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arXiv:2401.06188 · Future Generation Computer Systems

State of practice: Evaluating GPU performance of state vector and tensor network methods

Marzio Vallero, Paolo Rech, Flavio Vella

Published May 31, 2025• 4 citations
arXivHTMLPDF

Abstract

The frontier of quantum computing (QC) simulation on classical hardware is quickly reaching the hard scalability limits for computational feasibility. Nonetheless, there is still a need to simulate large quantum systems classically, as the Noisy Intermediate Scale Quantum (NISQ) devices are yet to be considered fault tolerant and performant enough in terms of operations per second. Each of the two main exact simulation techniques, state vector and tensor network simulators, boasts specific limitations. This article investigates the limits of current state-of-the-art simulation techniques on a test bench made of eight widely used quantum subroutines, each in different configurations, with a special emphasis on performance. We perform both single process and distributed scaleability experiments on a supercomputer. We correlate the performance measures from such experiments with the metrics that characterise the benchmark circuits, identifying the main reasons behind the observed performance trends. Specifically, we perform distributed sliced tensor contractions, and we analyse the impact of pathfinding quality on contraction time, correlating both results with topological circuit characteristics. From our observations, given the structure of a quantum circuit and the number of qubits, we highlight how to select the best simulation strategy, demonstrating how preventive circuit analysis can guide and improve simulation performance by more than an order of magnitude.

DOI
10.1016/j.future.2025.107927

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The frontier of quantum computing (QC) simulation on classical hardware is quickly reaching the hard scalability limits for computational feasibility. Nonetheless, there is still a need to simulate large quantum systems classically, as the Noisy Intermediate Scale Quantum (NISQ) devices are yet to be considered fault tolerant and performant enough in terms of operations per second. Each of the two main exact simulation techniques, state vector and tensor network simulators, boasts specific limitations. This article investigates the limits of current state-of-the-art simulation techniques on a test bench made of eight widely used quantum subroutines, each in different configurations, with a special emphasis on performance. We perform both single process and distributed scaleability experiments on a supercomputer. We correlate the performance measures from such experiments with the metrics that characterise the benchmark circuits, identifying the main reasons behind the observed performance trends. Specifically, we perform distributed sliced tensor contractions, and we analyse the impact of pathfinding quality on contraction time, correlating both results with topological circuit characteristics. From our observations, given the structure of a quantum circuit and the number of qubits, we highlight how to select the best simulation strategy, demonstrating how preventive circuit analysis can guide and improve simulation performance by more than an order of magnitude.
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.
Classical simulation of quantum systems is indispensable for validating quantum algorithms, benchmarking near-term quantum hardware, and understanding quantum advantage boundaries. As quantum systems scale beyond 50 qubits -- entering the regime where exact statevector simulation requires 2^n complex amplitudes (16 petabytes for n=50) -- approximate and structure-exploiting classical simulation methods become essential. This paper proposes the Classical Quantum Simulation Benchmark (CQSB) framework, a systematic evaluation of six simulation techniques -- statevector simulation, tensor network contraction (MPS and MERA), Clifford circuit simulation, stabiliser state methods, Monte Carlo wavefunction simulation, and approximate tensor network methods -- across 48 quantum circuit benchmarks spanning 8 to 127 qubits. CQSB introduces the Simulation Efficiency Index (SEI) combining accuracy, runtime, and memory usage, and identifies the optimal simulation regime for each technique. Key results: MPS tensor networks achieve exact simulation to 127 qubits for circuits with bond dimension χ <= 512; Clifford simulation scales to 10,000 qubits in O(n2) time; approximate tensor network contraction produces fidelity > 0.95 for 72-qubit random circuits within 4.8 hours on a 256-GPU cluster. The framework provides simulation regime selection guidance and an open benchmark suite for the quantum computing community.
Executing large quantum circuits is not feasible using the currently available NISQ (noisy intermediate-scale quantum) devices. The high costs of using real quantum devices make it further challenging to research and develop quantum algorithms. As a result, performing classical simulations is usually the preferred method for researching and validating large-scale quantum algorithms. However, these simulations require a huge amount of resources, as each additional qubit exponentially increases the computational space required. Distributed Quantum Computing (DQC) is a promising alternative to reduce the resources required for simulating large quantum algorithms at the cost of increased runtime. This study presents a comparative analysis of two simulation methods: circuit-splitting and full-circuit execution using distributed memory, each having a different type of overhead. The first method, using CutQC, cuts the circuit into smaller subcircuits and allows us to simulate a large quantum circuit on smaller machines. The second method, using Qiskit-Aer-GPU, distributes the computational space across a distributed memory system to simulate the entire quantum circuit. Results indicate that full-circuit executions are faster than circuit-splitting for simulations performed on a single node. However, circuit-splitting simulations show promising results in specific scenarios as the number of qubits is scaled.
Executing large quantum circuits is not feasible using the currently available NISQ (noisy intermediate-scale quantum) devices. The high costs of using real quantum devices make it further challenging to research and develop quantum algorithms. As a result, performing classical simulations is usually the preferred method for researching and validating large-scale quantum algorithms. However, these simulations require a huge amount of resources, as each additional qubit exponentially increases the computational space required. Distributed Quantum Computing (DQC) is a promising alternative to reduce the resources required for simulating large quantum algorithms at the cost of increased runtime. This study presents a comparative analysis of two simulation methods: circuit-splitting and full-circuit execution using distributed memory, each having a different type of overhead. The first method, using CutQC, cuts the circuit into smaller subcircuits and allows us to simulate a large quantum circuit on smaller machines. The second method, using Qiskit-Aer-GPU, distributes the computational space across a distributed memory system to simulate the entire quantum circuit. Results indicate that full-circuit executions are faster than circuit-splitting for simulations performed on a single node. However, circuit-splitting simulations show promising results in specific scenarios as the number of qubits is scaled.
In the current NISQ (Noisy Intermediate-Scale Quantum) era, simulating and verifying noisy quantum circuits is crucial but faces challenges such as quantum state explosion and complex noise representations, constraining simulation and equivalence checking to circuits with a limited number of qubits. This paper introduces an approximation algorithm for simulating and assessing the equivalence of noisy quantum circuits, specifically designed to improve scalability under low-noise conditions. The approach utilizes a novel tensor network diagram combined with singular value decomposition to approximate the tensors of quantum noises. The implementation is based on Google’s TensorNetwork Python package for contraction. Experimental results on realistic quantum circuits with realistic hardware noise models indicate that our algorithm can simulate and check the equivalence of QAOA (Quantum Approximate Optimization Algorithm) circuits with around 200 qubits and 20 noise operators, outperforming state-of-the-art approaches in scalability and speed.
Tensor network contraction is a fundamental operation for dealing with high-dimensional data, which is now widely used in classical simulations of quantum circuits. To improve the performance of simulations, existing methods are implemented by optimizing contraction methods. However, with the increasing size of the tensor network, the contraction efficiency of these methods is difficult to satisfy the performance requirements and also suffers from the challenge of contracting tensor tasks that exceed GPU memory. In this paper, we propose a high-performance chunking method for tensor contraction. By chunking the given tensor, we obtain small tensors or vectors assign the corresponding threads, and contract them in parallel through the GPU. Solving high-order tensor contractions using distributed tensor contraction methods. Compared to the Einsum, our method achieves an average speedup of 22.28×. We also have experiments for large-scale tensor network contractions and our method achieves an average speedup of 13.56× compared to Tensordot.