Decomposition method, device and equipment for multi-control quantum phase shifting door and medium

Abstract

The invention relates to a decomposition method, device and equipment for a multi-control quantum phase shifting gate and a medium, and the method comprises the steps: decomposing the multi-control quantum phase shifting gate C {n-1} PS (theta) into n-1 quantum circuits, the n-1 quantum circuits are connected end to end from left to right, n is the total number of sub-bits acted by the multi-control quantum phase shifting gate, and n is greater than or equal to 3; 2x-1 controlled quantum gates are configured in the xth quantum circuit, the control bits of the controlled quantum gates are arranged at the xth quantum bit, the target bits of the controlled quantum gates are arranged at the nth quantum bit, and x ranges from 1 to n-1; 2 < x >-1 CNOT gates are configured in the x quantum circuit, 0 CNOT gates are configured in the first quantum circuit, and the CNOT gates and the controlled quantum gates are alternately arranged; the target bits of the first 2x-2 CNOT gates in the xth quantum circuit are arranged at the xth quantum bit, and the quantum bits where the control bits are located are sequentially arranged from the high bit to the low bit and then to the high bit from left to right. According to the decomposition mode, the number of quantum gates is reduced while the decomposition accuracy is ensured, and the efficiency of a quantum circuit is improved.

Description

Technical Field

[0001] The present application relates to the field of quantum computing technology, and in particular to a decomposition method, device, computing equipment and computer-readable storage medium for multi-controlled quantum phase-shift gates. Background Art

[0002] Quantum algorithms are advanced computing algorithms based on the principles of quantum mechanics. At their core, they utilize properties such as quantum superposition and quantum entanglement, and can perform better than classical algorithms in specific computing tasks. For example, Shor's algorithm demonstrates the potential of quantum computing in cryptography through efficient prime factorization of large numbers, while Grover's algorithm demonstrates its computational advantages in solving specific problems through rapid searches of unordered databases. The emergence of these quantum algorithms not only reveals the powerful capabilities of quantum computing, but also provides an important direction for the development of future computing technology.

[0003] In quantum computing, the quantum circuit model is the basic framework for describing and implementing quantum algorithms. The quantum circuit model consists of quantum bits and quantum logic gates (quantum gates for short). Common quantum gates include the Hadamard gate for generating superposition states and the CNOT gate for generating entangled states. Unlike classical circuits that transmit signals through metal wires, quantum circuits connect the various components through time evolution, and the state of the quantum bit changes when it passes through the quantum gate operation. The quantum gate operation is essentially the process of the unitary matrix acting on the quantum bit, so the entire quantum circuit can be regarded as a complex unitary matrix composed of multiple unitary matrices. This model greatly simplifies the design and implementation of quantum algorithms, making it easier to decompose complex quantum operations into a series of simple operations.

[0004] However, in actual quantum computers, there may be significant hardware challenges in implementing certain complex quantum gates. To this end, these complex quantum gates need to be decomposed into sequences of basic quantum gates (such as single-qubit gates and two-qubit gates). This decomposition not only reduces the hardware requirements and implementation difficulty, but also improves the efficiency and accuracy of quantum computing. However, the decomposition process of multi-controlled quantum gates (such as multi-controlled quantum gates with n-1 control bits) will lead to an exponential increase in the number of quantum gates. For a multi-controlled quantum gate with multiple control bits, the number of quantum gates and circuit depth required for its decomposition results will increase rapidly. For example, decomposing a multi-controlled quantum gate with C^{4} control bits requires 213 quantum gates with a circuit depth of 149; while decomposing a multi-controlled quantum gate with C^{5} control bits requires 1429 quantum gates with a circuit depth of up to 959. This exponential resource consumption makes the implementation of multi-controlled quantum gates in noisy intermediate-scale quantum (NISQ) computers extremely complex, becoming an important technical bottleneck on the road to the practical application of quantum computing.

