local quantum bit is

[0097] S5. The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0098] Specifically, the local node receives the joint projection measurement result transmitted by the central node via the classical channel. When the measurement result of the i-th flying bit is "1", the Z gate is performed on the i-th local quantum bit. After the feedforward operation, the quantum state of the local quantum bit becomes

[0099]

[0100] For example, when the flying bit is projected into the quantum state |g0> by the hypergraph analyzer, the measurement result h1h2…hm h m+ 1h m+2 …h m+n are all 0, just for the quantum state |ψ> s The generalized control Z gate is realized; when the flying bit is projected to the quantum state |g1>, h m+n is 1, and the rest are h i are all 0, then there will be an extra Z transformation on the m+nth local quantum bit, so it is necessary to perform another Z-gate unitary operation on the m+nth bit to offset the previous Z transformation, that is, ZZ=I, thereby realizing the quantum state |ψ> s The generalized control Z gate; by analogy, the flying bit performs a joint projection measurement projected onto the quantum state At this time, all local control bits and local target bits have a redundant Z transformation, and a unitary operation of a Z gate needs to be performed on all local control bits and local target bits to offset the aforementioned Z transformation.

[0101] In the process of communicating the measurement results through classical channels, it is necessary to temporarily store the local control bits and target bits using quantum storage technology, or other technologies to increase the time delay until the corresponding feedforward unitary operation is applied.

[0102] So far, this embodiment has used the above five steps to utilize the flying bit joint projection measurement and feedforward unitary operation to measure the m+n local quantum bits |ψ> s Generalized control Z gate The first m local qubits serve as control bits, and the last n local qubits serve as target bits.

[0103] Embodiment 3

[0104] The two-bit controlled NOT gate is a special case of the generalized controlled NOT gate, with m = n = 1, see Figure 5 (a) in , as one of the universal quantum gates, is analyzed separately here. Figure 5 (b) in the embodiment 3 of the present application is a method for implementing a distributed control NOT gate, and the method comprises the steps of:

[0105] S1. The local node initializes the flying bits.

[0106] The quantum state of the two local qubits can be in any quantum state |ψ> s =a0|00>+a1|01>+a2|10>+a3|11>, a0 is the quantum state |ψ> s The probability amplitude is |00>, and a1 is the quantum state |ψ> s The probability amplitude is in |01>, and a2 is the quantum state |ψ>s The probability amplitude is in |10>, and a3 is the quantum state |ψ> s The probability amplitude in |11>, the coefficient {a x}Satisfy the probability conservation law All flying bits are initialized to |0>, and the quantum state of the flying bits is |ψ> f =|00>.

[0107] S2. The local node performs a Hadamard gate operation on the local target quantum bit.

[0108] After operation|ψ> s →|ψ′> s =(I s1 H s2 )|ψ> s =b0|00>+b1|01>+b2|10>+b3|11>, where b0 is the quantum state |ψ′> s The probability amplitude of being in |00>, b1 is the quantum state |ψ′> s The probability amplitude is in |01>, b2 is the quantum state |ψ′> s The probability amplitude is in |10>, b3 is the quantum state |ψ′> s The probability amplitude of being in |11>, I s1 is the identity matrix acting on s1, H s2 It is a Hadamard gate acting on s2. Since single-bit operation does not introduce correlation, the present invention uses a set of new coefficients {h x} indicates that the coefficient {b x}Satisfy the probability conservation law At this time, the quantum states of the two local quantum bits and the two flying bits can be written as the direct product form

[0109] S3. The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit.

[0110] The local control bit or local target bit of each node performs a two-bit control NOT gate with the flying bit of the node. All flying bits are target bits in the two-bit controlled NOT gate, and the overall quantum state evolves as follows:

[0111] is a control NOT gate with s1 as the control bit and f1 as the target bit, It is the control NOT gate with s2 as the control bit and f2 as the target bit.

[0112] S4. Transmitting the flying bits to a central node via a quantum channel.

[0113] S5. The central node receives flying bits transmitted by multiple local nodes via the quantum channel, performs joint projection measurement on the flying bits, and transmits the joint projection measurement result to each of the local nodes.

