Parameterized quantum circuit construction method and device, storage medium and computer equipment

Abstract

The parameterized quantum circuit construction method, device, storage medium and computer device provided by the application utilize unitary matrix linear combination to reduce the depth and required quantum bit number of a variational circuit, thereby effectively constructing an arbitrary target quantum state, reducing the amount of training parameters, and optimizing the efficiency and accuracy of the variational quantum algorithm and improving the practicability of the algorithm under limited quantum resources; and the application is particularly suitable for a noisy intermediate-scale quantum (NISQ) device, and by proposing a circuit design with low depth and quantum bit number, the problem that the application of the prior art on the NISQ device is limited can be solved, for example, the application can efficiently solve VQA problems such as quantum state learning and Hamiltonian ground state solving on a quantum device, thereby opening up a new way for practical applications in the field of quantum chemistry.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and in particular to a method, apparatus, storage medium and computer device for constructing parameterized quantum circuits. Background Technology

[0002] With the advent of the era of big data and AI, the ever-increasing demand for classical computing resources poses an insurmountable challenge to existing computing frameworks. In researching problems in disciplines such as physics and chemistry, the required computing resources typically grow exponentially with the size of the problem. Even using the most advanced algorithms and supercomputers, it remains difficult to solve such problems. The extremely high computational cost required to simulate large-scale quantum systems or solve large-scale linear algebra problems has become a bottleneck for classical computers. Quantum computing, based on the principles of quantum mechanics, possesses the potential to accelerate computation compared to classical computing frameworks, offering a promising solution to overcome the limitations of classical computing.

[0003] Currently, noisy intermediate-scale quantum (NISQ) devices are considered to have enormous application potential. Variational quantum algorithms (VQA) using a classical-quantum hybrid approach on such devices open new avenues for solving the aforementioned challenges. VQA refers to a class of algorithms that construct parameterized quantum circuits (PQCs) on quantum devices and utilize classical computers to optimize the parameters of these circuits, thereby performing tasks such as optimization or machine learning. For example, in physics and chemistry, variational quantum eigenvalue solvers (VQEs) are used to calculate the ground-state energies of molecules, thereby studying their physicochemical properties; similarly, in applied mathematics and theoretical computer science, quantum approximate optimization algorithms (QAOA) are used to find optimal objects in finite sets.

[0004] The specific structure of the PQC has a decisive impact on the performance of VQA: from the problem-solving perspective, the PQC affects both the convergence speed and the accuracy of the output; from the perspective of quantum hardware execution, deeper circuits are more susceptible to errors caused by NISQ device noise, and too many parameters are difficult to optimize; some PQCs are also very expensive to construct. Given the characteristics of data generated by real physical systems, even relatively simple models can yield satisfactory results. Furthermore, in large-scale cases, deeper PQCs can lead to the Barren Plateau (BP) problem, where the stochastic initialization of the PQC results in exponentially small gradients in the loss function on large-scale problems, drastically reducing the efficiency of gradient estimation and making gradient descent algorithms difficult to implement.

[0005] Therefore, designing a PQC with fewer parameters, shallower circuitry, and lower construction costs, yet capable of effectively performing common tasks at present, is of great significance for improving the accuracy and efficiency of VQA and for further exploring related issues in various fields. Summary of the Invention

[0006] The purpose of this application is to at least solve one of the aforementioned technical defects, particularly the technical defects in the prior art where PQC has many parameters, deep circuits, and high construction costs, which leads to low accuracy and efficiency of VQA.

[0007] This application provides a method for constructing parameterized quantum circuits, the method comprising:

[0008] Determine a blank parameterized quantum circuit for 3N qubits, and determine a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate;

[0009] After applying the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit, the first quantum circuit is obtained;

[0010] After applying at least one of the parameterized multi-qubit controlled gates to the first quantum circuit, a second quantum circuit is obtained, wherein the first N qubits of the first quantum circuit are control circuits and the last 2N qubits are controlled circuits.

[0011] After applying the second parameterized circuit template to the first N qubits of the second quantum circuit, the initial quantum circuit is obtained;

[0012] After running the initial quantum circuit, the running results are obtained. The initial quantum circuit is then optimized based on the running results until a preset optimization target is reached, thus obtaining the target quantum circuit.

[0013] Optionally, after running the initial quantum circuit and obtaining the running result, the initial quantum circuit is optimized based on the running result until a preset optimization target is reached, thereby obtaining the target quantum circuit, including:

[0014] After running the initial quantum circuit, calculate the loss function value of the initial quantum circuit;

[0015] The loss function value is compared with a preset function threshold;

[0016] If the loss function value is less than the preset function threshold, then the initial quantum circuit is taken as the target quantum circuit;

[0017] If the loss function value is not less than the preset function threshold, the initial quantum circuit is further optimized until the preset optimization target is reached, thus obtaining the target quantum circuit.