[0005] Therefore, how to effectively decompose multi-controlled quantum gates to reduce the demand for hardware resources and improve the efficiency of quantum computing has become an important direction in quantum computing research. This research can not only promote the practical application of quantum computing, but also lay the foundation for its application in more fields. Summary of the invention

[0006] In view of the technical problems existing in the prior art, the present application proposes a decomposition method for a multi-controlled quantum phase shift gate, the method comprising: decomposing the multi-controlled quantum phase shift gate C^{n-1}PS(θ) into n-1 blocks of quantum circuits, the n-1 blocks of quantum circuits are connected end to end from left to right, the n is the total number of quantum bits of the multi-controlled quantum phase shift gate, the n≥3; configuring 2 in the xth block of quantum circuit x-1 A controlled quantum gate is configured, wherein the control bit of the controlled quantum gate is arranged at the xth quantum bit, and the target bit is arranged at the nth quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value of x ranges from 1 to n-1; 2 are configured in the xth quantum circuit. x-1 CNOT gates, wherein the first block of quantum circuits is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; wherein the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

[0007] According to the method described above, the first 2 x-2 The control bits of the CNOT gates are arranged between the x-1th quantum bit and the 1st quantum bit.

[0008] According to the method described above, when n is less than or equal to 5, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-1th qubit, until the 2 x-2 The CNOT gates are arranged.

[0009] According to the method described above, when n is equal to 6, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-2th qubit, until the 2 x-2The CNOT gates are arranged.

[0010] According to the method described above, the phase shift angle of the controlled quantum gate is related to the number of quantum bits n and the phase shift angle θ in the multi-controlled quantum phase shift gate C^{n-1}PS(θ).

[0011] According to the method described above, the phase shift angle of the controlled quantum gate is θ / 2 n-2 .

[0012] According to another aspect of the present application, a decomposition device of a multi-controlled quantum phase shift gate is proposed, comprising: a decomposition module, used to decompose the multi-controlled quantum phase shift gate C^{n-1}PS(θ) into n-1 blocks of quantum circuits, wherein the n-1 blocks of quantum circuits are connected end to end from left to right, wherein n is the total number of quantum bits of the multi-controlled quantum phase shift gate, wherein n≥3; a first configuration module, used to configure 2 in the xth block of quantum circuits x-1 a controlled quantum gate, wherein the control bit of the controlled quantum gate is arranged at the xth quantum bit, and the target bit is arranged at the nth quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value range of x is 1 to n-1; a second configuration module is used to configure 2 in the xth quantum circuit x-1 CNOT gates, wherein the first block of quantum circuits is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; wherein the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

[0013] According to another aspect of the present application, a computing device is provided, comprising: a processor; and a memory storing a computer program, wherein when the computer program is executed by the processor, the decomposition method for a multi-controlled quantum phase-shift gate as described above is implemented.

[0014] According to another aspect of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are executed by a processor, the decomposition method for a multi-controlled quantum phase-shift gate as described above is implemented.

[0015] Through the above decomposition method, the present application realizes modular decomposition of multi-controlled quantum phase-shift gates. This decomposition method not only ensures the accuracy of decomposition, but also simplifies the structure of the quantum circuit after decomposition, that is, reduces the number of quantum gates and circuit depth, improves the efficiency of quantum circuits, optimizes the feasibility of operations, and provides significant performance advantages, especially in complex quantum computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Below, the preferred embodiments of the present application will be further described in detail with reference to the accompanying drawings, wherein: Figure 1 It is a flow chart of a multi-controlled quantum phase-shift gate decomposition method according to an embodiment of the present application.

[0017] Figure 2 This is a decomposed quantum circuit diagram of a dual-controlled quantum phase-shift gate according to an embodiment of the present application.

[0018] Figure 3 This is a decomposed quantum circuit diagram of a three-controlled quantum phase-shift gate according to an embodiment of the present application.