[0114] That is, joint projection measurement is performed by two bit-complete orthogonal hypergraph analyzers, see Figure 6 , the corresponding eigenstates are 4 mutually orthogonal (inner product is 0) complete orthogonal hypergraph states. The analyzer contains control gates Hadamard Door Operation 2 single-bit computational ground state measurements, where For the control Z gate with the first flying bit f1 as the control bit and the second flying bit f2 as the target bit, is the Hadamard gate performed on the first flying bit f1, is the Hadamard gate performed on the second flying bit f2, and the overall quantum state |ψ> sf Before reaching m+n single-bit computing ground state measurements, it evolves to:

[0115]

[0116] Among them, I s2 is the identity matrix for the second local qubit s2, is a control Z gate with the first local qubit s1 as the control bit and the second local qubit s2 as the target bit, is the Z gate executed on the first local qubit s1, is the Z gate executed on the second local qubit s2, |00> f1f2 Indicates that the flying bit f1f2 is in the quantum state |00>, Indicates that the flying bit f1f2 is in the quantum state |01>, Indicates that the flying bit f1f2 is in the quantum state |10>, It means that the flying bits f1f2 are in the quantum state |11>.

[0117] The present invention uses h1h2 to represent the measurement result of the flying bit and uses h1h2 to represent the calculation ground state of the local quantum bit.

[0118] |x1x2> represents the calculation basis state in the above formula The result of the computational ground state measurement on the flying bit is h1h2, which is equivalent to the input quantum state of the two-bit complete orthogonal hypergraph state analyzer. At this time, the quantum state of the local quantum bit is in, represents the Z gate executed on the first local quantum bit s1 when h1=1, and the I gate executed on the first local quantum bit s1 when h1=0, It represents the Z gate executed on the second local quantum bit s2 when h2=1, and the I gate executed on the second local quantum bit s2 when h2=0.

[0119] S6. The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0120] The local node receives the joint projection measurement result transmitted by the central node via the classical channel. When the measurement result of the i-th flying bit is "1", the Z gate is performed on the i-th local quantum bit. After the feedforward operation, the quantum state of the local quantum bit becomes

[0121] For example, when the flying bit is projected to the quantum state |g0> by the two-bit hypergraph analyzer, the measurement results h1h2 are both 0, thus achieving the quantum state |ψ′> s When the flying bit is projected to the quantum state |g1> by the two-bit hypergraph analyzer, h1 is 0 and h2 is 1. Then, there will be a redundant Z transformation on the second local quantum bit. Therefore, it is necessary to perform another Z-gate unitary operation on this bit to offset the previous Z transformation, that is, ZZ=I, so as to realize the quantum state |ψ′> s Control the Z gate, and so on.

[0122] In the process of communicating the measurement results through classical channels, it is necessary to temporarily store the local control bits and target bits using quantum storage technology, or other technologies to increase the time delay until the corresponding feedforward unitary operation is applied.

[0123] S7. The local node performs a Hadamard gate operation on the local target quantum bit.

[0124] After the operation, the quantum state of the local qubit |ψ″> s The changes are:

[0125]

[0126] So far, this embodiment has used the above seven steps to utilize the flying bit joint projection measurement and feedforward unitary operation to measure the two local quantum bits |ψ> s Controlled NOT gate The local quantum bit s1 serves as the control bit and s2 serves as the target bit.

[0127] Embodiment 4

[0128] The three-bit Toffoli gate is a special case of the generalized controlled NOT gate, with m = 2 and n = 1, see Figure 7 (a) in , as one of the universal quantum gates, is analyzed separately here. Figure 7 (b) in the embodiment 4 of the present application is a method for implementing a distributed Toffoli gate, and the method comprises the steps of:

[0129] S1. The local node initializes the flying bits.

[0130] The quantum state of the three local qubits can be in any quantum state |ψ> s =a0|000>+a1|001>+a2|010>+a3|011>+a4|100>+a5|101>+a6|110>+a7|111>, a0 is the quantum state |ψ> s The probability amplitude is in |000>, and a1 is the quantum state |ψ> s The probability amplitude is in |001>, and a2 is the quantum state |ψ> s The probability amplitude is |010>, and a3 is the quantum state |ψ> s The probability amplitude is |011>, and a4 is the quantum state |ψ> s The probability amplitude is |100>, and a5 is the quantum state |ψ> s The probability amplitude is |101>, and a6 is the quantum state |ψ> s The probability amplitude is in |110>, and a7 is the quantum state |ψ> s The probability amplitude in |111>, the coefficient {a x}Satisfy the probability conservation law All flying bits are initialized to |0>, and the quantum state of the flying bits is |ψ> f =|000>.