[0018] Optionally, the adaptive index of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive index corresponds to an active state of a control bit;

[0019] The step of continuing to optimize the initial quantum circuit until a preset optimization target is reached, thereby obtaining the target quantum circuit, includes:

[0020] The corresponding adaptive sequence number is determined based on the current iteration number, and the corresponding number of parameterized multi-qubit controlled gates is determined based on the adaptive sequence number.

[0021] After replacing the blank parameterized quantum circuit with the initial quantum circuit, the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate are updated using a preset iterative algorithm. Then, the first parameterized circuit template is applied to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps. This process continues until the number of the adaptive sequence number reaches a preset sequence number threshold, thus obtaining the target quantum circuit.

[0022] Optionally, the first parameterized circuit template and the second parameterized circuit template are any one of the following: direct product parameterized circuit template, alternating layered circuit template, and hardware high-efficiency circuit template.

[0023] Optionally, the second parameterized circuit template is the conjugate transpose of the first parameterized circuit template.

[0024] This application also provides a parameterized quantum circuit construction apparatus, comprising:

[0025] The circuit determination module is used to determine the blank parameterized quantum circuit of 3N qubits, and to determine the first parameterized circuit template, the second parameterized circuit template, and at least one parameterized multi-qubit controlled gate;

[0026] The first action module is used to apply the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit.

[0027] The second action module is used to apply at least one of the parameterized multi-qubit controlled gates to the first quantum circuit to obtain a second quantum circuit, wherein the first N qubits in the first quantum circuit are control circuits and the last 2N qubits are controlled circuits.

[0028] The third action module is used to apply the second parameterized circuit template to the first N qubits of the second quantum circuit to obtain the initial quantum circuit.

[0029] The circuit optimization module is used to run the initial quantum circuit and obtain the running results, and optimize the initial quantum circuit according to the running results until a preset optimization target is reached to obtain the target quantum circuit.

[0030] Optionally, the circuit optimization module includes:

[0031] The loss function calculation module is used to calculate the loss function value of the initial quantum circuit after running the initial quantum circuit.

[0032] The function value comparison module is used to compare the loss function value with a preset function threshold;

[0033] A quantum circuit determination module is used to identify the initial quantum circuit as the target quantum circuit if the loss function value is less than the preset function threshold.

[0034] An iterative optimization module is used to continue optimizing the initial quantum circuit if the loss function value is not less than the preset function threshold, until the preset optimization target is reached, thereby obtaining the target quantum circuit.

[0035] Optionally, the adaptive index of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive index corresponds to an active state of a control bit;

[0036] The iterative optimization module includes:

[0037] An adaptive sequence number update module is used to determine the corresponding adaptive sequence number based on the current iteration number, and to determine the corresponding number of parameterized multi-qubit controlled gates based on the adaptive sequence number.

[0038] The parameter update module is used to replace the blank parameterized quantum circuit with the initial quantum circuit, update the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate using a preset iterative algorithm, and return to execute the first parameterized circuit template on the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps, until the number of the adaptive sequence number reaches a preset sequence number threshold to obtain the target quantum circuit.

[0039] This application also provides a computer-readable storage medium storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the parameterized quantum circuit construction method as described in any of the above embodiments.

[0040] This application also provides a computer device, including: one or more processors, and memory;

[0041] The memory stores computer-readable instructions, which, when executed by the one or more processors, perform the steps of the parameterized quantum circuit construction method as described in any of the above embodiments.

[0042] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0043] The parameterized quantum circuit construction method, apparatus, storage medium, and computer device provided in this application, after determining a blank parameterized quantum circuit of 3N qubits, and determining a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate, can apply the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit to obtain a first quantum circuit; then, after applying at least one of the parameterized multi-qubit controlled gates to the first quantum circuit, a second quantum circuit is obtained, wherein the first N qubits of the first quantum circuit are control circuits, and the last 2N qubits are controlled circuits, thus forming a unitary matrix linear combination, abbreviated as LCU (Linear Combination of Unitaries) architecture; next, after applying the second parameterized circuit template to the first N qubits of the second quantum circuit, an initial quantum circuit is obtained, and the initial quantum circuit is run to obtain the running result. Finally, the initial quantum circuit is optimized based on the running result until a preset optimization target is reached, thereby obtaining the target quantum circuit. This application utilizes linear combination of unitary matrices to reduce the depth of variational circuits and the number of required qubits, thereby effectively constructing arbitrary target quantum states, reducing the number of training parameters, and optimizing the efficiency and accuracy of variational quantum algorithms, improving the practicality of the algorithms under limited quantum resources. Furthermore, this application is particularly applicable to noisy medium-scale quantum (NISQ) devices. By proposing a circuit design with both low depth and low number of qubits, it can solve the problem of limited application of existing technologies on NISQ devices. For example, this application can efficiently solve VQA problems such as quantum state learning and Hamiltonian ground state solving on quantum devices, thus opening up new avenues for practical applications in fields such as quantum chemistry. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart illustrating a parameterized quantum circuit construction method provided in this application embodiment;

[0046] Figure 2 A schematic diagram of the iterative optimization process for parameterized quantum circuits provided in the embodiments of this application;

[0047] Figure 3 This is a schematic diagram of the structure of the parameterized quantum circuit provided in the embodiments of this application;

[0048] Figure 4 A schematic diagram of a three-qubit PQC for learning Bell states constructed according to the construction method of this application, provided for an embodiment of this application;

[0049] Figure 5 A comparison diagram of the learning gap between a universal two-qubit PQC and the PQC designed in this application for learning a target quantum state, taking a Bell state as an example, is provided for embodiments of this application.