[0019] Figure 4 This is a decomposed quantum circuit diagram of a four-controlled quantum phase-shift gate according to an embodiment of the present application.

[0020] Figure 5 This is a decomposed quantum circuit diagram of a five-controlled quantum phase-shift gate according to an embodiment of the present application.

[0021] Figure 6 The invention relates to a decomposition device of a multi-controlled quantum phase-shift gate according to an embodiment of the present application.

[0022] Figure 7 It is a structural principle block diagram of a computing device according to an embodiment of the present application. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0024] In the following detailed description, reference may be made to the various specification drawings that are part of the present application and are used to illustrate specific embodiments of the present application. In the accompanying drawings, similar reference numerals describe substantially similar components in different figures. The various specific embodiments of the present application are described below in sufficient detail so that a person of ordinary skill in the art with relevant knowledge and skills in the art can implement the technical solutions of the present application. It should be understood that other embodiments may also be used or structural, logical or electrical changes may be made to the embodiments of the present application.

[0025] The multi-controlled quantum phase shift gate (Multi-controlled Quantum PhaseShift gate, abbreviated as C^{n-1}PS) of the present application is a very common and important n-qubit gate in the implementation of quantum algorithms. It can be written as C^{n-1}PS(theta), that is, when the current n-1 control qubits are all 1, the PS(theta) gate is executed on the last target qubit, where n is the total number of qubits acted on by the multi-controlled quantum phase shift gate. For example, when n=1, it is recorded as PS(theta), which acts on a single qubit; when n=2, it is recorded as CPS(theta), which acts on a double qubit; when n=3, it is recorded as C^{2}PS(theta), which acts on a triple qubit. Where PS(theta)=diag[1,e^{i theta}], where i is an imaginary unit, theta is the parameter required to be input to the PS gate, and diag represents a diagonal matrix.

[0026] The multi-controlled quantum gate of the present application is a multi-controlled quantum phase-shift gate. Compared with other multi-controlled quantum gates, the multi-controlled quantum phase-shift gate has the following characteristics: Simplification of power operations: For general multi-controlled quantum gates, it is often difficult to calculate the analytical power operations, especially when the power is high. For example, finding the square root or high-order power of a matrix may require complex operations. However, for multi-controlled quantum phase-shift gates, due to their special diagonal matrix form, the gate operation parameters can be quickly determined through the decomposition rules of power exponents (such as the power exponential addition rule). This feature gives multi-controlled quantum phase-shift gates unique advantages in power operation scenarios; Simple structure of diagonal matrix: The multi-controlled quantum phase-shift gate is represented in the form of a diagonal matrix, and its matrix has non-zero values ​​only on the diagonal. This structure greatly simplifies the computational complexity and avoids the additional interference caused by non-diagonal elements. The characteristics of the diagonal matrix enable the multi-controlled quantum phase-shift gate to better meet the implementation requirements in the noisy intermediate-scale quantum (NISQ) computing environment; Simplification and availability of parameters: The key feature of the multi-controlled quantum phase-shift gate is the analyzability of its parameters. When the phase-shift parameters of the CPS gate (such as θ\thetaθ) are known, the corresponding gate matrix can be directly calculated through simple mathematical relationships. Compared with other multi-controlled quantum gates that require complex matrix operations, the parameter acquisition of the multi-controlled quantum phase-shift gate is more intuitive and efficient.

[0027] Figure 1 FIG. 1 is a flow chart of a multi-controlled quantum phase-shift gate decomposition method according to an embodiment of the present application. Figure 1 As shown, the method includes: Step S110, decomposing the multi-controlled quantum phase-shift gate C^{n-1}PS(θ) into n-1 quantum circuits, wherein the n-1 quantum circuits are connected end to end from left to right, wherein n is the total number of quantum bits acted on by the multi-controlled quantum phase-shift gate, and n≥3; Step S120, configuring 2 in the xth quantum circuit x-1 a controlled quantum gate, wherein the control bit of the controlled quantum gate is arranged at the x-th quantum bit, and the target bit is arranged at the n-th quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value of x ranges from 1 to n-1; Step S130, configuring 2 in the xth quantum circuit x-1 CNOT gates, wherein the first quantum circuit is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; Among them, the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