[0131] S2. The local node performs a Hadamard gate operation on the local target quantum bit.

[0132] After the operation, |ψ> s →|ψ′> s =(I s1 I s2 H s3 )|ψ> s =b0|000>+b1|001>+b2|010>+b3|011>+b4|100>+b5|101>+b6|110>+b7|111>, where b0 is the quantum state |ψ′> sThe probability amplitude is in |000>, b1 is the quantum state |ψ′> s The probability amplitude is in |001>, b2 is the quantum state |ψ′> s The probability amplitude is in |010>, b3 is the quantum state |ψ′> s The probability amplitude is in |011>, b4 is the quantum state |ψ′> s The probability amplitude is |100>, b5 is the quantum state |ψ′> s The probability amplitude is |101>, b6 is the quantum state |ψ′> s The probability amplitude is in |110>, b7 is the quantum state |ψ′> s The probability amplitude is |111>, is the identity matrix acting on s1, is the identity matrix acting on s2, It is a Hadamard gate acting on s3. Since single-bit operation does not introduce correlation, the present invention uses a set of new coefficients {b x} indicates that the coefficient {b x}Satisfy the probability conservation law At this time, the quantum states of the three local quantum bits and the three flying bits can be written as a direct product form

[0133]

[0134] S3. The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit.

[0135] The local control bit or local target bit of each node performs a two-bit control NOT gate with the flying bit of the node. All flying bits are target bits in the two-bit controlled NOT gate, and the overall quantum state evolves as follows: is a control NOT gate with s1 as the control bit and f1 as the target bit, is the control NOT gate with s2 as the control bit and f2 as the target bit, It is the control NOT gate with s3 as the control bit and f3 as the target bit.

[0136] S4. Transmitting the flying bits to a central node via a quantum channel.

[0137] S5. The central node receives flying bits transmitted by multiple local nodes via the quantum channel, performs joint projection measurement on the flying bits, and transmits the joint projection measurement result to each of the local nodes.

[0138] Specifically, joint projection measurement is performed by a three-bit complete orthogonal hypergraph analyzer, see Figure 8 , the corresponding eigenstates are 8 mutually orthogonal (inner product is 0) complete orthogonal hypergraph states. The analyzer contains a three-bit control Z gate Hadamard Door Operation 3 single-bit computational ground state measurements, where For a three-bit controlled Z gate with the first flying bit f1 and the second flying bit f2 as control bits and the third flying bit f3 as target bit, is the Hadamard gate performed on three flying bits, and the overall quantum state |ψ> sf Before reaching m+n single-bit computing ground state measurements, it evolves to:

[0139]

[0140] in, is the identity matrix for 3 local qubits, for, is a three-bit controlled Z-gate with the first local qubit s1 and the second local qubit s2 as control bits and the third local qubit s3 as target bit, Indicates that the flying bit f1f2f3 is in the quantum state |000>, Indicates that the flying bit f1f2f3 is in the quantum state |001>, Indicates that the flying bit f1f2f3 is in the quantum state |010>, Indicates that the flying bit f1f2f3 is in the quantum state |011>, Indicates that the flying bit f1f2f3 is in the quantum state |100>, Indicates that the flying bits f1f2f3 are in a quantum state

[0141] |101>, Indicates that the flying bit f1f2f3 is in the quantum state |110>, Indicates that the flying bits f1f2f3 are in the quantum state |111>.

[0142] The present invention represents the measurement result of the flying bit as h1h2h3, where h3 represents the measurement result of the third flying bit, and the calculation basis state of the local quantum bit is represented by |x1x2x3>. The result of the computational ground state measurement on the flying bit is h1h2h3, which is equivalent to the input quantum state of the three-bit complete orthogonal hypergraph state analyzer. At this time, the quantum state of the local quantum bit is in, represents the Z gate executed on the first local quantum bit s1 when h1=1, and the I gate executed on the first local quantum bit s1 when h1=0, represents the Z gate executed on the second local quantum bit s2 when h2=1, and the I gate executed on the second local quantum bit s2 when h2=0, It indicates that when h3=1, a Z gate is executed on the third local quantum bit s3, and when h3=0, an I gate is executed on the third local quantum bit s1.