[0050] Figure 6 A schematic diagram of a 6-qubit PQC constructed according to this application for solving the ground state energy of a 4-qubit Ising model, provided as an embodiment of this application;

[0051] Figure 7 A schematic diagram of the structure of a single-layer linear entangled circuit provided in an embodiment of this application;

[0052] Figure 8 A schematic diagram of a single-layer strongly entangled circuit for qubits provided in an embodiment of this application;

[0053] Figure 9 A comparison diagram of convergence of three PQC solutions for Hamiltonian ground state energy provided in the embodiments of this application;

[0054] Figure 10 This is a schematic diagram of a parameterized quantum circuit construction device provided in an embodiment of this application;

[0055] Figure 11 This is a schematic diagram of the internal structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0056] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0057] In one embodiment, such as Figure 1 As shown, Figure 1 This is a flowchart illustrating a parameterized quantum circuit construction method provided in an embodiment of this application; this application provides a parameterized quantum circuit construction method, which may include:

[0058] S110: Determine the blank parameterized quantum circuit for 3N qubits, and determine the first parameterized circuit template, the second parameterized circuit template, and at least one parameterized multi-qubit controlled gate.

[0059] In this step, when constructing a parameterized quantum circuit, a blank parameterized quantum circuit with 3N qubits can be determined first, and then a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate can be determined. In this way, the first parameterized circuit template, the second parameterized circuit template, and at least one parameterized multi-qubit controlled gate can be applied to the blank parameterized quantum circuit in sequence to realize a linear combination of any target quantum state.

[0060] Understandably, in quantum computing, quantum circuits consist of a series of quantum gate operations used to manipulate qubits to achieve specific computational tasks. A parameterized circuit template is a template for constructing quantum circuits in a parameterized manner. Parameterization means that the quantum gate operations in the circuit are controlled by parameters that can take values ​​within a certain range. By changing these parameters, the function and output of the quantum circuit can be adjusted.

[0061] In this application, the first and second parameterized circuit templates can be any one of a direct product parameterized circuit template, an alternating layered circuit template, and a hardware-efficient circuit template. For the direct product parameterized circuit template, parameterization allows for the flexible construction of various quantum circuits. For example, in quantum machine learning applications, by adjusting parameters, quantum circuits can be adapted to different data and computational tasks; when simulating the quantum states of molecules, adjusting parameters allows the circuit to better match the Hamiltonian structure of the molecule, thereby more accurately simulating properties such as energy levels; in quantum image classification tasks, the direct product parameterized circuit template can adjust parameters according to the characteristics of the image data to achieve classification of different image categories. Choosing an alternating layered circuit template or a hardware-efficient circuit template allows the parameterized quantum circuits to adapt to a variety of different application scenarios.

[0062] Furthermore, the second parameterized circuit template of this application can be the conjugate transpose of the first parameterized circuit template, which can reduce the number of trainable parameters of the circuit. The controlled gates of this application involve control qubits and target qubits. Multi-qubit controlled gates are quantum gates that perform control operations between multiple qubits. Parameterized multi-qubit controlled gates introduce parameterization characteristics into multi-qubit controlled gates. This means that this application can not only determine the operation of the target qubit based on the state of the control qubit, but also finely adjust this operation through parameters.

[0063] For example, the parameterized multi-qubit controlled gate of this application can be expressed as: ,in For adaptive serial numbers, Serial Number This indicates the active state of the control bit. , This corresponds to the parameterized circuit template. The parameters in, where arrive Training parameters Initialize to the parameter values ​​from the previous optimization step, and Then, random initialization is performed within the feasible region. This application achieves this by... Continuous adjustments are made to optimize the constructed quantum circuit.

[0064] S120: After applying the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit, the first quantum circuit is obtained.

[0065] In this step, since the operation of quantum gates on different qubits or groups of qubits is like building a complex machine, each quantum gate is a component. Through reasonable combination and order, an algorithm that realizes the advantages of quantum computing can be constructed. Therefore, after determining the blank parameterized quantum circuit of 3N qubits and the first parameterized circuit template through S110, this application can apply the first parameterized circuit template on the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit.

[0066] For example, when a quantum gate acts on a single qubit, it is primarily used to change the quantum state of that qubit. For instance, a rotation gate can be used to rotate the state of a qubit on a Bloch sphere. When a quantum gate acts on a group of qubits, such as a controlled-NOT (CNOT) gate, it is used to create entanglement between the qubits. For two qubits, a CNOT gate uses the first qubit as the control qubit and the second qubit as the target qubit. When the control qubit is... At that time, the state of the target bit is flipped. This causes the two qubits to enter an entangled state, which is a key resource for quantum computing and quantum information processing, enabling quantum systems to exhibit correlation properties that surpass those of classical systems.

