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arXiv:2410.11146

Theoretical Analysis of the Efficient-Memory Matrix Storage Method for Quantum Emulation Accelerators with Gate Fusion on FPGAs

Thuyen Le, Hoai Luan Pham, Vu Tuan Hai, Vu Trung Duong Le, Yasuhiko Nakashima

Published Oct 15, 2024• 0 citations
arXivHTMLPDF

Abstract

Quantum emulators play an important role in the development and testing of quantum algorithms, especially given the limitations of the current FTQC era. Developing high-speed, memory-optimized quantum emulators is a growing research trend, with gate fusion being a promising technique. However, existing gate fusion implementations often struggle to efficiently support large-scale quantum systems with a high number of qubits due to a lack of optimizations for the exponential growth in memory requirements. Therefore, this study proposes the EMMS (Efficient-Memory Matrix Storage) method for storing quantum operators and states, along with an EMMS-based Quantum Emulator Accelerator (QEA) architecture that incorporates multiple processing elements (PEs) to accelerate tensor product and matrix multiplication computations in quantum emulation with gate fusion. The theoretical analysis of the QEA on the Xilinx ZCU102 FPGA, using varying numbers of PEs and different depths of unitary and local data memory, reveals a linear increase in memory depth with the number of qubits. This scaling highlights the potential of the EMMS-based QEA to accommodate larger quantum circuits, providing insights into selecting appropriate memory sizes and FPGA devices. Furthermore, the estimated performance of the QEA with PE counts ranging from $2^2$ to $2^5$ on the Xilinx ZCU102 FPGA demonstrates that increasing the number of PEs significantly reduces the computation cycle count for circuits with fewer than 18 qubits, making it significantly faster than previous works.

