Method for efficiently simulating large-scale quantum random access memory

Abstract

The invention discloses a method for efficiently simulating a large-scale quantum random access memory, which comprises the following steps of: constructing a base vector tracking method to update a base vector through unitary operation on a quantum system, and selecting the base vector meeting gate type constraint, entanglement region constraint and control bit constraint for simulation; under the framework of a base vector tracking method, task parallelization processing is carried out on an evolution path of a base vector to be simulated so as to realize calculation acceleration of a simulation process; based on the state of the base vector and the parallel execution queue dynamic screening path, the simulation process focuses on the base vector evolution path having important influence on the final result so as to optimize the simulation performance. According to the invention, simulation time and memory requirements can be reduced, and efficient simulation of a large-scale QRAM is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum computing, and particularly relates to a method for efficiently simulating a large-scale quantum random access memory. Background Art

[0002] In an actual quantum computing device, a quantum random access memory (QRAM), as a key component in the quantum computing architecture, its performance stability and reliability are directly related to the efficiency and accuracy of the entire quantum computing system. However, QRAM faces significant challenges caused by quantum noise in practical applications. Quantum noise, as an inherent source of uncertainty in quantum systems, is mainly manifested through the decoherence effect of qubits, which is quantified by two core parameters, the relaxation time (T1) and the decoherence time (T2). These two parameters jointly determine the time window during which qubits can maintain coherence when performing computational tasks, which is crucial for ensuring the accuracy and reliability of quantum computing.

[0003] To quantify the impact of quantum noise on quantum circuits, it is usually necessary to calculate the circuit fidelity. Although fidelity analysis provides a powerful tool for understanding the noise characteristics of QRAM, the current quantum computing technology is still in the NISQ era. Quantum devices at this stage are limited by relatively short coherence times and are difficult to support the efficient operation of large-scale QRAM. Against this background, using a classical computer to simulate QRAM has become an important means to evaluate its performance and diagnose potential problems. Classical simulation methods such as the Schrödinger algorithm and the Feynman path algorithm reproduce the behavior of quantum circuits on a classical computer through numerical calculations, providing a way to study the characteristics of QRAM without actual quantum hardware. However, as the number of QRAM layers increases, that is, as its storage capacity and complexity increase, classical simulation methods often encounter the bottleneck of exponential computational overhead, facing huge challenges in terms of computational efficiency and feasibility, highlighting the urgency of developing more efficient quantum hardware and algorithms.

[0004] From a technical implementation perspective, the data input process of QRAM relies on the initialization of qubits and the precise control of quantum gate operations. By encoding classical data into quantum states, QRAM can achieve quantum parallel access to data, which is a significant advantage over classical memories. However, the implementation of this process requires highly precise control operations to ensure the correct entanglement between addresses and data, thereby enabling efficient quantum information retrieval. However, there are currently few existing QRAM hardware implementations. The main challenge lies in the lack of a simulator specifically for QRAM simulation on physical quantum machines to simulate the access process in QRAM and guide hardware implementation. Existing simulation methods are divided into accurate and approximate simulations, as well as methods customized for specific circuit types, such as stabilizer circuits, which ignore the inherent characteristics in QRAM circuits and cannot efficiently simulate large-scale noiseless QRAM circuits.

[0005] Therefore, under the dual challenges of quantum noise and the limitations of the NISQ era, error correction and efficient circuit design have become the keys to improving QRAM performance. Future research should focus on extending the coherence time and optimizing resource usage to efficiently simulate and implement large-scale QRAM. Summary of the Invention

[0006] In view of the above, the object of the present invention is to provide a method for efficiently simulating a large-scale quantum random access memory, which can reduce the simulation time and memory requirements, thereby achieving efficient simulation of large-scale QRAM and being applicable to reducing the computational resource consumption of quantum circuit simulation on classical computers and accelerating the simulation process.

