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arXiv:1801.01037 · Bulletin of the American Physical Society

Distributed Memory Techniques for Classical Simulation of Quantum Circuits

Ryan LaRose

Published Jan 2, 2018• 7 citations
arXivHTMLPDF

Abstract

In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed matrix-vector multiplication with one-dimensional partitioning and discuss the shortcomings of this method due to the exponential memory requirements in simulating quantum computers. We then describe a more efficient method that stores only the $2^n$ amplitudes of the $n$ qubit state vector $|ψ\rangle$ and optimize its single node performance. In our multi-node implementation, we use a single amplitude communication protocol that maximizes the number of qubits able to be simulated and minimizes the ratio of qubits that require communication to those that do not, and we present an algorithm for efficiently determining communication pairs among processors. We simulate up to 30 qubits on a single node and 33 qubits with the state vector partitioned across 64 nodes. Lastly, we discuss the advantages and disadvantages of our communication scheme, propose potential improvements, and describe other optimizations such as storing the state vector non-sequentially in memory to map communication requirements to idle qubits in the circuit.

DOI
10.48550/arxiv.1801.01037

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In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed matrix-vector multiplication with one-dimensional partitioning and discuss the shortcomings of this method due to the exponential memory requirements in simulating quantum computers. We then describe a more efficient method that stores only the 2n2^n2n amplitudes of the nnn qubit state vector ∣ψ⟩|ψ\rangle∣ψ⟩ and optimize its single node performance. In our multi-node implementation, we use a single amplitude communication protocol that maximizes the number of qubits able to be simulated and minimizes the ratio of qubits that require communication to those that do not, and we present an algorithm for efficiently determining communication pairs among processors. We simulate up to 30 qubits on a single node and 33 qubits with the state vector partitioned across 64 nodes. Lastly, we discuss the advantages and disadvantages of our communication scheme, propose potential improvements, and describe other optimizations such as storing the state vector non-sequentially in memory to map communication requirements to idle qubits in the circuit.
Software quantum simulators are essential tools for designing and testing quantum algorithms on classical computing architectures, especially given the current limitations of physical quantum hardware. This work focuses on studying and evaluating memory management strategies for scalable quantum state simulation. We examine full-state representation, dynamic state pruning, shared-memory parallelization with OpenMP, distributed memory execution using MPI, and error-bounded floating-point compression with ZFP. These techniques are implemented in a prototype simulator and assessed using the quantum Fourier transform as a benchmark, with performance compared against leading open-source simulators such as Intel-QS, QuEST, and qsim. The results show the trade-offs between computational overhead and memory efficiency, and demonstrate that hybrid approaches combining distributed memory and compression can significantly extend the number of qubits that can be simulated. This work contributes practical insights for improving the scalability of software quantum simulators on classical hardware through optimized memory usage.
Efficient full-state quantum circuit simulations are useful tools for the design of quantum algorithms. Multi-node distributed systems are commonly employed as such simulations require a large amount of computation power and memory space. In distributed systems, communication overhead can be the performance bottleneck. This paper presents a distributed simulation framework called QuanTrans. A quantum circuit is composed of many levels of quantum gates. The simulation is conducted level by level. For circuits with particular structures, it employs a hybrid simulation approach to replace intermediate multi-level communications with one level of final merge operation, whose communication volume is comparable to that of one level of simulation in previous work. A circuit without such structures is sliced to find applicable sub-circuits with a single or multiple consecutive level(s). One level of communication is required for each sub-circuit, so we further propose a polynomial-time optimal circuit slicing algorithm. It can transform any circuit such that the number of sliced sub-circuits is the minimum after transformation. Experimental results show that QuanTrans can effectively reduce communication time and simulation time.
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.
Software quantum simulators are the most accessible tools for designing and testing quantum algorithms. This paper presents a comprehensive approach to building a software-based quantum simulator based on classical computing architectures. We explore fundamental quantum computing concepts, including state vector representations, quantum gates, and memory management techniques. The simulator prototype implements various memory optimization strategies, such as full-state representation, dynamic state pruning, and shared memory parallelization with OpenMP and distributed memory models using MPI. Additionally, data compression techniques, like ZFP, are explored to enhance simulation performance by reducing memory footprint. The results are validated through performance comparisons with leading open-source quantum simulators, such as Intel-QS, QuEST, and qsim. Our findings highlight the trade-offs between computational overhead and memory efficiency. This demonstrates that a hybrid approach using distributed memory and compression offers the best scalability for simulating large quantum systems. This work provides a foundation for developing efficient quantum simulators supporting more complex quantum algorithms on classical hardware.
Quantum computer simulators are widely used for evaluating the performance of quantum algorithms.In quantum computer simulations, the amount of necessary memory increases exponentially with the number of quantum bits.When performing quantum computer simulations with distributed memory parallel computers, many communications between two nodes are needed.The communication costs between two nodes increase exponentially with the number of quantum bits.In this paper, a fast simulation algorithm for distributed memory parallel computers is proposed.The method can reduce communication costs between nodes by inserting swap gates to the original quantum circuit.The performance of the proposed method was evaluated by experiments.In the experiments, a Ripple carry adder circuit, a Quantum Fourier Transform circuit, a Modular addition circuit, and a Modular multiplication circuit were used.As a result, it has been shown that the proposed method can reduce communication costs.