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IEEE International Conference on Quantum Computing and Engineering (QCE)

Exploiting Block Sparsity for Quantum Circuit Simulation

Innocenzo Fulginiti, Christian B. Mendl

Published Aug 30, 2025• 0 citations
Publisher

Abstract

Simulating quantum circuits on classical hardware remains essential for developing and validating quantum algorithms, particularly in this era of noisy and limited quantum devices. Classical simulation is computationally demanding, due to the exponential growth of the Hilbert space with the number of qubits, because of quantum entanglement. Tensor networks offer a versatile tool for quantum circuit simulation, helping to reduce the associated computational cost. While tensor networks leverage entanglement to represent quantum states in compressed form, many quantum systems also exhibit additional symmetries, such as conserved particle number, that induce block sparsity in quantum states and quantum operators. We demonstrate through numerical experiments how block sparsity can be exploited to enhance the performance of the simulation of quantum circuits, in terms of execution time and memory usage.

DOI
10.1109/qce65121.2025.10480

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Simulating quantum circuits on classical hardware remains essential for developing and validating quantum algorithms, particularly in this era of noisy and limited quantum devices. Classical simulation is computationally demanding, due to the exponential growth of the Hilbert space with the number of qubits, because of quantum entanglement. Tensor networks offer a versatile tool for quantum circuit simulation, helping to reduce the associated computational cost. While tensor networks leverage entanglement to represent quantum states in compressed form, many quantum systems also exhibit additional symmetries, such as conserved particle number, that induce block sparsity in quantum states and quantum operators. We demonstrate through numerical experiments how block sparsity can be exploited to enhance the performance of the simulation of quantum circuits, in terms of execution time and memory usage.
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.
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to special structure in the algorithm or even in the underlying problem. We thus introduce a new simulation method that exploits this sparsity to reduce memory usage and simulation runtime. Moreover, our prototype implementation includes optimizations such as gate (re)scheduling, which amortizes data structure accesses and reduces memory usage. To benchmark our implementation, we run quantum algorithms for factoring, for computing integer and elliptic curve discrete logarithms, and for chemistry. Our simulator successfully runs a factoring instance of a 20-bit number using 102 qubits, and elliptic curve discrete logarithm over a 10-bit curve with 110 qubits. While previous work needed a supercomputer to simulate such instances of factoring, our approach succeeds in less than four minutes using a single core and less than 100 MB of memory. To the best of our knowledge, we are the first to fully simulate a quantum algorithm to compute elliptic curve discrete logarithms.
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 exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.
Abstract Quantum computing promises advantages for problems in physics, chemistry, and optimization, yet current noisy and small-scale devices limit the implementation of large quantum algorithms. Classical simulation therefore remains essential for algorithm design, verification, and performance benchmarking. However, existing Schrödinger- and Feynman-based simulators suffer from exponential scaling or limited oracle integration. Here we present SparQSim, a C++-based, Feynmaninspired simulator that exploits state sparsity to reduce memory consumption and supports registerlevel operations with integrated quantum random access memory (QRAM). Benchmarks from QASMBench and MQTBench show that for circuits with substantial state space sparsity, which represent the core application scenario of SparQSim, the method surpasses Schrödinger style simulators in both runtime and memory efficiency. Moreover, full-process simulations of quantum linear-system solvers yield results consistent with theoretical predictions. SparQSim provides a flexible and scalable platform for efficient simulation and optimization of quantum algorithms.
Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum gates as tensors. For high numbers of qubits, performing tensor multiplications for these simulations becomes quite expensive, since NNN-qubit gates correspond to 2N2^{N}2N-dimensional tensors. One way to accelerate such a simulation is to use field programmable gate array (FPGA) hardware to efficiently compute the matrix multiplications. Though FPGAs can efficiently perform tensor multiplications, they are memory bound, having relatively small block random access memory. One way to potentially reduce the memory footprint of a quantum computing system is to represent it as a tensor network; tensor networks are a formalism for representing compositions of tensors wherein economical tensor contractions are readily identified. Thus we explore tensor networks as a means to reducing the memory footprint of quantum computing systems and broadly accelerating simulations of such systems.