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IEEE International Conference on Quantum Computing and Engineering (QCE)

mpiQulacs: A Scalable Distributed Quantum Computer Simulator for ARM-based Clusters

Akihiro Tabuchi, Satoshi Imamura, Masafumi Yamazaki, Takumi Honda, Akihiko Kasagi, Hiroshi Nakao, Naoto Fukumoto, Kohta Nakashima

Published Sep 17, 2023• 10 citations
Publisher

Abstract

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.

DOI
10.1109/qce57702.2023.00110

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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.
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, are available to simulate an arbitrary form of quantum circuits, debug quantum applications, and validate future quantum computers. However, the time and space complexity grows exponentially with the number of qubits and easily exceeds the capability of a single machine. Therefore, we develop a distributed state vector simulator, mpiQulacsmpiQulacsmpiQulacs, that is optimized for large-scale simulation on A64FX-based cluster systems. A64FX is an ARM-based CPU that is also equipped in the world's top Fugaku supercomputer. We evaluate weak and strong scaling of mpiQulacs with up to 36 qubits on a new 64-node A64FX-based cluster system named TodorokiTodorokiTodoroki. By comparing mpiQulacs with existing distributed state vector simulators, we show that mpiQulacs achieves the highest performance for large-scale simulation on tens of nodes while sustaining a nearly ideal scalability. Besides, we define a new metric, quantumB/Fratioquantum B/F ratioquantumB/Fratio, and use it to demonstrate that mpiQulacs running on Todoroki fits the requirements of distributed state vector simulation rather than the existing simulators running on general purpose CPU-based or GPU-based cluster systems.
Advances in quantum simulator technology are increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially with respect to the number of qubits; furthermore, in a variational quantum algorithm, the large number of repeated runs by classical optimization is also a heavy load. This problem has been addressed by preparing numerous computing nodes or simulation frameworks that operate effectively. This study aimed to accelerate quantum simulation using two newly proposed methods: to efficiently utilize limited computational resources by adjusting the ratio of the MPI and distributed processing parallelism corresponding to the target problem settings and to slim down the Hamiltonian by considering the effect of accuracy on the calculation result. Ground-state energy calculations of a fermionic model were performed using a variational quantum eigensolver (VQE) on an HPC cluster with up to 1024 FUJITSU Processor A64FX connected to each other by InfiniBand; the processor is also used on supercomputer Fugaku. We achieved 200 times higher speed over VQE simulations and demonstrated 32 qubits ground-state energy calculations in acceptable time. This result indicates that > 30 qubit state vector simulations can be realistically utilized for further research on variational quantum algorithms.
Quantum circuit simulations play a critical role in bridging the gap between theoretical quantum algorithms and their practical realization on physical quantum hardware, yet they face computational challenges due to the exponential growth of quantum state spaces with increasing qubit size. This work presents PennyLane-Lightning MPI, an MPI-based extension of the PennyLane-Lightning suite, developed to enable scalable quantum circuit simulations through parallelization of quantum state vectors and gate operations across distributed-memory systems. The core of this implementation is an index-dependent, gate-specific parallelization strategy, which fully exploits the characteristic of individual gates as well as the locality of computation associated with qubit indices in partitioned state vectors. Benchmarking tests with single gates and well-designed quantum circuits show that the present method offers advantages in performance over general methods based on unitary matrix operations and exhibits excellent scalability, supporting simulations of up to 41-qubit with hundreds of thousands of parallel processes. Being equipped with a Python plug-in for seamless integration to the PennyLane framework, this work contributes to extending the PennyLane ecosystem by enabling high-performance quantum simulations in standard multi-core CPU clusters with no library-specific requirements, providing a back-end resource for the cloud-based service framework of quantum computing that is under development in the Republic of Korea.
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.
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 computing simulation on a classical computer is difficult due to the exponential runtime and memory overhead. Previous work addresses the difficulty by utilizing multiple Graphical Processing Units (GPUs) and multi-node computers. GPUs are efficient for handling runtime issues but have limited total accessible memory space. Meanwhile, the memory of a multi-node computer can be scaled to the petabytes order, but its bandwidth for access from host computers (CPUs) is narrow. To simultaneously accelerate simulation and enlarge the total memory space, we propose a heterogeneous parallelization approach by combining GPUs and CPUs. Our simulator allocates memory to the GPUs first, and then to the CPUs. It thus accelerates simulation by using the full capabilities of the GPUs if memory for the simulation fits in the GPUs on a cluster. Allocating memory to the CPUs reduces benefits of the GPUs but enlarges the capacity of qubits in the simulation. In such case, it can exploit the memory of the GPUs to add one more qubit in the simulation if the size of memory in a node is the power of two (such as 512GB). We show empirical performance evaluations of our simulator in a distributed environment of POWER9.