[0067] S130: After applying at least one parameterized multi-qubit controlled gate to the first quantum circuit, a second quantum circuit is obtained.

[0068] In this step, after applying the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit through S120 to obtain the first quantum circuit, this application can further apply at least one parameterized multi-qubit controlled gate to the first quantum circuit to obtain the second quantum circuit. In the first quantum circuit of this application, the first N qubits are the control circuit and the last 2N qubits are the controlled circuit.

[0069] Understandably, when constructing large-scale, complex quantum computing or quantum communication systems, the concepts of control bits and target bits can be extended to control circuits and controlled circuits. This hierarchical architecture helps to better organize and understand the implementation of algorithms. For example, in quantum simulation algorithms, control circuits can be used to selectively activate different controlled circuits according to the stage and requirements of the simulation to simulate different parts of the quantum system, just as conditional statements control the execution of different code blocks in classical computer programming. This makes the implementation of quantum algorithms more modular and easier to manage.

[0070] In this application, the first N qubits of the first quantum circuit are used as the control circuit, and the last 2N qubits are used as the controlled circuit. Since the parameterized multi-qubit controlled gate introduces parameterization characteristics into the multi-qubit controlled gate, this application can apply at least one parameterized multi-qubit controlled gate to the first quantum circuit to obtain the second quantum circuit. Subsequently, when iteratively optimizing the initial quantum circuit, the parameters in the parameterized multi-qubit controlled gate can be updated, and the updated parameterized multi-qubit controlled gate can be applied to the iterated first quantum circuit to optimize the initial quantum circuit and obtain the final target quantum circuit.

[0071] Furthermore, by applying at least one parameterized multi-qubit controlled gate to the first quantum circuit in this application, an LCU structure can be constructed. This application does not limit the form of the control circuit gate in the LCU structure. Other more general parameterized control circuit gates can be used to reduce the number of control bits, thereby optimizing the solution of larger-scale problems.

[0072] S140: After applying the second parameterized circuit template to the first N qubits of the second quantum circuit, the initial quantum circuit is obtained.

[0073] In this step, after obtaining the second quantum circuit by applying at least one parameterized multi-qubit controlled gate to the first quantum circuit through S130, this application can also apply a second parameterized circuit template to the first N qubits of the second quantum circuit to obtain an initial quantum circuit. Then, this application can optimize and iterate the initial quantum circuit to obtain the final target quantum circuit.

[0074] S150: After running the initial quantum circuit, the running results are obtained. The initial quantum circuit is optimized based on the running results until the preset optimization target is reached, and the target quantum circuit is obtained.

[0075] In this step, after applying the second parameterized circuit template to the first N qubits of the second quantum circuit through S140, an initial quantum circuit is obtained. Then, this application can run the initial quantum circuit to obtain the running result, and optimize the initial quantum circuit based on the running result until the second parameterized circuit template is applied to the first N qubits of the second quantum circuit to obtain the initial quantum circuit.

[0076] In the above embodiments, after determining a blank parameterized quantum circuit with 3N qubits, and determining a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate, the first parameterized circuit template can be applied to the first N qubits of the blank parameterized quantum circuit to obtain a first quantum circuit; then, at least one of the parameterized multi-qubit controlled gates is applied to the first quantum circuit to obtain a second quantum circuit, wherein the first N qubits of the first quantum circuit are control circuits, and the last 2N qubits are controlled circuits, thus forming an LCU architecture; next, the second parameterized circuit template is applied to the first N qubits of the second quantum circuit to obtain an initial quantum circuit, and the initial quantum circuit is run to obtain the running result. Finally, the initial quantum circuit is optimized based on the running result until a preset optimization target is reached, thereby obtaining the target quantum circuit. This application utilizes linear combination of unitary matrices (LCU) to reduce the depth of variational circuits and the number of qubits required, thereby effectively constructing arbitrary target quantum states, reducing the number of training parameters, and optimizing the efficiency and accuracy of variational quantum algorithms, improving the practicality of the algorithms under limited quantum resources. Furthermore, this application is particularly applicable to noisy medium-scale quantum (NISQ) devices. By proposing a circuit design with both low depth and low number of qubits, it can solve the problem of limited application of existing technologies on NISQ devices. For example, this application can efficiently solve VQA problems such as quantum state learning and Hamiltonian ground state solving on quantum devices, thus opening up new avenues for practical applications in fields such as quantum chemistry.

[0077] In one embodiment, after running the initial quantum circuit in S150 and obtaining the running result, the initial quantum circuit is optimized based on the running result until a preset optimization target is reached, thereby obtaining the target quantum circuit, which may include:

[0078] S151: After running the initial quantum circuit, calculate the loss function value of the initial quantum circuit.

[0079] S152: Compare the loss function value with a preset function threshold.