[0028] As can be seen from the above, each quantum circuit of the present application is composed of a controlled quantum phase shift gate and / or a CNOT gate. Multiple quantum circuits are connected and executed from left to right in the order from 1 to x. The quantum bits in the quantum circuit are arranged in quantum bits from 1 to n from top to bottom, and the quantum bits increase gradually from low bits to high bits from top to bottom.

[0029] The control bit and target bit of the quantum gate are important components for implementing specific quantum operations. They determine how the quantum gate responds and which quantum bits it acts on. The control bit is the quantum bit used to activate the action of the quantum gate. When the control bit is in a specific state (usually |1>), the operation of the quantum gate will act on the target bit. If the control bit is in |0>, the operation of the quantum gate will not be activated and the target bit will remain unchanged. The target bit is the quantum bit acted on by the quantum gate, and its state will change according to the function of the quantum gate and the state of the control bit.

[0030] Through the above decomposition method, the present application realizes modular decomposition of multi-controlled quantum phase-shift gates. This decomposition method not only ensures the accuracy of decomposition, but also simplifies the structure of the quantum circuit after decomposition, that is, reduces the number of quantum gates and circuit depth, improves the efficiency of quantum circuits, optimizes the feasibility of operations, and provides significant performance advantages, especially in complex quantum computing.

[0031] According to one embodiment of the present application, the first 2 x-2 The control bits of the CNOT gates are arranged between the x-1th qubit and the 1st qubit. In the xth quantum circuit, the first 2 x-2 The control bits of each CNOT gate are between the 1st to x-1th qubits, and are arranged in order from high-order bits to low-order bits and then to high-order bits, ensuring that the interoperation between qubits can be implemented accurately.

[0032] Furthermore, when n is less than or equal to 5, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-1th qubit, until the 2 x-2 The CNOT gates are arranged.

[0033] When n is equal to 6, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-2th qubit, until the 2 x-2 The CNOT gates are arranged.

[0034] In the above decomposition scheme, for different numbers of multi-controlled quantum phase-shift gates, a clear allocation rule for the control gates and target bits of the CNOT gate is proposed, which can minimize the circuit depth and the number of gates. Whether n≤5 or n=6, the core logic of the multi-controlled quantum phase-shift gate decomposition can be implemented in a simple way.

[0035] According to one embodiment of the present application, the phase shift angle of the controlled quantum gate is related to the number of quantum bits n and the phase shift angle θ in the multi-controlled quantum phase shift gate C^{n-1}PS(θ). Further, the phase shift angle of the controlled quantum gate is θ / 2 n-2 . In the controlled quantum phase shift gate and its conjugate transposition in the controlled quantum gate, θ / 2 is applied n-2 The phase shift angle is adjusted to ensure the overall correct operation of the line.

[0036] The above describes the implementation method and advantages of the embodiments of the present application through multiple embodiments. This application describes the specific processing process of the embodiments of the present application in detail with specific examples. Generally speaking, when considering quantum gate decomposition, it is necessary to decompose complex quantum gates into single-qubit gates or double-qubit gates. Therefore, quantum gates with more than 3 bits, i.e., n≥3, are usually decomposed to simplify operations and improve computing efficiency.

[0037] Figure 2 1 is a decomposed quantum circuit diagram of a dual-controlled quantum phase-shift gate according to an embodiment of the present application. Figure 2 As shown, according to Figure 1 The decomposition method decomposes the double-controlled quantum phase-shift gate C^{2}U (n=3) into the quantum circuit diagram on the right side of the figure. Figure 2 The quantum circuit diagram on the right includes two quantum circuits, namely the first quantum circuit and the second quantum circuit. The first quantum circuit diagram includes a controlled quantum gate, the control bit of which is arranged on the first quantum bit, and the target bit is arranged on the third quantum bit. The controlled quantum gate is a controlled quantum phase shift gate V. When the double-controlled quantum phase shift gate U = PS(θ), the controlled quantum phase shift gate V = PS(θ / 2).

