In the current era of Noisy Intermediate Scale Quantum (NISQ) computing, efficient digital simulation of quantum systems holds significant importance for quantum algorithm development, verification and validation. However, analysis of sparsity within these simulations remains largely unexplored. In this paper, we present a novel observation regarding the prevalent sparsity patterns inherent in quantum circuits. We introduce DiaQ, a new sparse matrix format tailored to exploit this quantum-specific sparsity, thereby enhancing simulation performance. Our contribution extends to the development of libdiaq, a numerical library implemented in C++ with OpenMP for multi-core acceleration and SIMD vectorization, featuring essential mathematical kernels for digital quantum simulations. Furthermore, we integrate DiaQ with SV-Sim, a state vector simulator, yielding substantial performance improvements across various quantum circuits (e.g., ~26.67% for GHZ-28 and ~32.72% for QFT-29 with multi-core parallelization and SIMD vectorization on Frontier). Evaluations conducted on benchmarks from SupermarQ and QASMBench demonstrate that DiaQ represents a significant step towards achieving highly efficient quantum simulations.
In the current era of Noisy Intermediate Scale Quantum (NISQ) computing, efficient digital simulation of quantum systems holds significant importance for quantum algorithm development, verification and validation. However, analysis of sparsity within these simulations remains largely unexplored. In this paper, we present a novel observation regarding the prevalent sparsity patterns inherent in quantum circuits. We introduce DiaQ, a new sparse matrix format tailored to exploit this quantum-specific sparsity, thereby enhancing simulation performance. Our contribution extends to the development of libdiaq, a numerical library implemented in C++ with OpenMP for multi-core acceleration and SIMD vectorization, featuring essential mathematical kernels for digital quantum simulations. Furthermore, we integrate DiaQ with SV-Sim, a state vector simulator, yielding substantial performance improvements across various quantum circuits (e.g., ~26.67% for GHZ-28 and ~32.72% for QFT-29 with multi-core parallelization and SIMD vectorization on Frontier). Evaluations conducted on benchmarks from SupermarQ and QASMBench demonstrate that DiaQ represents a significant step towards achieving highly efficient quantum simulations.
Classical simulation of quantum circuits is critical for the development of implementations of quantum algorithms: it does not require access to specialized hardware, facilitates debugging by allowing direct access to the quantum state, and is the only way to test on inputs that are too big for current NISQ computers. Many quantum algorithms rely on invariants that result in sparsity in the state vector. A sparse state vector simulator only computes with non-zero amplitudes. For important classes of algorithms, this results in an asymptotic improvement in simulation time. While promising prior work has investigated ways to exploit sparsity, it is still unclear what is the best way to scale sparse simulation to modern multi-core architectures. In this work, we address this challenge and present qblaze , a highly optimized sparse state vector simulator based on (i) a compact sorted array representation, and (ii) new, easily parallelizable and highly-scalable algorithms for all quantum operations. Our extensive experimental evaluation shows that qblaze is often orders-of-magnitude more efficient than prior sparse state vector simulators even on a single thread, and also that qblaze scales well to a large number of CPU cores. Overall, our work enables testing quantum algorithms on input sizes that were previously out of reach.
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.
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.
High-performance quantum circuit simulation in a classic HPC is still imperative in the NISQ era. Observing that the major obstacle of scalable state-vector quantum simulation arises from the massively fine-grained irregular data-exchange with remote nodes, in this paper we present SV-Sim to apply the PGAS-based communication models (i.e., direct peer access for intra-node CPUs/GPUs and SHMEM for inter-node CPU/GPU clusters) for efficient generalpurpose quantum circuit simulation. Through an orchestrated design based on device functional pointer, SV-Sim is able to abstract various quantum gates across multiple heterogeneous backends, including IBM/Intel/AMD CPUs, NVIDIA/AMD GPUs, and Intel Xeon Phi, in a unified framework, but still asserting outstanding performance and tractable interface to higher-level quantum programming environments, such as IBM Qiskit, Microsoft Q# and Google Cirq. Circumventing the obstacle from the lack of polymorphism in GPUs and leveraging the device-initiated one-sided communication, SV-Sim can process circuit that are dynamically generated in Python using a single GPU/CPU kernel without the need of expensive JIT or runtime parsing, significantly simplifying the programming complexity and improving performance for QC simulation. This is especially appealing for the variational quantum algorithms given the circuits are synthesized online per iteration. Evaluations on the latest NVIDIA DGX-A100, V100-DGX-2, ALCF Theta, OLCF Spock, and OLCF Summit HPCs show that SV-Sim can deliver scalable performance on various state-of-the-art HPC platforms, offering a useful tool for quantum algorithm validation and verification. SV-Sim has been released at http://github.com/pnnl/sv-sim. A version specially tweaked for Q#/QDK is also provided.
The classical simulation of quantum algorithms is a crucial tool for circuit development, testing, and validation. Although acceleration using GPUs significantly reduces simulation time, most high-performance simulators rely on vendor-specific frameworks that target data-center hardware. To broaden access to quantum simulation, this work proposes a vendor-agnostic approach targeting the integrated GPUs commonly found in consumer-grade laptops. A primary challenge in state-vector simulation is its inherently poor spatial locality, which creates a memory bandwidth bottleneck. Consequently, baseline implementations experience a severe degradation in relative GPU speedup as the number of simulated qubits increases. To address this limitation, we introduce a state partitioning optimization that reorganizes the quantum state vector to maximize the last-level cache locality and minimize costly main memory fetches. We evaluate this strategy using a Quantum Phase Estimation algorithm across diverse architectures from Intel, AMD, and Apple. The experimental results demonstrate that the proposed optimization successfully mitigates performance degradation at larger qubit scales. In particular, for a 28-qubit simulation, the optimization reversed a performance deficit on an Intel Core i5, improving the GPU speedup over the CPU from 0.95x to 1.89x, and increased the Apple M1 Pro speedup from 3.71x to 5.88x. Overall, this approach yields consistent execution time improvements, demonstrating the viability of integrated GPUs for efficient quantum circuit simulation.
Quantum simulation plays a critical role in advancing our understanding and development of quantum algorithms, quantum computing hardware, and quantum information science. Despite the availability of various quantum circuit simulators, they often face challenges in terms of maintainability and extensibility. In this paper, we introduce Lightweight Functional Quantum Simulator (LFQS), a compilation-based framework that addresses these issues by leveraging an intermediate language to synthesize efficient quantum simulators in C and CUDA. The intermediate language exploits the underlying structured sparsity behind the matrix representation of quantum gates. Our framework generates efficient code for multi-core CPUs and GPUs and outperforms state-of-the-art simulators, such as Qiskit, Catalyst, and QuEST, as well as a representative of dense tensor frameworks, NumPy, in both micro-benchmark and macro-benchmark circuits.