[0007] To achieve the above object of the invention, the technical solution provided by the present invention is as follows:

[0008] A method for efficiently simulating a large-scale quantum random access memory provided by an embodiment of the present invention includes the following steps:

[0009] Construct a basis vector tracking method to update the basis vectors of the quantum system through unitary operations, and select the basis vectors that satisfy the gate type constraint, entanglement region constraint, and control bit constraint for simulation;

[0010] Under the framework of the basis vector tracking method, perform task parallelization on the evolution paths of the basis vectors to be simulated to achieve computational acceleration of the simulation process;

[0011] Dynamically screen paths based on the states of the basis vectors and the parallel execution queue, so that the simulation process focuses on the evolution paths of the basis vectors that have an important impact on the final result to optimize the simulation performance.

[0012] Preferably, the constructing a basis vector tracking method to update the basis vectors of the quantum system through unitary operations includes:

[0013] The construction basis vector tracking method only updates the basis vectors instead of the coefficients of the entire Hilbert space. That is, applying a unitary matrix U to the state |ψ> of an n-bit quantum system to update the basis vectors, which is expressed as:

[0014]

[0015] where a i represents the i-th complex coefficient, satisfying the normalization condition These updated vectors form a new set of basis vectors.

[0016] Preferably, the construction basis vector tracking method updates the basis vectors of the quantum system through unitary operations, including:

[0017] Selecting the basis vectors that satisfy the gate type constraint, entanglement region constraint, and control bit constraint for simulation, including:

[0018] For a quantum circuit with n bits, the circuit entangles m bits and collects them in set E, and the initial states of the remaining (n - m) bits are |0>. The bits to which the H gate is applied are collected in set F. When the circuit satisfies the following constraint conditions, no more than 2 m basis vectors will be used for simulation:

[0019] Gate type constraint C1: The circuit only contains SWAP gates, Pauli gates, CSWAP gates, CX gates, CY gates, CZ gates, and H gates;

[0020] Entanglement region constraint C2: No H gate is applied in set E;

[0021] Control bit constraint C3: There is no control bit in set F.

[0022] Preferably, the construction basis vector tracking method updates the basis vectors of the quantum system through unitary operations, including:

[0023] Performing task parallelization on the evolution paths of the basis vectors for simulation to achieve computational acceleration of the simulation process, including:

[0024] The task execution stage of simulating the evolution path of the basis vector is divided into an address setting stage, a data extraction stage, and an inverse calculation stage; in the address setting stage, a tree structure is constructed, and a path is established from the root node of the tree to the bottom, and this path corresponds to the address of the data item to be queried; in the data extraction stage, the data is first transferred from the data bus register to the root node of the tree, then transferred to the storage node to retrieve the data bits, and finally returned to the bus; in the inverse calculation stage, the process of the address setting stage is executed in reverse to restore the system to its initial state; the operations in each stage need to be executed in sequence, and the operations in the data acquisition stage are grouped to minimize the total number of operations, and the operations within each stage are executed in parallel to reduce the simulation latency time and achieve computational acceleration.

[0025] Preferably, the method for constructing the basis vector tracking updates the basis vector for the quantum system through unitary operations, including:

[0026] Furthermore, the simulation performance is improved by constructing an acceleration matrix, including:

[0027] The address setting stage, the data extraction stage, and the inverse calculation stage are constructed into a pipeline. For the simulated (n, k)-QRAM, where n represents the size of the address space for data storage, that is, the number of layers mapped to the quantum circuit, and k represents the number of bits of data stored in each storage unit, that is, the number of qubits mapped to the quantum circuit, and QRAM represents the quantum random access memory. It is executed layer by layer in the quantum circuit and the execution order is optimized to construct the corresponding acceleration matrix, and the execution queue is quickly constructed according to the acceleration matrix.

[0028] Preferably, the method for constructing the basis vector tracking updates the basis vector for the quantum system through unitary operations, including:

[0029] Optimizing the execution order includes: interleaving the sequential commands in the quantum circuit through the pipeline and performing a combined routing operation in the data acquisition stage to reduce the number of operations.

