Evaluating quantum algorithms at utility-scale—involving more than 100 qubits—is a key step toward advancing real-world applications of quantum computing. In this study, we benchmark seven state-of-the-art quantum emulators employing techniques such as tensor networks, matrix product states (MPS), decision diagrams, and factorized ket based methods, running on CPU based hardware and focusing on effectively exact simulations. Performance is assessed on 13 benchmark circuits from the MQTBench library, spanning circuit sizes from 4 to 1,024 qubits. Our results reveal that MPS-based emulators outperform other approaches overall, successfully solving 8 benchmarks up to the maximum size of 1,024 qubits and 12 benchmarks up to at least 100 qubits in less than 5 minutes. We find evidence that all circuits except a random one can be simulated in polynomial time. This work demonstrates that quantum emulators can faithfully simulate a broad range of large and complex universal quantum circuits with high fidelity, far beyond the limits of statevector simulators and today’s quantum hardware.
Evaluating quantum algorithms at utility-scale—involving more than 100 qubits—is a key step toward advancing real-world applications of quantum computing. In this study, we benchmark seven state-of-the-art quantum emulators employing techniques such as tensor networks, matrix product states (MPS), decision diagrams, and factorized ket based methods, running on CPU based hardware and focusing on effectively exact simulations. Performance is assessed on 13 benchmark circuits from the MQTBench library, spanning circuit sizes from 4 to 1,024 qubits. Our results reveal that MPS-based emulators outperform other approaches overall, successfully solving 8 benchmarks up to the maximum size of 1,024 qubits and 12 benchmarks up to at least 100 qubits in less than 5 minutes. We find evidence that all circuits except a random one can be simulated in polynomial time. This work demonstrates that quantum emulators can faithfully simulate a broad range of large and complex universal quantum circuits with high fidelity, far beyond the limits of statevector simulators and today’s quantum hardware.
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.
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.
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum kernel framework using a Matrix Product State (MPS) simulator and employ it to perform a classification task with 165 features and 6400 training data points, well beyond the scale of any prior work. We make use of a circuit ansatz on a linear chain of qubits with increasing interaction distance between qubits. We assess the MPS simulator performance on CPUs and GPUs and, by systematically increasing the qubit interaction distance, we identify a crossover point beyond which the GPU implementation runs faster. We show that quantum kernel model performance improves as the feature dimension and training data increases, which is the first evidence of quantum model performance at scale.
The increasing complexity of quantum algorithms and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware underscore the importance of efficient classical simulators. To support informed decision-making by users of quantum circuit simulators, we benchmark seven statevector-based quantum circuit simulators (Qiskit, Qulacs, Qibo, Qsimov, Cirq, Pennylane and the Intel Quantum Simulator (IQS)) on a multicore node of the Lusitania high-performance computing (HPC) system. We evaluate their performance in terms of execution time, memory usage and core scalability using Grover’s algorithm, the quantum Fourier transform (QFT), and quantum volume (QV) circuits, across qubit counts ranging from 3 to 30. Our results reveal that Qulacs offers the best performance for circuits below 22 qubits, while Qiskit becomes the fastest for larger and more complex circuits. Qiskit and Qulacs achieve the most efficient parallel performance across multiple cores, while others display limited scaling benefits. IQS shows the lowest memory consumption in QFT and QV benchmarks for systems under 24 qubits; however, it suffers from higher execution times, particularly for Grover’s algorithm. The experimental implementation of Qsimov consistently underperforms in both runtime and scalability; for this reason, it is employed as a baseline in our measurements, serving to highlight the importance of performance optimizations in statevector-based quantum circuit simulators. Previous findings provide a comprehensive performance landscape to guide researchers in selecting appropriate simulators for both standard and large-scale quantum workloads on HPC infrastructures.
Quantum Hamiltonian simulation is one of the most promising applications of quantum computing and forms the basis for many quantum algorithms. Benchmarking them is an important gauge of progress in quantum computing technology. We present a methodology and software framework to evaluate various facets of the performance of gate-based quantum computers on Trotterized quantum Hamiltonian evolution. We propose three distinct modes for benchmarking: (i) comparing simulation on a real device to that on a noiseless classical simulator, (ii) comparing simulation on a real device with exact diagonalization results, and (iii) using scalable mirror circuit techniques to assess hardware performance in scenarios beyond classical simulation methods. We demonstrate this framework on five Hamiltonian models from the HamLib library: the Fermi and Bose-Hubbard models, the transverse field Ising model, the Heisenberg model, and the Max3SAT problem. Experiments were conducted using Qiskit's Aer simulator, BlueQubit's CPU cluster and GPU simulators, and IBM's quantum hardware. Our framework, extendable to other Hamiltonians, provides comprehensive performance profiles that reveal hardware and algorithmic limitations and measure both fidelity and execution times, identifying crossover points where quantum hardware outperforms CPU/GPU simulators.
This article presents a comprehensive study of the performance of quantum circuit simulation using the Matrix Product State (MPS) method within Qiskit Aer. The primary focus is on comparing the computational efficiency of implementations on central processing unit (CPU) and graphics processing unit (GPU) across various simulation platforms. Four key quantum algorithms are experimentally examined: the Variational Quantum Eigensolver (VQE), the Quantum Fourier Transform (QFT), the Quantum Approximate Optimization Algorithm (QAOA), and the Greenberger– Horne–Zeilinger (GHZ) state. For each algorithm, graphs are constructed showing the dependence of execution time on the number of qubits and the type of simulator. A single diagram is also provided to compare all four algorithms using the MPS method in Qiskit Aer. The results indicate that although the MPS simulator in Qiskit Aer is currently implemented only for CPU, it outperforms the traditional statevector simulator for low-entanglement circuits. At the same time, the lack of GPU acceleration limits the scalability of the MPS simulator. Analysis shows that implementing hardware acceleration of SVD operations using NVIDIA's cuQuantum and cuTensorNet libraries can provide a speedup of up to seven times. A comparative analysis of GPU implementations in Qiskit Aer and CUDA-Q is also conducted, including libraries such as cuStateVec, LAPACK, and cuSOLVER. Graphs are created to demonstrate the strengths and weaknesses of the simulators and simulation methods in Qiskit Aer. Notably, the MPS method remains one of the fastest by computation speed on CPU, but is sometimes surpassed by other methods on GPU. Further optimization directions for MPS are proposed, including the development of a hybrid CPU/GPU architecture and the utilization of modern GPU libraries to accelerate critical operations. Keywords: quantum computing, quantum simulation, Qiskit Aer, MPS, statevector, cudaq.