Abstract Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation algorithm and software implementation designed to perform HPC simulation of layers of rotations around a string of Pauli operators. We demonstrate robust scalability of the simulation method on large distributed CPU and GPU systems. Our distributed computation harnessed up to 16384 CPU cores and 512 NVIDIA H100 GPUs, using 32 TB of memory. The simulator significantly outperforms other high-performance libraries, showing a typical speedup of 10-100 for large-scale multi-GPU workloads. As a first application of our approach, we report a numerical experiment aimed at simulating exactly Hamiltonian dynamics of up to 40 qubits to investigate the Trotter error for a quantum chemistry problem. Bounding the Trotter error is important for evaluating the cost of quantum algorithms for chemistry, and rigorous bounds are often conservative, as our simulations confirm. Our software, specifically designed for quantum time evolution applications, is also well equipped to manage circuits that utilize standard gate sets.
Abstract Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation algorithm and software implementation designed to perform HPC simulation of layers of rotations around a string of Pauli operators. We demonstrate robust scalability of the simulation method on large distributed CPU and GPU systems. Our distributed computation harnessed up to 16384 CPU cores and 512 NVIDIA H100 GPUs, using 32 TB of memory. The simulator significantly outperforms other high-performance libraries, showing a typical speedup of 10-100 for large-scale multi-GPU workloads. As a first application of our approach, we report a numerical experiment aimed at simulating exactly Hamiltonian dynamics of up to 40 qubits to investigate the Trotter error for a quantum chemistry problem. Bounding the Trotter error is important for evaluating the cost of quantum algorithms for chemistry, and rigorous bounds are often conservative, as our simulations confirm. Our software, specifically designed for quantum time evolution applications, is also well equipped to manage circuits that utilize standard gate sets.
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum circuits are essential for determining the problem size at which quantum solutions outperform classical methods. In this work, we present a novel hybrid simulation approach, forming a hybrid of a fullstate and a Clifford simulator, specifically designed to address the computational challenges associated with the time evolution of quantum chemistry Hamiltonians. Our method focuses on the efficient emulation of multi-qubit rotations, a critical component of Trotterized Hamiltonian evolution. By optimizing the representation and execution of multi-qubit operations leveraging the Pauli frame, our approach significantly reduces the computational cost of simulating quantum circuits, enabling more efficient simulations. Beyond its impact on chemistry applications, our emulation strategy has broad implications for any computational workload that relies heavily on multi-qubit rotations. By increasing the efficiency of quantum simulations, our method facilitates more accurate and cost-effective studies of complex quantum systems. We quantify the performance improvements and computational savings for this emulation strategy, and we obtain a speedup of a factor ≈18 (≈22 with MPI) for our evaluated chemistry Hamiltonians with 24 qubits. Thus, we evaluate our integration of this emulation strategy into the Intel Quantum SDK, further bridging the gap between theoretical algorithm development and practical quantum software implementations.
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.
Large-scale quantum circuit simulation on high-performance computing (HPC) systems is crucial for developing and verifying quantum algorithms to overcome the limitations of current noisy quantum computers. However, existing simulators face scalability bottlenecks due to memory limits and communication overhead. Many state-of-the-art approaches rely on static circuit partitioning, which makes it difficult to address the exponential growth in problem size as the number of qubits increases. To overcome these challenges, we present ScaleQsim, a highly scalable quantum circuit simulation framework for large-scale HPC systems. ScaleQsim focuses on providing a unified representation of the full qubit state, yet provides scalability through efficient synchronization and communication. ScaleQsim adopts a novel full state vector partitioning strategy that evenly distributes the full state vector across multiple nodes and GPUs. This distributed structure enables efficient parallel gate execution without costly synchronization, and ScaleQsim applies adaptive kernel configuration, which adjusts execution parameters based on GPU resources and task granularity to enhance simulation efficiency. Our evaluation on the Perlmutter supercomputer with up to 512 GPUs demonstrates that ScaleQsim simulates quantum circuits with up to 42 qubits and outperforms state-of-the-art simulators by up to 77.40× across various quantum circuits.