[0143] S6. The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0144] The local node receives the joint projection measurement result transmitted by the central node via the classical channel. When the measurement result of the i-th flying bit is "1", the Z gate is performed on the i-th local quantum bit. After the feedforward operation, the quantum state of the local quantum bit becomes

[0145] For example, when the flying bit is projected to the quantum state |g0> by the three-bit hypergraph analyzer, the measurement results h1h2h3 are all 0, thus achieving the quantum state |ψ′> s The three-bit control Z gate of the three-bit hypergraph analyzer; when the flying bit is projected to the quantum state |g1> by the three-bit hypergraph analyzer, h1 is 0, h2 is 0, and h3 is 1. Then, there will be a redundant Z transformation on the third local quantum bit. Therefore, it is necessary to perform another Z gate unitary operation on this bit to offset the previous Z transformation, that is, ZZ=I, so as to realize the quantum state |ψ′> s The three bits control the Z gate, and so on.

[0146] In the process of communicating the measurement results through classical channels, it is necessary to temporarily store the local control bits and target bits using quantum storage technology, or other technologies to increase the time delay until the corresponding feedforward unitary operation is applied.

[0147] S7. The local node performs a Hadamard gate operation on the local target quantum bit.

[0148] The quantum state of the local qubit |ψ″> s The change is

[0149]

[0150] So far, this embodiment has used the above seven steps to utilize the flying bit joint projection measurement and feedforward unitary operation to measure the three local quantum bits |ψ> s Toffoli gate The first two local qubits are used as control bits, and the last local qubit is used as the target bit.

[0151] Embodiment 5

[0152] Specifically, see Fig. 9 , Embodiment 5 of the present application is a method for implementing a distributed multi-bit quantum controlled NOT gate, which is used to control a central node and multiple local nodes.

[0153] Multiple local nodes hold a total of n+1 local qubits {s1,s2,s3,…,s n+1} and n+1 flying bits {f1,f2,f3,…,f n+1}, s1 represents the first local quantum bit, s2 represents the second local quantum bit, s3 represents the third local quantum bit, s n+1 represents the n+1th local quantum bit, f1 represents the first flying bit, f2 represents the second flying bit, f3 represents the third flying bit, and f n+1 represents the n+1th flying bit. In this embodiment, the first one is called the local control qubit, and the next n ones are called local target qubits. The n+1 local qubits can be in any quantum state, that is, The computational ground state of the n+1 local qubits is represented by |x> s , a x is the quantum state |ψ> s In |x> s The probability amplitude, coefficient {a x}Satisfy the probability conservation law Quantum state |ψ> s In |x> s The probability of |a x | 2 Each local node contains an unlimited number of local quantum bits and an equal number of flying bits, and the central node completes the joint projection measurement of the flying bits, which is the complete orthogonal hypergraph analyzer.

[0154] S1. The local node initializes the flying bits.

[0155] Specifically, all flying bits are initialized to |0>, and the quantum state of the flying bits is

[0156] S2. The local node performs a Hadamard gate operation on the local target quantum bit.

[0157] After the operation, the quantum state of the local quantum bit |ψ> s becomes Since single-bit operation does not introduce correlation, the present invention uses a set of new coefficients {b x} indicates that the coefficient {b x}Satisfy the probability conservation law At this time, the overall quantum state of n+1 local quantum bits and n+1 flying bits can be written as the quantum state of the local quantum bit |ψ′> s and the quantum state of the flying bit |ψ> f The direct product form

[0158] S3. Perform a control NOT gate operation on the flying bit according to the local quantum bit.