[0080] S153: If the loss function value is less than the preset function threshold, then the initial quantum circuit is taken as the target quantum circuit.

[0081] S154: If the loss function value is not less than the preset function threshold, then continue to optimize the initial quantum circuit until the preset optimization target is reached, and obtain the target quantum circuit.

[0082] In this embodiment, when iteratively optimizing the initial quantum circuit, this application can calculate the loss function value of the initial quantum circuit after running it. This loss function value can be compared with a preset function threshold to determine its relative value. If the loss function value is less than the preset function threshold, it indicates that the current loss function value has reached the minimum function value, and the entire process can be terminated, with the initial quantum circuit becoming the target quantum circuit. If the loss function value is not less than the preset function threshold, it indicates that the current loss function value has not reached the minimum function value, and the initial quantum circuit can continue to be optimized until the preset optimization target is reached, thus obtaining the final target quantum circuit.

[0083] In one embodiment, the adaptive index of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive index corresponds to an active state of a control bit.

[0084] In step S154, the initial quantum circuit is further optimized until a preset optimization target is reached, resulting in a target quantum circuit, which may include:

[0085] S1541: Determine the corresponding adaptive sequence number based on the current iteration number, and determine the corresponding number of parameterized multi-qubit controlled gates based on the adaptive sequence number.

[0086] S1542: After replacing the blank parameterized quantum circuit with the initial quantum circuit, the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate are updated using a preset iterative algorithm. Then, the first parameterized circuit template is applied to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps. This process continues until the number of the adaptive sequence number reaches a preset sequence number threshold to obtain the target quantum circuit.

[0087] In this embodiment, when the loss function value is not less than the preset function threshold, it indicates that the current loss function value has not reached the minimum function value. At this time, the initial quantum circuit can continue to be optimized until the preset optimization target is reached, and the final target quantum circuit can be obtained.

[0088] Specifically, when further optimizing the initial quantum circuit, the parameterized multi-qubit controlled gate of this application can be expressed as follows: ,in For adaptive serial numbers, It is positively correlated with the number of iterations, such as when initializing training, it can be set to... However, during the first iteration, it can be set... This is done to achieve iterative optimization. Furthermore, due to the serial number of this application... This indicates the active state of the control bit. , This corresponds to the parameterized circuit template. The parameters in the text. Therefore, this application aims to... Continuous adjustments are made to optimize the constructed quantum circuit.

[0089] In one specific implementation, when continuing to optimize the initial quantum circuit, this application can first determine the corresponding adaptive sequence number based on the current iteration number, and then determine the corresponding number of parameterized multi-qubit controlled gates based on the adaptive sequence number. Next, this application can replace the blank parameterized quantum circuit from the initial training with the current initial quantum circuit, and then use a preset iterative algorithm to update the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate. For example, this application can use classical gradient descent or a non-gradient method to update the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate, and continue to apply the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit to obtain... The process involves several steps: first, applying at least one parameterized multi-qubit controlled gate to the first quantum circuit to obtain a second quantum circuit; second, applying a second parameterized circuit template to the first N qubits of the second quantum circuit to obtain an initial quantum circuit; third, running the initial quantum circuit and calculating its loss function value, comparing it to a preset function threshold; fourth, if the loss function value is less than the preset function threshold, it indicates that the current loss function value has reached the minimum function value, and the entire process can end, with the initial quantum circuit serving as the target quantum circuit; and fifth, if the loss function value is not less than the preset function threshold, it indicates that the current loss function value has not reached the minimum function value, and the initial quantum circuit can continue to be optimized until the preset optimization target is reached, thus obtaining the final target quantum circuit.

[0090] Indicatively, such as Figure 2 As shown, Figure 2 A schematic diagram of the iterative optimization process for parameterized quantum circuits provided in the embodiments of this application; Figure 2 In this application, the preset function threshold is first set to... (like ), Initialize adaptive sequence number The complete parameterized LCU structure is constructed through the following steps:

[0091] 1. Prepare one Blank PQC for qubits, selecting parameterized circuit template (like (e.g., single-qubit rotating gate) acts on the front On a qubit circuit, where the vector This represents the parameters in the corresponding circuit;

[0092] 2. Acting in sequence All parameterized multi-qubit controlled gates corresponding to adaptive indices To the whole In the circuit of qubits, where the first One quantum bit is used for the control circuit, the last two... Each qubit is a controlled circuit used to practically implement VQA. Specifically, for the direct product parameterized circuit template... ,have:

[0093]

[0094]

[0095] in, .

[0096] 3. Select the parametric circuit template And act before On qubits, where vector This represents the parameters in the corresponding circuit;

[0097] 4. Run the entire PQC to compute the loss function, and minimize the loss function value using classical gradient descent or a non-gradient method. Until convergence. If If it stops, then the entire process is stopped; otherwise, Then return to step 1; record the current training parameter results. ;

[0098] 5. Repeat the above steps until... To complete VQA under the LCU architecture, in special cases, it can be configured. To limit the expressive power of PQC, thereby increasing trainability;

[0099] 6. Finally, add the above steps after the quantum gate. The PQC of the qubit is used as the output of this scheme.