[0038] The second quantum circuit diagram includes two controlled quantum gates. The control bit of the controlled quantum gate is arranged on the second quantum bit, and the target bit is arranged on the third quantum bit. The two controlled quantum gates are the controlled quantum phase shift gate V and the conjugate transposition of the controlled quantum phase shift gate V. † , the controlled quantum phase-shift gate V and its conjugate transpose V † When the double-controlled quantum phase-shift gate U = PS(θ), the controlled quantum gate V and its conjugate transposition V † =PS(θ / 2).

[0039] The second quantum circuit diagram includes two CNOT gates. The CNOT gates and the controlled quantum gates are arranged alternately. The control bits of the two CNOT gates are both arranged on the first quantum bit, and the target bits are both arranged on the second quantum bit.

[0040] Figure 31 is a decomposed quantum circuit diagram of a three-control quantum phase-shift gate according to an embodiment of the present application. Figure 3 As shown, according to Figure 1 The decomposition method decomposes the three-controlled quantum phase-shift gate C^{3}W (n=4) into the quantum circuit diagram on the right side of the figure. The quantum circuit diagram on the right side of the figure includes three quantum circuits, namely the first quantum circuit, the second quantum circuit and the third quantum circuit. The structural arrangement in the first and second quantum circuits is similar to Figure 2 When the three-controlled quantum phase-shift gate W = PS(θ), the controlled quantum gates (K or K) in the first and second quantum circuits are † )=PS(θ / 4).

[0041] The third quantum circuit diagram includes four controlled quantum gates, the control bit of which is arranged on the third quantum bit, and the target bit is arranged on the fourth quantum bit. The four controlled quantum gates include two controlled quantum phase shift gates K and two conjugate transpositions of the controlled quantum phase shift gates K. † , the controlled quantum phase-shift gate K and its conjugate transpose K † When the three-controlled quantum phase-shift gate W = PS(θ), the controlled quantum gate (K or K † )=PS(θ / 4).

[0042] The third quantum circuit diagram includes four CNOT gates, which are arranged alternately with the controlled quantum gates. The arrangement of the first two CNOT gates is the same as that of the last two CNOT gates. The control bits of the first two CNOT gates are arranged on the second quantum bit and the first quantum bit from left to right, respectively, and the target bits are all arranged on the third quantum bit.

[0043] Figure 4 1 is a decomposed quantum circuit diagram of a four-control quantum phase-shift gate according to an embodiment of the present application. Figure 4 As shown, according to Figure 1 The decomposition method decomposes the four-controlled quantum phase-shift gate C^{4}A (n=5) into the quantum circuit diagram on the right side of the figure. The quantum circuit diagram on the right side of the figure includes four quantum circuits, namely the first quantum circuit, the second quantum circuit, the third quantum circuit and the fourth quantum circuit. The structural arrangement in the first, second and third quantum circuits is similar to Figure 3 When the four-controlled quantum phase-shift gate A = PS(θ), the controlled quantum gates (B or B) in the first, second, and third quantum circuits are † )=PS(θ / 8).

[0044] The fourth quantum circuit diagram includes 8 controlled quantum gates. The control bit of the controlled quantum gate is arranged on the 4th quantum bit, and the target bit is arranged on the 5th quantum bit. The 8 controlled quantum gates include 4 controlled quantum phase shift gates B and 4 conjugate transpositions of the controlled quantum phase shift gates B. † , controlled quantum phase-shift gate B and its conjugate transpose B † When the four-controlled quantum phase-shift gate A = PS(θ), the controlled quantum gate (B or B † )=PS(θ / 8).