Quantum computer simulators running on classical computers are essential for developing real quantum computers and emerging quantum applications. In particular, state vector simulators, which store a full state vector in memory and update it in every quantum operation, can be used to simulate an arbitrary form of quantum circuits, debug quantum applications, and validate future quantum computers. Since the time and space complexity grows exponentially with the number of qubits and easily exceeds the capability of a single machine, various distributed state vector simulators are developed. However, these are tuned for common CPUs and GPUs, not for ARM CPUs. Therefore, we develop a distributed state vector simulator, mpiQulacs, that is optimized for large-scale simulation on A64FX-based cluster systems. A64FX is a 48-core ARM-based CPU having high-bandwidth memory (HBM2) and also used in one of the world's top supercomputers, Fugaku. As computational optimization, we vectorize qubit operations with Scalable Vector Extension (SVE) to fully utilize its HBM2. To reduce the amount of inter-node communication for scalable simulation, mpiQulacs provides a fused-swap gate that collectively performs multiple swap operations as one operation and a quantum circuit optimizer that automatically adds fused-swap gates to a circuit. We evaluate weak and strong scaling of mpiQulacs with up to 39 qubits on our 512-node A64FX-based cluster system. The result shows that mpiQulacs achieves high-scalability on hundreds of nodes in benchmark and practical quantum circuits, and its performance is comparable with the existing well-known distributed state vector simulators.
Simulating quantum many-body dynamics is important both for fundamental understanding of physics and practical applications for quantum information processing. Therefore, classical simulation methods have been developed so far. Specifically, the Trotter-Suzuki decomposition can analyze a highly complex quantum dynamics, if the number of qubits is sufficiently small so that main memory can store the state vector. However, simulation of quantum dynamics via Trotter-Suzuki decomposition requires a huge number of steps, each of which accesses the state vector, and hence the simulation time becomes impractically long. To settle this issue, we propose a technique to accelerate simulation of quantum dynamics via simultaneous diagonalization of mutually commuting Pauli groups, which is also attracting a lot of attention to reduce the measurement overheads in quantum algorithms. We group the Hamiltonian into mutually commuting Pauli strings, and each of them is diagonalized in the computational basis via a Clifford transformation. Since diagonal operators are applied on the state vector simultaneously with minimum memory access, this method successfully uses performance of highly parallel processors such as Graphics Processing Units (GPU). Compared to both CPU and GPU implementations using fast quantum circuit simulator “qulacs,” the numerical experiments have shown that our method provides a few tens of times acceleration.
Quantum circuit simulation is crucial for the development of quantum algorithms, particularly given the high cost and noise limitations of physical quantum hardware. While full-state quantum circuit simulation is commonly employed for prototyping and debugging, it poses challenges because of the exponential increase in simulation time for large quantum systems. In this work, we propose an extensible framework designed to enhance simulation performance by optimizing both data locality and computational efficiency, thereby addressing these challenges. This framework is seamlessly integrated with an optimizer that restructures quantum circuits and a simulator that adjusts execution strategies for various quantum operations. For the newly developed components, merge booster and diagonal detector, the underlying algorithms are inspired by the principles of quantum entanglement and gate fusion, as well as by the limitations identified in existing third-party simulation libraries. The experiments were conducted on eight DGX-H100 workstations, each equipped with eight NVIDIA H100 GPUs, employing both gate-level and circuit-level benchmarks. The results indicate a speedup of up to 160 times for circuit-level benchmarks and an acceleration of up to 34 times for diagonal-heavy gate-level benchmarks compared to existing simulators. The proposed methodologies are anticipated to deliver more robust and faster quantum circuit simulations, thereby fostering the advancement of novel quantum algorithms.