[0100] The above method can be used to obtain the following: Figure 3 The parameterized quantum circuit shown, Figure 3 This involves constructing a 4-qubit PQC circuit template based on an LCU using parameterized controlled gate structures, where... This invention serves as a parameterized circuit template. By cleverly combining LCU technology with variational quantum circuits, it enables efficient solving of VQA problems such as quantum state learning and Hamiltonian ground state determination on quantum devices, opening new avenues for practical applications in fields such as quantum chemistry. The core idea is to utilize linear combinations of unitary matrices to reduce the depth of the variational circuit and the required number of qubits, probabilistically achieving a pure-state decomposition of any target quantum state, i.e.:

[0101]

[0102] The above method improves the practicality of the algorithm with limited quantum resources. It also introduces a preprocessing step based on classical computation to estimate the coupling strength between different systems in the quantum state. Based on the prior knowledge of the quantum system, the number of controlled parameterization gates is reduced, thus accelerating the convergence of subsequent variational optimization. Furthermore, this method represents a significant step towards the industrial application of quantum computing technology.

[0103] The following will be adopted Figure 3 The PQC constructed in this paper and conventional parameterized quantum circuits were used to handle the same VQA task, and the final experimental results were compared to illustrate the effectiveness, universality, and accuracy of the PQC constructed in this paper. Figures 4-9 The two typical cases listed in this application are as follows: Figure 4 A schematic diagram of a three-qubit PQC for learning Bell states constructed according to the construction method of this application, provided as an embodiment of this application. Figure 5 A comparison diagram showing the convergence gap between learning a target quantum state using a Bell state as an example, provided for embodiments of this application, using a universal two-qubit PQC and the PQC designed in this application. Figure 6 A schematic diagram of a 6-qubit PQC constructed according to this application for solving the ground state energy of a 4-qubit Isingmodel, provided as an embodiment of this application. Figure 7 This is a schematic diagram of the structure of a single-layer linear entangled circuit provided in an embodiment of this application. Figure 8 This is a schematic diagram of the structure of a single-layer strongly entangled circuit for qubits provided in an embodiment of this application. Figure 9 A comparison diagram of convergence of the three PQC solutions for Hamiltonian ground state energy provided in the embodiments of this application.

[0104] Depend on Figure 4 It can be seen that, in Bell's state As the target state to be learned, the single-qubit rotating gate As respectively The four universal single-qubit gates U3 are respectively used as , , , According to this application, a PQC (with 14 parameters in total, the specific circuit is as follows) is constructed on three qubits. Figure 4 As shown in the figure, this PQC is compared with a universal two-qubit PQC (with a total of 15 parameters), and the experimental results are as follows. Figure 5 As shown, Figure 5 The horizontal axis represents the number of iterations, and the vertical axis represents the difference between the target quantum state and the actually learned state. The blue dashed line indicates that the difference is 0 under ideal conditions, the black line represents the learning result using a universal two-qubit PQC, and the red line represents the learning result using the PQC constructed using the scheme of this patent. It can be seen that the design scheme of this application can achieve the effect of accurately learning the target quantum state using a universal quantum gate with a small number of parameters. Therefore, it shows that the circuit construction scheme designed in this application can not only construct large-scale circuits using small-scale circuits, but also that the constructed circuits are effective and inexpensive.

[0105] Depend on Figure 6 As can be seen, this application takes the Hamiltonian selection of the four-qubit Ising model as an example, and uses a 16-qubit single-qubit rotating gate. ( The PQC (with a total of 16 parameters, the specific circuit is as follows) operating on six qubits according to the construction method of this application. Figure 6 As shown), this PQC is compared with commonly used strongly entangled parameterized quantum circuits (complex entangled layer) and linear entangled templates (examples of the two circuits are shown below). Figure 7 and Figure 8 As shown in the figure, the strongly entangled circuit used has 12 parameters, and the linearly entangled circuit has 16 parameters. The experimental results are as follows. Figure 9 As shown, Figure 9 In the graph, the horizontal axis represents the number of iterations, the vertical axis represents the expected value of the Hamiltonian, the blue dashed line represents the ground state energy of the Hamiltonian theory, the black line represents the calculation result using a strongly entangled circuit, the purple line represents the calculation result using a linearly entangled circuit, and the red line represents the calculation result using the PQC constructed in this application. It can be seen that, under the premise of approximate parameter quantities, the design scheme of this application converges faster, is closer to the theoretical value, and has higher accuracy; therefore, this application is practical.

[0106] The parameterized quantum circuit construction apparatus provided in the embodiments of this application is described below. The parameterized quantum circuit construction apparatus described below and the parameterized quantum circuit construction method described above can be referred to in correspondence.

