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Quantum Frontiers Journal

Classical Simulation Techniques for Large-Scale Quantum Systems

Pierre Lindberg

Published Jul 14, 2025• 0 citations
OpenAlex

Abstract

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.

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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.
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Quantum circuit simulation at scale demands high-performance computing (HPC) frameworks capable of distributing exponentially growing state vectors and tensor networks across heterogeneous compute clusters. As quantum algorithm development accelerates and circuits approach 50-100 qubits in practical workloads, simulation bottlenecks shift from single-node memory constraints to inter-node communication overhead, GPU memory bandwidth, and framework-level scheduling inefficiencies. This paper proposes the HPC Quantum Simulation Framework Benchmark (HQSFB), a systematic evaluation of five leading quantum simulation frameworks -- Qiskit Aer, Cirq on GCP, cuQuantum (NVIDIA), QuEST, and Intel Quantum Simulator (IQS) -- across six HPC deployment configurations spanning single-GPU workstations to 512-GPU supercomputer partitions. HQSFB introduces the Framework Efficiency Score (FES) combining simulation throughput, GPU utilisation, inter-node communication overhead, and memory scaling efficiency. Key results: cuQuantum achieves the highest FES (0.924) with 94.2% GPU utilisation and 42x speedup over CPU baseline at 512 GPUs; QuEST achieves the best memory scaling efficiency (0.962) for distributed statevector simulation; Qiskit Aer provides the broadest circuit compatibility with FES = 0.842. The framework provides HPC configuration guidance and an open benchmark suite for quantum simulation infrastructure planning.
Quantum computer simulators are an indispensable tool for prototyping quantum algorithms and verifying the functioning of existing quantum computer hardware. The current largest quantum computers feature more than one thousand qubits, challenging their classical simulators. Statevector quantum simulators are challenged by the exponential increase of representable quantum states with respect to the number of qubits, making more than fifty qubits practically unfeasible. A more appealing approach for simulating quantum computers is adopting the tensor network approach, whose memory requirements fundamentally depend on the level of entanglement in the quantum circuit, and allows simulating the current largest quantum computers. This work investigates and evaluates the CUDA-Q tensor network simulators on an Nvidia Grace Hopper system, particularly the Matrix Product State (MPS) formulation. We compare the performance of the CUDA-Q state vector implementation and validate the correctness of MPS simulations. Our results highlight that tensor network-based methods provide a significant opportunity to simulate large-qubit circuits, albeit approximately. We also show that current GPUaccelerated computation cannot fully utilize GPU efficiently in the case of MPS simulations.
Recent years have seen a rapid growth in literature presenting new methods for simulating non-Clifford quantum circuits with classical hardware. These methods span a range of approaches, including stabiliser decomposition and tensor contraction techniques, varying in efficiency depending on circuit class, depth, non-Clifford gate count, and other metrics. A notable limitation of this literature is the lack of a standardised approach to benchmarking, with each new paper outlining its own specification, simulating its own set of circuits on the authors' own hardware. This paper seeks to address this issue by presenting a standardised and canonical benchmark suite and infrastructure for quantifying the efficiency of non-Clifford classical simulators, with a consistent dataset of circuits and providing consistent (virtual) hardware, thereby enabling a fair comparison of results.
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and software. Tensor networks have become forefront mathematical tools for these tasks. Here we introduce a method to approximately simulate quantum circuits using sparsely-populated tensors. We describe a sparse tensor data structure that can represent quantum states with no underlying symmetry, and outline algorithms to efficiently contract and truncate these tensors. We show that the data structure and contraction algorithm are efficient, leading to expected runtime scalings versus qubit number and circuit depth. Our results motivate future research in optimization of sparse tensor networks for quantum simulation.
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.