[0030] Preferably, the method for constructing the basis vector tracking updates the basis vector for the quantum system through unitary operations, including:

[0031] The dependency relationship of the acceleration matrix is defined by its data dependency. If there is no other operation acting on the target layer of the current operation, the current operation is added to the execution queue.

[0032] Preferably, the method for constructing the basis vector tracking updates the basis vector for the quantum system through unitary operations, including:

[0033] Dynamically screening the path based on the state of the basis vector and the parallel execution queue enables the simulation process to focus on the evolution path of the basis vector that has an important impact on the final result to optimize the simulation performance, including:

[0034] Under the parallel execution queue framework, an active qubit table is constructed based on the state information of the basis vectors. The active qubit table uses a dynamic tracking mechanism to record in real time all qubits that are not in the |0> state, so as to accurately identify the qubits that need to perform operations or are interfered by noise, and realize the dynamic screening and optimization management of the evolution paths of qubits containing non-|0> states.

[0035] Compared with the prior art, the beneficial effects of the present invention at least include:

[0036] The present invention updates the basis vectors through the basis vector tracking method, so that the evolution of the quantum state remains in a smaller Hilbert space, avoiding redundant storage and calculation. Combining parallel execution and dynamic tracking strategies within the framework of the basis vector tracking method can significantly improve the simulation efficiency and reduce memory consumption, and finally realize the efficient simulation of large-scale QRAM, which helps to fully exert the potential of quantum computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0038] Figure 1 It is a schematic flowchart of a method for efficiently simulating a large-scale quantum random access memory provided by an embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of the execution process of QRAM based on quantum circuit parallel optimization provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] To make the purpose, technical solutions and advantages of the present invention more clearly understood, the following further describes the present invention in detail with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the protection scope of the present invention.

[0041] The inventive concept of the present invention is: aiming at the problems of large consumption of computing resources and low simulation efficiency in the classical simulation method of QRAM in the prior art, an embodiment of the present invention provides a method for efficiently simulating a large-scale quantum random access memory. By optimizing the basis vector tracking and combining parallel execution and dynamic tracking strategies, the simulation efficiency can be significantly improved, the memory consumption can be reduced, and the efficient simulation of large-scale QRAM can be realized.

[0042] Figure 1It is a schematic flow chart of a method for efficiently simulating a large-scale quantum random access memory provided by an embodiment of the present invention. As Figure 1 shown, the embodiment provides a method for efficiently simulating a large-scale quantum random access memory, including the following steps:

[0043] S1, constructing a basis vector tracking method to update the basis vectors of the quantum system through unitary operations, and selecting basis vectors that satisfy the gate type constraint, entanglement region constraint, and control bit constraint for simulation.

[0044] In an n-bit system, usually 2 n basis vectors are used to represent the state, as follows:

[0045] |ψ> = a 0…00 |0…00> + a 0…01 |0…01> + … + a 1…11 |1…11>

[0046] where a i represents a complex coefficient, satisfying the normalization condition

[0047] Such a system can be described using a 2 n dimensional Hilbert space, and the basis vectors can be selected as needed. For example, for a single-bit system, the basis vectors can be selected as {|0>, |1>}, {|+>, |->}, or other suitable choices. The key is that the selected basis vectors must be normalized and mutually orthogonal. For an n-bit system, assuming a set of basis vectors is used as the basis of a 2 n dimensional Hilbert space, then the state of the n-bit system can be represented as:

[0048]

[0049] where a i represents a complex coefficient, satisfying the normalization condition

[0050] In the embodiment, a basis vector tracking method (BVTT) is constructed to update only the basis vectors rather than the entire Hilbert space coefficients. That is, applying a unitary matrix U to the state |ψ> of the n-bit quantum system to update the basis vectors, which is expressed as:

[0051]

[0052] where a i represents the i-th complex coefficient, satisfying the normalization condition These updated vectors form a new set of basis vectors.