[0107] In one embodiment, such as Figure 10 As shown, Figure 10 This is a schematic diagram of a parameterized quantum circuit construction device provided in an embodiment of this application. This application also provides a parameterized quantum circuit construction device, which may include a circuit determination module 210, a first function module 220, a second function module 230, a third function module 240, and a circuit optimization module 250, specifically including the following:

[0108] The circuit determination module 210 is used to determine a blank parameterized quantum circuit for 3N qubits, and to determine a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate.

[0109] The first action module 220 is used to apply the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit.

[0110] The second action module 230 is used to apply at least one of the parameterized multi-qubit controlled gates to the first quantum circuit to obtain a second quantum circuit, wherein the first N qubits in the first quantum circuit are control circuits and the last 2N qubits are controlled circuits.

[0111] The third action module 240 is used to apply the second parameterized circuit template to the first N qubits of the second quantum circuit to obtain the initial quantum circuit.

[0112] The circuit optimization module 250 is used to run the initial quantum circuit and obtain the running results, and optimize the initial quantum circuit according to the running results until the preset optimization target is reached, so as to obtain the target quantum circuit.

[0113] In the above embodiments, after determining a blank parameterized quantum circuit with 3N qubits, and determining a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate, the first parameterized circuit template can be applied to the first N qubits of the blank parameterized quantum circuit to obtain a first quantum circuit; then, at least one of the parameterized multi-qubit controlled gates is applied to the first quantum circuit to obtain a second quantum circuit, wherein the first N qubits of the first quantum circuit are control circuits, and the last 2N qubits are controlled circuits, thus forming an LCU architecture; next, the second parameterized circuit template is applied to the first N qubits of the second quantum circuit to obtain an initial quantum circuit, and the initial quantum circuit is run to obtain the running result. Finally, the initial quantum circuit is optimized based on the running result until a preset optimization target is reached, thereby obtaining the target quantum circuit. This application utilizes linear combination of unitary matrices to reduce the depth of variational circuits and the number of required qubits, thereby effectively constructing arbitrary target quantum states, reducing the number of training parameters, and optimizing the efficiency and accuracy of variational quantum algorithms, improving the practicality of the algorithms under limited quantum resources. Furthermore, this application is particularly applicable to noisy medium-scale quantum (NISQ) devices. By proposing a circuit design with both low depth and low number of qubits, it can solve the problem of limited application of existing technologies on NISQ devices. For example, this application can efficiently solve VQA problems such as quantum state learning and Hamiltonian ground state solving on quantum devices, thus opening up new avenues for practical applications in fields such as quantum chemistry.

[0114] In one embodiment, the circuit optimization module 250 may include:

[0115] The loss function calculation module is used to calculate the loss function value of the initial quantum circuit after running the initial quantum circuit.

[0116] The function value comparison module is used to compare the loss function value with a preset function threshold.

[0117] A quantum circuit determination module is used to identify the initial quantum circuit as the target quantum circuit if the loss function value is less than the preset function threshold.

[0118] An iterative optimization module is used to continue optimizing the initial quantum circuit if the loss function value is not less than the preset function threshold, until the preset optimization target is reached, thereby obtaining the target quantum circuit.

[0119] In one embodiment, the adaptive index of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive index corresponds to an active state of a control bit.

[0120] The iterative optimization module may include:

[0121] The adaptive sequence number update module is used to determine the corresponding adaptive sequence number based on the current iteration number, and to determine the corresponding number of parameterized multi-qubit controlled gates based on the adaptive sequence number.

[0122] The parameter update module is used to replace the blank parameterized quantum circuit with the initial quantum circuit, update the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate using a preset iterative algorithm, and return to execute the first parameterized circuit template on the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps, until the number of the adaptive sequence number reaches a preset sequence number threshold to obtain the target quantum circuit.

[0123] In one embodiment, this application also provides a computer-readable storage medium storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the parameterized quantum circuit construction method as described in any of the above embodiments.

[0124] In one embodiment, this application also provides a computer device, including: one or more processors, and memory.

[0125] The memory stores computer-readable instructions, which, when executed by the one or more processors, perform the steps of the parameterized quantum circuit construction method as described in any of the above embodiments.

[0126] Indicatively, such as Figure 11 As shown, Figure 11 This is a schematic diagram of the internal structure of a computer device 300 provided in an embodiment of this application. The computer device 300 can be provided as a server. (Refer to...) Figure 11 The computer device 300 includes a processing component 302, which further includes one or more processors, and memory resources represented by memory 301 for storing instructions, such as application programs, that can be executed by the processing component 302. The application programs stored in memory 301 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 302 is configured to execute instructions to perform the parameterized quantum circuit construction method of any of the above embodiments.

[0127] The computer device 300 may also include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input / output (I / O) interface 305. The computer device 300 may operate on an operating system stored in memory 301, such as Windows Server™, Mac OS X™, Unix™, Linux™, Free BSD™, or similar.

