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HybriD-GM: A Framework for Quantum Computing Simulation Targeted to Hybrid Parallel Architectures

Anderson Ávila, Hélida Santos, Anderson Paiva Cruz, Samuel Xavier‐de‐Souza, Giancarlo Lucca, Bruno Moura, Adenauer Yamin, Renata Reiser

Published Mar 14, 2023• 5 citations
Publisher

Abstract

This paper presents the HybriD-GM model conception, from modeling to consolidation. The D-GM environment is also extended, providing efficient parallel executions for quantum computing simulations, targeted to hybrid architectures considering the CPU and GPU integration. By managing projection operators over quantum structures, and exploring coalescing memory access patterns, the HybriD-GM model enables granularity control, optimizing hardware resources in distributed computations organized as tree data structures. In the HybriD-GM evaluation, simulations of Shor's and Grover's algorithms achieve significant performance improvements in comparison to the previous D-GM version, and also with other related works, for example, LIQUi|⟩ and ProjectQ simulators.

DOI
10.3390/e25030503

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This paper presents the HybriD-GM model conception, from modeling to consolidation. The D-GM environment is also extended, providing efficient parallel executions for quantum computing simulations, targeted to hybrid architectures considering the CPU and GPU integration. By managing projection operators over quantum structures, and exploring coalescing memory access patterns, the HybriD-GM model enables granularity control, optimizing hardware resources in distributed computations organized as tree data structures. In the HybriD-GM evaluation, simulations of Shor's and Grover's algorithms achieve significant performance improvements in comparison to the previous D-GM version, and also with other related works, for example, LIQUi|⟩ and ProjectQ simulators.
Currently quantum computers require specialized hardware to be used, until they become more feasibly the testing of quantum algorithms is done by simulation, which is a task of high temporal and spacial complexity. To address this issue, the HybriD-GM simulator, and many others around the world, are under research and improvement, this paper is an ongoing work on improvements for the multi-core support of the HybriD-GM simulator, the experiments are done with the Shor and Grover algorithms, while varying the number of cores and qubits for each, to improve the scalability the removal of critical regions by the usage of tasks and other OpenMP resources is exploited, and the study about the impact of others variables on the simulator is already planned, as well improvements for future works on the GPU, and GPU-CPU approaches and expansion to distributed computing for horizontal scalability of the system.
Exponential increase and global access to read/write memory states in quantum computing (QC) simulation limit both the number of qubits and quantum transformations which can be currently simulated. Although QC simulation is parallel by nature, spatial and temporal complexity are major performance hazards, making this a nontrivial application for high performance computing. A new methodology employing reduction and decomposition optimizations has shown relevant results, but its GPU implementation could be further improved. In this work, we develop a new kernel for in situ GPU simulation that better explores its resources without requiring further hardware. Shor’s and Grover’s algorithms are simulated up to 25 and 21 qubits respectively and compared to our previous version, to [Formula: see text] simulator and to ProjectQ framework, showing better results with relative speedups up to 4.38×, 3357.76× and 333× respectively.
The simulation of algorithms from quantum computing is currently the most affordable solution for development of new applications. Due to the high computational cost of such simulation, solutions towards novel features that increase the performance are always desired. This work proposes an extension for the D-GM's simulation framework, establishing the support for GPU-aware distributed quantum simulation. The project explores the concepts of heterogeneous computing, merging distributed and GPU computing in a single programming environment. Our results comprehend the distributed simulation of systems comprised by Hadamard transformations up to 21 qubits. Detailed analysis and a performance comparison between PyCUDA and JCUDA frameworks for our application are discussed. This work is a significant step towards the ultimate goal of our project, which is the hybrid simulation of quantum algorithms, i.e., exploring multi-core CPUs and GPUs distributed along a cluster, achieving scalability when larger systems are simulated.
The D-GM execution environment improves distributed simulation of quantum algorithms in heterogeneous computing environments comprising both multi-core CPUs and GPUs. The main contribution of this work consists in the optimization of the environment VirD-GM, conceived in three steps: ( i ) the theoretical studies and implementation of the abstractions of the Mixed Partial Process defined in the qGM model, focusing on the reduction of the memory consumption regarding multidimensional QTs; ( ii ) the distributed/parallel implementation of such abstractions allowing its execution on clusters of GPUs; ( iii ) and optimizations that predict multiplications by zero-value of the quantum states/transformations, implying reduction in the number of computations. The results obtained in this work embrace the distribute/parallel simulation of Hadamard gates up to 21 qubits, showing scalability with the increase in the number of computing nodes.
The exponential increase in the temporal and spatial complexities is one of the main challenges in the widespread use of quantum algorithm simulation, especially in dense quantum transformations (QTs) such as the Hadamard transformation (H), which has found wide applications in computer and communication science and also comprising the simplest quantum universal set of QTs. The main reason for these costs is the expansion of QTs by using tensor product in multi-dimension quantum applications. In this work, new optimizations for the execution of reduction and decomposition based on the Identity operator are introduced in the Distributed Geometric Machine framework (D-GM). Instead of executing the quantum transformation in a single step, they are divided in sub-quantum transformations and only the values different from Identity transformations are stored. Mixed Partial Processes provide control over the increase in the size of read/write memory states in the calculation of a QT, thus contributing to increase the scalability of applications regarding hardware-GPUs memory limit. In the evaluation of this D-GM extension, Hadamard Transformations were simulated up to 28 qubits applications over a single GPU. Our new simulator is 10, 829χ faster and allows for the simulation of more qubits when compared to our previous implementation running on the same GPU.
Due to the unavailability of quantum computers, simulation of quantum algorithms using classical computers is still the most affordable option for research of algorithms and models for quantum computing. As such simulation requires high computing power and memory resources, and computations are regular and data-intensive, GPUs become a suitable solution for accelerating the simulation of quantum algorithms. This work introduces an extension of the execution library for the VPE-qGM environment to support GPU acceleration. Hadamard gates with up to 20 quantum bits were simulated, and speedups of up to approximately 540× over a sequential simulation and of approximately 85× over a 8-core distributed simulation in the VirD-GM environment were achieved.