[0045] The fourth quantum circuit diagram includes 8 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately. Among them, the arrangement of the first 4 CNOT gates is the same as that of the last 4 CNOT gates. The control bits of the first 4 CNOT gates are arranged in order from high bit to low bit and then to high bit from left to right, that is, from left to right, they are arranged on the 3rd quantum bit, the 2nd quantum bit, the 1st quantum bit, and the 2nd quantum bit, and the target bits are all arranged on the 4th quantum bit.

[0046] Figure 5 1 is a decomposed quantum circuit diagram of a five-control quantum phase-shift gate according to an embodiment of the present application. Figure 5 As shown, according to Figure 1 The decomposition method decomposes the four-controlled quantum phase-shift gate C^{5}D (n=6) into the quantum circuit diagram on the right side of the figure. The quantum circuit diagram on the right side of the figure includes 5 quantum circuits, namely the first quantum circuit, the second quantum circuit, the third quantum circuit, the fourth quantum circuit and the fifth quantum circuit. The structural arrangement in the first, second, third and fourth quantum circuits is similar to Figure 4 When the five-controlled quantum phase-shift gate D = PS(θ), the controlled quantum gates (E or E † )=PS(θ / 16).

[0047] The fifth quantum circuit diagram includes 16 controlled quantum gates. The control bit of the controlled quantum gate is arranged on the fifth quantum bit, and the target bit is arranged on the sixth quantum bit. The 16 controlled quantum gates include 8 controlled quantum phase shift gates E and 8 conjugate transpositions of controlled quantum phase shift gates E. † , the controlled quantum phase-shift gate E and its conjugate transpose E † When the five-controlled quantum phase-shift gate D = PS(θ), the controlled quantum gate (E or E † )=PS(θ / 16).

[0048] The fifth block of quantum circuit diagram includes 16 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately. Among them, the arrangement of the first 8 CNOT gates is the same as that of the last 8 CNOT gates. The control bits of the first 8 CNOT gates are arranged from left to right from high bits to low bits and then to high bits. At the same time, its specific arrangement is slightly different from the fourth block. The control bits of the first 8 CNOT gates are arranged from left to right on the 4th quantum bit, the 3rd quantum bit, the 2nd quantum bit, the 1st quantum bit, the 2nd quantum bit, the 3rd quantum bit, the 2nd quantum bit, and the 1st quantum bit, and the target bits are all arranged on the 5th quantum bit.

[0049] refer to Figure 4 and Figure 5 As shown, by executing the quantum gates on the right side of the equal sign in sequence, the quantum gate on the left side of the equal sign can be realized. Compared with the conventional decomposition algorithm, this algorithm can greatly reduce resource consumption. Specifically, when decomposing four-controlled quantum phase-shift gates, the conventional algorithm requires 213 quantum gates and a circuit depth of 149, while only 29 two-qubit gates need to be executed at this time, and the circuit depth is only 29. When decomposing five-controlled quantum phase-shift gates, the conventional algorithm requires 1429 quantum gates and a circuit depth of 959, while only 61 two-qubit gates need to be executed at this time, and the circuit depth is only 61. This decomposition method not only ensures the correctness of the decomposition, but also because of its simplicity and low circuit depth, it is easier to implement in physical experiments, making it easier to execute quantum algorithms on NISQ computers, thereby helping to promote the practical application and optimization of quantum computing.

[0050] In order to verify the correctness of the technical solution of this application, this application uses the quantum computing software MindQuantum to simulate the solution of the technology of this application when n-1=4 and 5. It is found that the simulation results are completely consistent with the theoretical results, which further proves the feasibility and effectiveness of the technical solution of this application. In addition, this solution highlights the importance of quantum gate decomposition and provides valuable inspiration for further exploring the use of quantum gate decomposition to realize various quantum algorithms.