[0128] Those skilled in the art will understand that Figure 11 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0129] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0130] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0131] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for constructing parameterized quantum circuits, characterized in that, The method includes: Determine a blank parameterized quantum circuit for 3N qubits, and determine a first parameterized circuit template, a second parameterized circuit template, and at least one parameterized multi-qubit controlled gate; After applying the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit, the first quantum circuit is obtained; After applying at least one of the parameterized multi-qubit controlled gates to the first quantum circuit, a second quantum circuit is obtained, wherein the first N qubits of the first quantum circuit are control circuits and the last 2N qubits are controlled circuits. After applying the second parameterized circuit template to the first N qubits of the second quantum circuit, the initial quantum circuit is obtained; After running the initial quantum circuit, the running results are obtained. The initial quantum circuit is then optimized based on the running results until a preset optimization target is reached, thus obtaining the target quantum circuit.

2. The method for constructing parameterized quantum circuits according to claim 1, characterized in that, After running the initial quantum circuit, the running results are obtained. Based on the running results, the initial quantum circuit is optimized until a preset optimization target is reached, thus obtaining the target quantum circuit, including: After running the initial quantum circuit, calculate the loss function value of the initial quantum circuit; The loss function value is compared with a preset function threshold; If the loss function value is less than the preset function threshold, then the initial quantum circuit is taken as the target quantum circuit; If the loss function value is not less than the preset function threshold, the initial quantum circuit is further optimized until the preset optimization target is reached, thus obtaining the target quantum circuit.

3. The method for constructing parameterized quantum circuits according to claim 2, characterized in that, The adaptive sequence number of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive sequence number corresponds to an active state of a control bit. The process of continuing to optimize the initial quantum circuit until a preset optimization target is reached, thereby obtaining the target quantum circuit, includes: The corresponding adaptive sequence number is determined based on the current iteration number, and the corresponding number of parameterized multi-qubit controlled gates is determined based on the adaptive sequence number. After replacing the blank parameterized quantum circuit with the initial quantum circuit, the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate are updated using a preset iterative algorithm. Then, the first parameterized circuit template is applied to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps. This process continues until the number of the adaptive sequence number reaches a preset sequence number threshold to obtain the target quantum circuit.

4. The method for constructing parameterized quantum circuits according to claim 1 or 2, characterized in that, The first parameterized circuit template and the second parameterized circuit template are any one of the following: direct product parameterized circuit template, alternating layered circuit template, and hardware high-efficiency circuit template.

5. The method for constructing parameterized quantum circuits according to claim 1 or 2, characterized in that, The second parameterized circuit template is the conjugate transpose of the first parameterized circuit template.

6. A parameterized quantum circuit construction device, characterized in that, include: The circuit determination module is used to determine the blank parameterized quantum circuit of 3N qubits, and to determine the first parameterized circuit template, the second parameterized circuit template, and at least one parameterized multi-qubit controlled gate; The first action module is used to apply the first parameterized circuit template to the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit. The second action module is used to apply at least one of the parameterized multi-qubit controlled gates to the first quantum circuit to obtain a second quantum circuit, wherein the first N qubits in the first quantum circuit are control circuits and the last 2N qubits are controlled circuits. The third action module is used to apply the second parameterized circuit template to the first N qubits of the second quantum circuit to obtain the initial quantum circuit. The circuit optimization module is used to run the initial quantum circuit and obtain the running results, and optimize the initial quantum circuit according to the running results until a preset optimization target is reached to obtain the target quantum circuit.

7. The parameterized quantum circuit construction apparatus according to claim 6, characterized in that, The circuit optimization module includes: The loss function calculation module is used to calculate the loss function value of the initial quantum circuit after running the initial quantum circuit. The function value comparison module is used to compare the loss function value with a preset function threshold; A quantum circuit determination module is used to identify the initial quantum circuit as the target quantum circuit if the loss function value is less than the preset function threshold. An iterative optimization module is used to continue optimizing the initial quantum circuit if the loss function value is not less than the preset function threshold, until the preset optimization target is reached, thereby obtaining the target quantum circuit.

8. The parameterized quantum circuit construction apparatus according to claim 7, characterized in that, The adaptive sequence number of the parameterized multi-qubit controlled gate is positively correlated with the number of iterations, and each adaptive sequence number corresponds to an active state of a control bit. The iterative optimization module includes: An adaptive sequence number update module is used to determine the corresponding adaptive sequence number based on the current iteration number, and to determine the corresponding number of parameterized multi-qubit controlled gates based on the adaptive sequence number. The parameter update module is used to replace the blank parameterized quantum circuit with the initial quantum circuit, update the parameters in the first parameterized circuit template, the second parameterized circuit template, and each parameterized multi-qubit controlled gate using a preset iterative algorithm, and return to execute the first parameterized circuit template on the first N qubits of the blank parameterized quantum circuit to obtain the first quantum circuit and its subsequent steps, until the number of the adaptive sequence number reaches a preset sequence number threshold to obtain the target quantum circuit.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the parameterized quantum circuit construction method as described in any one of claims 1 to 5.

10. A computer device, characterized in that, include: One or more processors, and memory; The memory stores computer-readable instructions that, when executed by the one or more processors, perform the steps of the parameterized quantum circuit construction method as described in any one of claims 1 to 5.

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