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MPI-Batched TBPM: A Distributed-Memory Framework for Large-Scale Quantum Simulations

Zewen Wu, Shengjun Yuan

Published Dec 8, 2025• 0 citations
Publisher

Abstract

The Tight-Binding Propagation Method (TBPM) is a robust computational framework for large-scale quantum simulations with linear scaling in memory and computational time. Building upon shared-memory implementations, this study presents an MPI-accelerated batched TBPM algorithm to exploit distributed-memory high-performance computing systems through domain decomposition and cross-node parallel execution. The approach distributes both the Hamiltonian matrix and wave function states across multiple nodes, enabling memory aggregation and simultaneous utilization of computational resources throughout clusters. The maximum tractable system size is determined primarily by the number of available supercomputing nodes. The batched processing strategy transforms the computational characteristics by reducing matrix access frequency and enhancing computational intensity by a factor of 64, shifting the algorithm from memory-bound to compute-bound regimes. Comprehensive benchmarks on graphene and twisted bilayer graphene demonstrate substantial speedup and memory scalability improvements. Super-linear speedup is consistently observed across both systems, attributed to superior cache efficiency when local Hamiltonian partitions fit within the Last Level Cache, confirming the efficiency and broad applicability of this MPIbased distributed architecture for ultra-large-scale tight-binding calculations.

DOI
10.36227/techrxiv.176523425.53646593/v1

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The Tight-Binding Propagation Method (TBPM) is a robust computational framework for large-scale quantum simulations with linear scaling in memory and computational time. Building upon shared-memory implementations, this study presents an MPI-accelerated batched TBPM algorithm to exploit distributed-memory high-performance computing systems through domain decomposition and cross-node parallel execution. The approach distributes both the Hamiltonian matrix and wave function states across multiple nodes, enabling memory aggregation and simultaneous utilization of computational resources throughout clusters. The maximum tractable system size is determined primarily by the number of available supercomputing nodes. The batched processing strategy transforms the computational characteristics by reducing matrix access frequency and enhancing computational intensity by a factor of 64, shifting the algorithm from memory-bound to compute-bound regimes. Comprehensive benchmarks on graphene and twisted bilayer graphene demonstrate substantial speedup and memory scalability improvements. Super-linear speedup is consistently observed across both systems, attributed to superior cache efficiency when local Hamiltonian partitions fit within the Last Level Cache, confirming the efficiency and broad applicability of this MPIbased distributed architecture for ultra-large-scale tight-binding calculations.
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.
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.
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Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.
Quantum computing holds great potential to accelerate the process of solving complex combinatorial optimization problems. The Distributed Quantum Approximate Optimization Algorithm (DQAOA) addresses high-dimensional, dense problems using current quantum computing techniques and high-performance computing (HPC) systems. In this work, we improve the scalability and efficiency of DQAOA through advanced problem decomposition and parallel execution using message passing on the Frontier CPU/GPU supercomputer. Our approach ensures efficient quantum-classical workload management by distributing large problem instances across classical and quantum resources. Experimental results demonstrate that enhanced decomposition strategies and GPU-accelerated quantum simulations significantly improve DQAOA's performance, achieving up to 10x speedup over CPU-based simulations. This advancement enables better scalability for large problem instances, supporting the practical deployment of GPU systems for hybrid quantum-classical applications. We also highlight ongoing integration efforts using the Quantum Framework (QFw) to support future HPC-quantum computing systems.