[0053] Consider a quantum circuit with n qubits. This circuit entangles m qubits and collects them in set E, and the initial state of the remaining (n - m) qubits is |0>. The qubits to which the H gate is applied are collected in set F. When the circuit satisfies the following constraints, no more than 2 m basis vectors will be used for simulation:

[0054] Gate type constraint C1: The circuit only contains SWAP gates, Pauli gates, CSWAP gates, CX gates, CY gates, CZ gates, and H gates;

[0055] Entangled region constraint C2: No H gate is applied to the qubits in set E;

[0056] Control bit constraint C3: There are no control bits in set F.

[0057] For the basis vector tracking method (BVTT) provided in the embodiments, the initial state is in a 2 m -dimensional Hilbert space. Under the condition of satisfying the above constraints, the evolution of the quantum state can always be maintained in this 2 m -dimensional Hilbert space.

[0058] S2. Under the framework of the basis vector tracking method, task parallelization is performed on the evolution paths of the basis vectors for simulation to achieve computational acceleration in the simulation process.

[0059] In the embodiments, the task execution stage of the basis vector evolution path simulation is divided into an address setting stage, a data extraction stage, and an inverse calculation stage; in the address setting stage, a tree structure is constructed, and a path is established from the root node of the tree to the bottom, and this path corresponds to the address of the data item to be queried; in the data extraction stage, the data is first transferred from the data bus register to the root node of the tree, then transferred to the storage node to retrieve the data bits, and finally returned to the bus; in the inverse calculation stage, the process of the address setting stage is executed in reverse to restore the system to the initial state; the operations in each stage need to be executed in sequence, and the operations in the data acquisition stage are grouped to minimize the total number of operations, and the operations within each stage are executed in parallel to reduce the simulation latency time and achieve computational acceleration.

[0060] Meanwhile, these three stages are constructed into a pipeline, and an acceleration matrix is designed to improve the performance of the simulator. As Figure 2 shown, taking a (3, 2)-QRAM as an example, in Figure 2Part (a) in [Figure] shows a part of the execution process of the original (3,2)-QRAM, which includes five operations: data bus input, internal swap, routing, data bus input / output, and data copy, required to complete the entire process. This circuit-like representation highlights the layer-by-layer execution, because vertically parallel quantum circuits can execute operations simultaneously. By using the pipelining method to interleave these sequential commands, the total length of the execution queue is effectively reduced. For (n,k)-QRAM, during the data acquisition phase, there is an opportunity to merge some routing operations, such as Figure 2 the gradient coloring process shown in part (b) of [Figure]. Initially, the yellow routing operation transmits the data information (D0) of the 0th bit upward, while the green routing operation transmits the data information (D1) of the 1st bit downward. These two operations can be effectively merged to reduce the number of operations without affecting the final execution result. By optimizing the execution order, an acceleration matrix is constructed, as shown in Figure 2 part (c) of [Figure], where A0, A1, and A2 represent the address inputs for transmitting the 0th, 1st, and 2nd bits respectively, S represents the internal swap, R represents the routing operation, DC represents the interaction between qubits and classical bits, and the cells spanning two grid spaces indicate that operations must be performed on these two layers. The acceleration matrix is used to quickly construct the execution queue, and the dependencies of this matrix are defined by its data dependencies. If there are no other operations acting on the target layer of the current operation, the current operation can be added to the queue.

[0061] S3, dynamically filters paths based on the states of the basis vectors and the parallel execution queue, making the simulation process focus on the evolution paths of the basis vectors that have an important impact on the final result to optimize the simulation performance.

[0062] During the simulation process, most of the time complexity is caused by two key operations: InternalSwap and Routing. The time complexity of these two operations is O(2 n ·m), that is, exponential growth with the number of QRAM layers.