[0051] Figure 6 The decomposition device 100 of a multi-controlled quantum phase-shift gate according to an embodiment of the present application includes: Decomposition module 110, used for decomposing the multi-controlled quantum phase shift gate C^{n-1}PS(θ) into n-1 blocks of quantum circuits, wherein the n-1 blocks of quantum circuits are connected end to end from left to right, wherein n is the total number of quantum bits acted by the multi-controlled quantum phase shift gate, and n≥3; The first configuration module 120 is used to configure 2 in the x-th quantum circuit. x-1a controlled quantum gate, wherein the control bit of the controlled quantum gate is arranged at the x-th quantum bit, and the target bit is arranged at the n-th quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value of x ranges from 1 to n-1; The second configuration module 130 is used to configure 2 in the x-th quantum circuit. x-1 CNOT gates, wherein the first quantum circuit is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; Among them, the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

[0052] In another aspect, the present application also provides a computing device, see Figure 7 , Figure 7 1 is a block diagram of the structural principle of a computing device according to an embodiment of the present application. Figure 7 As shown, the computing device includes a processor 601 and a memory 602 storing computer program instructions; when the processor 601 executes the computer program instructions, the decomposition method for a multi-controlled quantum phase-shift gate in the above-mentioned embodiment is implemented.

[0053] Specifically, the processor 601 may include a central processing unit (CPU) or a graphics processing unit (GPU), or an application specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application. The memory 602 may include a memory for data or instructions. For example, the memory 602 may be at least one of the following: a hard disk drive (HDD), a read-only memory (ROM), a random access memory (RAM), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a tape, a universal serial bus (USB) drive, or other physical / tangible memory storage device. For another example, the memory 602 includes a removable or non-removable (or fixed) medium. For another example, the memory 602 may be inside or outside the integrated gateway disaster recovery device. The memory 602 may be a non-volatile solid-state memory. In other words, typically the memory 602 includes a tangible (non-transitory) computer-readable storage medium (such as a memory device) encoded with executable instructions, wherein when the stored executable instructions are executed by the processor 601 (such as executed by one or more processors), the decomposition method for a multi-controlled quantum phase-shift gate in an embodiment of the present application can be implemented.

[0054] In one example, Figure 7 The electronic device shown may also include a communication interface 603 and a bus 610. The processor 601, the memory 602, and the communication interface 603 are connected and communicate with each other via the bus 610. The communication interface 603 is mainly used to implement communication between modules, devices, units, and / or devices in the electronic device.

[0055] The bus 610 includes hardware, software or both, and can couple the components of the online data traffic billing device to each other. For example, the bus may include at least one of the following: an accelerated graphics port (AGP) or other graphics bus, an enhanced industrial standard architecture (EISA) bus, a front-side bus (FSB), a hypertransport (HT) interconnect, an industrial standard architecture (ISA) bus, an infinite bandwidth interconnect, a low pin count (LPC) bus, a memory bus, a microchannel architecture (MCA) bus, a peripheral component interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a serial advanced technology attachment (SATA) bus, a video electronics standard association local (VLB) bus or other suitable bus. The bus 610 may include one or more buses. Although the embodiments of the present application describe or show a specific bus, the embodiments of the present application may consider any suitable bus or interconnection method.

[0056] On the other hand, an embodiment of the present application further provides a computer-readable storage medium having computer program instructions stored thereon, and when the computer program instructions are executed by a processor, the aforementioned decomposition method for a multi-controlled quantum phase-shift gate is implemented.

[0057] The above exemplarily describes the flowchart and / or block diagram of the method and system of the embodiment of the present application, and describes the relevant various aspects. It should be understood that each box or combination thereof in the flowchart and / or block diagram can be implemented by computer program instructions, or can be implemented by special hardware that performs a specified function or action, or can be implemented by a combination of special hardware and computer instructions. For example, these computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to form a machine that enables these instructions executed by such a processor to enable the implementation of the functions / actions specified in each box or combination thereof in the flowchart and / or block diagram. Such a processor can be a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit.