DOI
10.48550/arxiv.2410.11146

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Quantum emulators play an important role in the development and testing of quantum algorithms, especially given the limitations of the current FTQC era. Developing high-speed, memory-optimized quantum emulators is a growing research trend, with gate fusion being a promising technique. However, existing gate fusion implementations often struggle to efficiently support large-scale quantum systems with a high number of qubits due to a lack of optimizations for the exponential growth in memory requirements. Therefore, this study proposes the EMMS (Efficient-Memory Matrix Storage) method for storing quantum operators and states, along with an EMMS-based Quantum Emulator Accelerator (QEA) architecture that incorporates multiple processing elements (PEs) to accelerate tensor product and matrix multiplication computations in quantum emulation with gate fusion. The theoretical analysis of the QEA on the Xilinx ZCU102 FPGA, using varying numbers of PEs and different depths of unitary and local data memory, reveals a linear increase in memory depth with the number of qubits. This scaling highlights the potential of the EMMS-based QEA to accommodate larger quantum circuits, providing insights into selecting appropriate memory sizes and FPGA devices. Furthermore, the estimated performance of the QEA with PE counts ranging from 222^222 to 252^525 on the Xilinx ZCU102 FPGA demonstrates that increasing the number of PEs significantly reduces the computation cycle count for circuits with fewer than 18 qubits, making it significantly faster than previous works.
Quantum emulators play an important role in the development and testing of quantum algorithms, especially given the limitations of the current FTQC era. Developing high-speed, memory-optimized quantum emulators is a growing research trend, with gate fusion being a promising technique. However, existing gate fusion implementations often struggle to efficiently support large-scale quantum systems with a high number of qubits due to a lack of optimizations for the exponential growth in memory requirements. Therefore, this study proposes the MEMS (Memory-Efficient Matrix Storage) method for storing quantum operators and states, along with a MEMS-based Quantum Emulator Accelerator (QEA) architecture that incorporates multiple processing elements (PEs) to accelerate tensor product and matrix multiplication computations in quantum emulation with gate fusion. The theoretical analysis of the QEA on the Xilinx ZCU102 FPGA, using varying numbers of PEs and different depths of unitary and local data memory, reveals a linear increase in memory depth with the number of qubits. This scaling highlights the potential of the MEMS-based QEA to accommodate larger quantum circuits, providing insights into selecting appropriate memory sizes and FPGA devices. Furthermore, the estimated performance of the QEA with PE counts ranging from 22to 25on the Xilinx ZCU102 FPGA demonstrates that increasing the number of PEs significantly reduces the computation cycle count for circuits with fewer than 18 qubits, making it substantially faster than previous works.
Gate-based quantum computers, poised to surpass their classical counterparts, drive intense research interest. Emulating quantum systems relies on state vector-type simulators, hampered by soaring memory demands, especially for systems beyond 40 qubits. Our solution called Trefoil system combines multiple FPGAs and SATA disks. Trefoil features a main unit and eight storage subsystems, each with 32 SATA disks, providing 2 PBytes of memory for up to 47 qubits. Sector-level block transfers enable efficient quantum operations such as H, Z, CNOT, and unitary matrices. The results show an H gate for 30 qubits executes in 10 minutes without increased times using parallel processing. Our study advances scalable quantum computing simulations, surmounting memory limitations.
Quantum computing is regarded as the future of computing that hopefully provides exponentially large processing power compared to the conventional digital computing. However, current quantum computers do not have the capability to correct errors caused by environmental noise, so that it is difficult to run useful algorithms that require deep quantum circuits. Therefore, emulation of quantum circuits in digital computers is essential. However, emulation of large quantum circuits requires enormous amount of computations, and leads to a very large processing time. To reduce the processing time, we propose an FPGA emulator with high-bandwidth-memory to emulate quantum Fourier transform (QFT), which is a major part of many quantum algorithms. The proposed FPGA emulator is scalable in terms of both processing speed and the number of qubits, and extendable to multiple FPGAs. We performed QFT emulations up to 30 qubits using two FPGAs. According to the measured results, we have achieved 23.6 ~ 24.5 times speed-up compared to a fully optimized 24-core CPU emulator.
Abstract This paper presents a field-programmable gate array (FPGA) implementation of a quantum circuit simulator capable of processing 30-qubit systems, representing over 1.07 billion quantum states stored in 8 GB of memory. Built on the Xilinx Alveo U55C platform with High Bandwidth Memory (HBM) technology, our system demonstrates deterministic performance through a 16-bank parallel memory distribution architecture integrated with the Qiskit quantum computing framework. We achieved complete verification across all qubit configurations from 1 to 30 qubits, with execution times ranging from 5 milliseconds to approximately 49 minutes. The simulator supports a comprehensive quantum gate library including single-qubit operations (Hadamard, Pauli gates, rotation gates) and multi-qubit gates (CNOT, controlled-Z, Toffoli. Our performance analysis reveals distinct operational regimes where FPGA excels for small-scale circuits (1-12 qubits) but faces scalability challenges beyond 15 qubits when compared to GPU architectures. This work establishes FPGA as a practical platform for quantum algorithm development and circuit verification, particularly valuable for applications requiring deterministic timing and energy-efficient computation. The architecture provides clear pathways for expansion to 31+ qubits through memory configuration enhancements.
The area of quantum circuit simulation has attracted a lot of attention in recent years. However, due to the exponentially increasing computational costs, assessing and validating these models on large datasets poses significant obstacles. Despite plenty of research in quantum simulation, issues such as memory management, system adaptability, and execution efficiency remain unresolved. In this study, we introduce QEA, a state vector-based hardware accelerator that overcomes these difficulties with four key improvements: optimized memory allocation management, open PE, flexible ALU, and simplified CX swapper. To evaluate QEA's capabilities, we implemented and evaluated it on the AMD Alveo U280 board, which uses only 0.534 W of power. Experimental results show that QEA is extremely flexible, supporting a wide range of quantum circuits, has excellent fidelity, making it appropriate for standard quantum emulators, and outperforms powerful CPUs and related works up to153.16×153.16 \times153.16×better in terms of normalized gate speed. This study has considerable potential as a useful approach for quantum emulators in future works.
In recent years, there has been a growing interest in the development of quantum emulation. However, existing studies often struggle to achieve broad applicability, high performance, and efficient resource and memory utilization. To address these challenges, we provide HPQEA, a quantum emulator based on the state-vector emulation approach. HPQEA includes three main features: a high-performance computing core, an optimized controlled-NOT gate computation strategy, and effective utilization of high-bandwidth memory. Verification and evaluation on the Alveo U280 board show that HPQEA can emulate quantum circuits with up to 30 qubits while maintaining high fidelity and low mean square error. It outperforms comparable FPGA-based systems by producing faster execution, supporting a wider range of algorithms, and requiring low hardware resources. Furthermore, it exceeds the Nvidia A100 in normalized gate speed for systems with up to 20 qubits. These results demonstrate the scalability and efficiency of HPQEA as a platform for emulating quantum algorithms.