[0159] Specifically, the local control bit or local target bit of each node performs a two-bit control NOT gate with the flying bit of the node. Among them, s i represents the i-th local quantum bit, f i represents the i-th flying bit, where all flying bits are the target bits in the two-bit controlled NOT gate, and the overall quantum state evolves as Among them, |x> f is the computational ground state of all flying bits, is a control NOT gate with s1 as the control bit and f1 as the target bit, is the control NOT gate with s2 as the control bit and f2 as the target bit, Yes n+1 As a control bit, f n+1 Acts as a control NOT gate for the target bit.

[0160] S4. Transmitting the flying bits to a central node via a quantum channel.

[0161] S5. The central node receives flying bits transmitted by multiple local nodes via the quantum channel, performs joint projection measurement on the flying bits, and transmits the joint projection measurement result to each of the local nodes.

[0162] The joint projection measurement is performed by a complete orthogonal hypergraph analyzer, and the corresponding eigenstate is 2 n+1 mutually orthogonal (inner product is 0) complete orthogonal hypergraphs. The orthogonal hypergraph analyzer includes the generalized controlled Z gate Hadamard Door Operation n+1 single-bit computational ground state measurements, the overall quantum state |ψ> sf Before reaching n+1 single-bit computing ground state measurements, it evolves to:

[0163]

[0164]

[0165] The present invention uses |h> f is the computational ground state of the n+1 flying bits during the computational ground state measurement, h i represents the computational ground state of the ith flying bit. Since the ith local qubit corresponds to the ith flying bit, the same subscript is used here, and the definition is the same as |x> s Similarly. In addition, yes Specifically, Z 0 =I, Z 1 = Z. The calculated ground state in the above formula |h> f The result of performing the computational ground state measurement on the flying bit is h1h2h3…h n+1 , where h1 represents the calculation basis state of the first flying bit, h2 represents the calculation basis state of the second flying bit, h3 represents the calculation basis state of the third flying bit, and h n+1 represents the computational ground state of the n+1th flying bit, which is equivalent to the input quantum state of the complete orthogonal hypergraph state analyzer: At this time, the quantum state of the local quantum bit is

[0166] S6. The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

[0167] Specifically, the local node receives the joint projection measurement result transmitted by the central node via the classical channel. When the measurement result of the i-th flying bit is "1", the Z gate is performed on the i-th local quantum bit. After the feedforward operation, the quantum state of the local quantum bit becomes

[0168] For example, when the flying bit is projected into the quantum state |g0> by the hypergraph analyzer, the measurement result is h1h2h3…h n+1 are all 0, just for the quantum state |ψ′> s The generalized control Z gate is realized; when the flying bit is projected to the quantum state |g1>, h n+1 is 1, and the rest are h i are all 0, then there will be an extra Z transformation on the n+1th local quantum bit, so it is necessary to perform another Z-gate unitary operation on the n+1th bit to offset the previous Z transformation, that is, ZZ=I, thereby realizing the quantum state |ψ′> s The generalized control Z gate; by analogy, the flying bit performs a joint projection measurement projected onto the quantum state At this time, all local control bits and local target bits have a redundant Z transformation, and a unitary operation of a Z gate needs to be performed on all local control bits and local target bits to offset the aforementioned Z transformation.

[0169] In the process of communicating measurement results through classical channels, it is necessary to use quantum storage technology to temporarily store local quantum bits, or other technologies to increase time delays until the corresponding feedforward unitary operation is applied.

[0170] S7. The local node performs a Hadamard gate operation on the local target quantum bit.

[0171] After the operation, the quantum state of the local quantum bit |ψ″> s The changes are:

[0172]

[0173]

[0174] So far, this embodiment has used the above seven steps to utilize the flying bit joint projection measurement and feedforward unitary operation to measure the n+1 local quantum bits |ψ> s A multi-bit controlled NOT gate is implemented on The first local qubit is used as the control bit, and the next n local qubits are used as the target bits.

[0175] It can be understood that, obviously, superimposing different single-bit operations on each quantum bit is equivalent to other types of multi-bit quantum gates. The variations based on the distributed generalized controlled NOT gate and generalized controlled Z gate implemented by the present invention should fall within the scope of protection of the claims attached to the present invention.

[0176] In summary, the present invention replaces the entanglement distribution in previous schemes by using joint projection measurement of flying bits, transfers the correlation between quantum bits from the quantum entanglement source to quantum measurement, avoids the preparation of a large number of entangled states, and reduces the number of quantum bits consumed. It further improves the distribution distance of distributed quantum logic gates and realizes a distributed quantum gate system of multiple bits.