[0063] In the embodiments, the key observation for optimization is that in a binary tree (a data structure composed of bits), qubits along irrelevant paths maintain the state |0>. Thus, one can focus on the qubits within the desired paths and their corresponding operations, thereby restricting the operations to'm' paths, such that the operations at the 'n'-th layer grow linearly, and the complexity becomes O(m·m), rather than exponential growth. In the presence of noise, the situation remains similar. Pauli noise causes qubit flips and adds new paths. Based on this, a "lazy execution" algorithm is provided in the embodiments. Its main objective is to perform operations only when necessary. Specifically, in the framework of a parallel execution queue, an active qubit table is constructed and maintained based on the state information of the basis vectors. The active qubit table records all qubits not in the |0> state in real time through a dynamic tracking mechanism to accurately identify those qubits that need to perform operations or are affected by noise, realizing dynamic screening and optimized management of the evolution paths containing non-|0> state qubits to prevent the generation of incorrect results.

[0064] In summary, the embodiments of the present invention provide a method for efficiently simulating a large-scale quantum random access memory, which has a significant effect on improving the simulation performance: there is no Qiskit Aer backend in the prior art that can efficiently simulate a large-scale QRAM. The state vector, density matrix, and extended stabilizer methods encounter memory limitations and cannot simulate an address length exceeding 4. The matrix product state method can handle longer address lengths, but the simulation speed is slow, and when the address space is restricted to a subset, there are differences in the sampling counts between different addresses. These differences may indicate the existence of sampling bugs within the Qiskit framework. Therefore, in the embodiments, the simulation capabilities of four commonly used Qiskit Aer backends are evaluated: the state vector, density matrix, extended stabilizer, and matrix product state, and it is found that none of them can efficiently simulate QRAM, especially when dealing with large-scale simulations. Furthermore, in the embodiments, the simulation time of a simulator (hereinafter referred to as QRAMsim) constructed using the simulation method of the present invention and the existing Qiskit framework is further compared under noise-free conditions. When QRAM reaches 8 layers, the simulation time of Qiskit is as high as 46 hours. In contrast, QRAMsim shows a significant reduction in simulation time, only 0.3 seconds. After optimization, the time can be further reduced to 0.003 seconds. Without optimization, QRAMsim is approximately 10 4 to 10 5 times faster. This acceleration is more significant at deeper levels because the execution time of Qiskit grows exponentially. And the optimized QRAMsim achieves an acceleration of up to 10 8The exponential speedup ratio. In addition, the memory consumption of QRAMsim is also significantly lower than that of Qiskit. Under a fixed address space, the memory consumption of QRAMsim remains at approximately 100 MB at different levels, while the memory consumption of Qiskit grows exponentially with the number of layers and reaches 32 GB at the 8th layer.

[0065] In addition, the performance of QRAMsim under noisy conditions was also evaluated. Ninety random noise instances were introduced on qubits and logic gates, and two cases were considered: requiring a complete address and only a partial address (20 in the experiment). Using QRAMsim, it is possible to efficiently simulate a QRAM up to 17 layers within 100 seconds. It is worth noting that when the address is fixed, the simulation time of QRAMsim remains almost constant at different levels, and the multiple of the time difference between the noisy and noiseless cases is basically the same among different levels, which is consistent with the complexity analysis results in the previous step S3.

[0066] The specific embodiments described above have elaborated on the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, supplements, equivalent replacements, etc. made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for efficiently simulating a large-scale quantum random access memory, characterized in that, Including the following steps: Construct a basis vector tracking method to update the basis vectors of a quantum system through unitary operations, and select basis vectors that satisfy the gate type constraint, entanglement region constraint, and control bit constraint for simulation; Under the framework of the basis vector tracking method, perform task parallelization on the evolution paths of the basis vectors being simulated to accelerate the calculation during the simulation process; Dynamically filter paths based on the states of the basis vectors and the parallel execution queue, so that the simulation process focuses on the evolution paths of the basis vectors that have an important impact on the final result to optimize the simulation performance.