[0058] The functional blocks shown in the structural block diagram of the embodiment of the present application can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc.; when implemented in software, it is a program or code segment used to perform the required task. The program or code segment can be stored in a memory, or transmitted on a transmission medium or a communication link via a data signal carried in a carrier. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0059] The above embodiments are only used to illustrate the present application, and are not intended to limit the present application. Ordinary technicians in the relevant technical field may make various changes and modifications without departing from the scope of the present application. Therefore, all equivalent technical solutions should also fall within the scope disclosed in the present application.

Claims

1. A decomposition method for a multi-controlled quantum phase-shift gate, characterized in that: The method comprises: Decompose the multi-controlled quantum phase-shift gate C^{n-1}PS(θ) into n-1 quantum circuits, wherein the n-1 quantum circuits are connected end to end from left to right, wherein n is the total number of quantum bits acted by the multi-controlled quantum phase-shift gate, and n≥3; Configure 2 in the xth quantum circuit x-1 a controlled quantum gate, wherein the control bit of the controlled quantum gate is arranged at the x-th quantum bit, and the target bit is arranged at the n-th quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value of x ranges from 1 to n-1; Configure 2 in the xth quantum circuit x-1 CNOT gates, wherein the first quantum circuit is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; Among them, the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

2. The method according to claim 1, characterized in that The first 2 in the xth quantum circuit x-2 The control bits of the CNOT gates are arranged between the x-1th quantum bit and the 1st quantum bit.

3. The method according to claim 1, characterized in that: When n is less than or equal to 5, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-1th qubit, until the 2 x-2 The CNOT gates are arranged.

4. The method according to claim 1, characterized in that When n is equal to 6, the first 2 x-2 The target bit of the CNOT gate is placed at the xth qubit, and the control bit starts from the x-1th qubit, decreases from left to right to the 1st qubit, and then gradually increases to the x-2th qubit, until the 2 x-2 The CNOT gates are arranged.

5. The method according to claim 1, characterized in that The phase shift angle of the controlled quantum gate is related to the number of quantum bits n and the phase shift angle θ in the multi-controlled quantum phase shift gate C^{n-1}PS(θ).

6. The method according to claim 1, characterized in that The phase shift angle of the controlled quantum gate is θ / 2 n-2 .

7. A decomposition device for a multi-controlled quantum phase-shift gate, characterized in that: include: A decomposition module is used to decompose the multi-controlled quantum phase shift gate C^{n-1}PS(θ) into n-1 quantum circuits, wherein the n-1 quantum circuits are connected end to end from left to right, wherein n is the total number of quantum bits acted by the multi-controlled quantum phase shift gate, and n≥3; The first configuration module is used to configure 2 in the x-th quantum circuit. x-1 a controlled quantum gate, wherein the control bit of the controlled quantum gate is arranged at the x-th quantum bit, and the target bit is arranged at the n-th quantum bit, wherein the controlled quantum phase shift gate and the conjugate transposition of the controlled quantum phase shift gate in the controlled quantum gate are arranged alternately, and the value of x ranges from 1 to n-1; The second configuration module is used to configure 2 in the xth quantum circuit. x-1 CNOT gates, wherein the first quantum circuit is configured with 0 CNOT gates, and the CNOT gates and the controlled quantum gates are arranged alternately; Among them, the first 2 x-2 CNOT gate and 2 x-2 The CNOT gates are arranged in the same way. The first 2 x-2 The target bit of a CNOT gate is arranged at the xth qubit, and the qubits where the control bits are located are arranged from left to right in the order from high-order bits to low-order bits and then to high-order bits.

8. A computing device, characterized in that include: processor; A memory storing a computer program, which, when executed by a processor, implements the decomposition method for a multi-controlled quantum phase-shift gate according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and when the computer instructions are executed by a processor, the decomposition method for a multi-controlled quantum phase-shift gate described in any one of claims 1 to 6 is implemented.

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