[0177] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or terminal including the element.

[0178] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for implementing a distributed generalized controlled NOT gate, characterized in that: The method is used to control a central node and multiple local nodes, the multiple local nodes hold m+n local quantum bits and m+n flying bits in total, the local quantum bits include m local control quantum bits and n local target quantum bits, and the method includes: The local node initializes the flying bits; The local node performs a Hadamard gate operation on the local target quantum bit; The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit; The local node transmits the flying bit to the central node via the quantum channel; The central node receives flying bits transmitted by multiple local nodes via quantum channels, performs joint projection measurement on the flying bits, and transmits the joint projection measurement results to each of the local nodes; The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result; The local node performs a Hadamard gate operation on the local target quantum bit.

2. A method for implementing a distributed generalized controlled NOT gate according to claim 1, characterized in that: The local quantum bits include photons, atoms, ions and superconducting quantum bits.

3. A method for implementing a distributed generalized controlled NOT gate according to claim 1, characterized in that: The joint projection measurement of the flying bits is specifically performed by using a complete orthogonal hypergraph analyzer to perform joint projection measurement of the flying bits.

4. A method for implementing a distributed generalized controlled NOT gate according to claim 3, characterized in that: The complete orthogonal hypergraph state analyzer includes a Hadamard gate and a generalized controlled Z gate, and the joint projection measurement of the flying bits specifically includes: Using the flying bits corresponding to the local control qubits as control bits and the flying bits corresponding to the local target qubits as target bits, executing a generalized control Z gate; Performing a Hadamard gate on each of the flying bits; A calculation base state measurement is performed on each of the flying bits to obtain the joint projection measurement result.

5. The method for implementing a distributed generalized controlled NOT gate according to claim 1, characterized in that: The performing a feedforward operation on the local quantum bit according to the measurement result specifically includes: Determine in turn whether the measurement values ​​corresponding to all flying bits are 1; If the measurement value corresponding to the flying bit is 1, a feed-forward Z gate is executed on the local quantum bit corresponding to the flying bit.

6. A method for implementing a distributed generalized control Z gate, characterized in that: The method is used to control a central node and multiple local nodes, the multiple local nodes hold m+n local quantum bits and m+n flying bits in total, the local quantum bits include m local control quantum bits and n local target quantum bits, the method includes The local node initializes the flying bits; The local node performs a two-bit controlled NOT gate operation using the local quantum bit as the control bit and the flying bit as the target bit; Transmitting the flying bits to a central node via a quantum channel; The central node receives flying bits transmitted by multiple local nodes via quantum channels, performs joint projection measurement on the flying bits, and transmits the joint projection measurement results to each of the local nodes; The local node receives the joint projection measurement result transmitted by the central node via a classical channel, and performs a feedforward operation on the local quantum bit according to the measurement result.

7. A distributed generalized control Z-gate implementation method according to claim 6, characterized in that: The local quantum bits include photons, atoms, ions and superconducting quantum bits.

8. A method for implementing a distributed generalized controlled NOT gate according to claim 6, characterized in that: The joint projection measurement of the flying bits is specifically performed by using a complete orthogonal hypergraph analyzer to perform joint projection measurement of the flying bits.

9. A distributed generalized control Z-gate implementation method according to claim 8, characterized in that: The complete orthogonal hypergraph state analyzer includes a Hadamard gate and a generalized controlled Z gate, and the joint projection measurement of the flying bits specifically includes: Using the flying bits corresponding to the local control qubits as control bits and the flying bits corresponding to the local target qubits as target bits, executing a generalized control Z gate; Performing a Hadamard gate on each of the flying bits; A calculation base state measurement is performed on each of the flying bits to obtain the joint projection measurement result.

10. A distributed generalized control Z-gate implementation method according to claim 6, characterized in that: The performing a feedforward operation on the local quantum bit according to the measurement result specifically includes: Determine in turn whether the measurement values ​​corresponding to all flying bits are 1; If the measurement value corresponding to the flying bit is 1, a feed-forward Z gate is executed on the local quantum bit corresponding to the flying bit.

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