2. The method for efficiently simulating a large-scale quantum random access memory according to claim 1, wherein, The construction of the basis vector tracking method to update the basis vectors of a quantum system through unitary operations includes: The constructed basis vector tracking method only updates the basis vectors rather than the coefficients of the entire Hilbert space. That is, applying a unitary matrix U to the state |ψ> of an n-bit quantum system to update the basis vectors, expressed as: where a i represents the i-th complex coefficient, satisfying the normalization condition These updated vectors form a new set of basis vectors.

3. The method for efficiently simulating a large-scale quantum random access memory according to claim 1 or 2, characterized in that, The selection of basis vectors that satisfy the gate type constraint, entanglement region constraint, and control bit constraint for simulation includes: For a quantum circuit with n bits, the circuit entangles m bits and collects them in set E, the initial state of the remaining (n - m) bits is |0>, and the bits to which the H gate is applied are collected in set F. When the circuit satisfies the following constraints, no more than 2 m basis vectors will be used for simulation: Gate type constraint C1: The circuit only contains SWAP gates, Pauli gates, CSWAP gates, CX gates, CY gates, CZ gates, and H gates; Entanglement region constraint C2: No H gates are applied in the set E; Control bit constraint C3: There are no control bits in the set F.

4. The method for efficiently simulating a large-scale quantum random access memory according to claim 1, wherein The implementation of task parallelization on the evolution paths of the basis vectors being simulated to accelerate the calculation during the simulation process includes: Divide the task execution stage of the basis vector evolution path simulation into an address setting stage, a data extraction stage, and an inverse calculation stage; in the address setting stage, construct a tree structure and establish a path from the root node of the tree to the bottom, and this path corresponds to the address of the data item being queried; in the data extraction stage, the data is first transferred from the data bus register to the root node of the tree, then transferred to the storage node to retrieve the data bits, and finally returned to the bus; in the inverse calculation stage, the process of the address setting stage is executed in reverse to restore the system to its initial state; each stage needs to execute operations in sequence, and group the operations within the data acquisition stage to minimize the total number of operations. By executing the operations within each stage in parallel, the simulation latency time is reduced to achieve calculation acceleration.

5. The method for efficiently simulating a large-scale quantum random access memory according to claim 4, wherein Further improve the simulation performance by constructing an acceleration matrix, including: Construct the address setting stage, the data extraction stage, and the inverse calculation stage into a pipeline. For the simulated (n, k)-QRAM, where n represents the size of the address space for data storage, that is, the number of layers mapped to the quantum circuit, and k represents the number of bits of data stored in each storage unit, that is, the number of bits mapped to the quantum circuit, and QRAM represents a quantum random access memory. Execute layer by layer in the quantum circuit and optimize the execution order to construct the corresponding acceleration matrix, and quickly construct an execution queue according to the acceleration matrix.

6. The method for efficiently simulating a large-scale quantum random access memory according to claim 5, wherein Optimizing the execution order includes: interleaving the sequential commands in the quantum circuit through the pipeline and performing a combined routing operation during the data acquisition stage to reduce the number of operations.

7. The method for efficiently simulating a large-scale quantum random access memory according to claim 5, wherein The dependency relationship of the acceleration matrix is defined by its data dependency. If there are no other operations acting on the target layer of the current operation, add the current operation to the execution queue.

8. The method for efficiently simulating a large-scale quantum random access memory according to claim 1, wherein The state based on the basis vectors and the parallel execution queue dynamically filter paths, enabling the simulation process to focus on the evolution paths of the basis vectors that have an important impact on the final result to optimize the simulation performance, including: Under the parallel execution queue framework, an active qubit table is constructed based on the state information of the basis vectors. The active qubit table uses a dynamic tracking mechanism to record all qubits that are not in the |0> state in real time, so as to accurately identify the qubits that need to perform operations or are affected by noise, and achieve dynamic screening and optimized management of the evolution paths containing qubits in non-|0> states.

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