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IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid)

High-Performance Quantum Computing Simulation for the Quantum Geometric Machine Model

A. Maron, Renata Reiser, Mauricio Lima Pilla

Published May 1, 2013• 14 citations
Publisher

Abstract

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.

DOI
10.1109/ccgrid.2013.50

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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.
Quantum computing proposes quantum algorithms exponentially faster than their clas- sical analogues when executed by a quantum computer. As quantum computers are currently unavailable for general use, one approach for analyzing the behavior and re- sults of such algorithms is the simulation using classical computers. As this simulation is inefficient due to the exponential growth of the temporal and spatial complexities, solutions for these two problems are essential in order to increase the simulation capa- bilities of any simulator. This work proposes the development of a methodology defined by two main steps: the first consists of the sequential implementation of the abstractions corresponding to the Quantum Processes and Quantum Partial Processes defined in the qGM model for reduction in memory consumption related to multidimensional quantum transformations; the second is the parallel implementation of such abstractions allowing its execution on GPUs. The results obtained by this work embrace the sequential simu- lation of controlled transformations up to 24 qubits. In the parallel simulation approach, Hadamard gates up to 20 qubits were simulated with a speedup of ? 50× over an 8-core parallel simulation, which is a significant performance improvement in the VPE-qGM environment when compared with its previous limitations.
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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 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.
This work describes a proposal for a platform focused on modeling and simulation (sequential or distributed) of quantum algorithms. More specifically, the integration between the environments VPE-qGM and VirD-GM is considered, providing a solution to the high computational cost associated to the simulation of quantum algorithms on classical computers. In this context, the algorithms are visually programmed and the details of distribution, communication and synchronization, required for the execution in distributed systems, are transparently managed by the execution environment. The validation and performance analysis consist in simulating a quantum search algorithm, obtaining results which demonstrate the performance gain of the platform compared to the sequential simulation.
Quantum computers are becoming practical for computing numerous applications. However, simulating quantum computing on classical computers is still demanding yet useful because current quantum computers are limited because of computer resources, hardware limits, instability, and noises. Improving quantum computing simulation performance in classical computers will contribute to the development of quantum computers and their algorithms. Quantum computing simulations on classical computers require long performance times, especially for quantum circuits with a large number of qubits or when simulating a large number of shots for noise simulations or circuits with intermediate measures. Graphical processing units (GPU) are suitable to accelerate quantum computer simulations by exploiting their computational power and high bandwidth memory and they have a large advantage in simulating relatively larger qubits circuits. However, GPUs are inefficient at simulating multi-shots runs with noises because the randomness prevents highly parallelization. In addition, GPUs have a disadvantage in simulating circuits with a small number of qubits because of the large overheads in GPU kernel execution. In this paper, we introduce optimization techniques for multi-shot simulations on GPUs. We gather multiple shots of simulations into a single GPU kernel execution to reduce overheads by scheduling randomness caused by noises. In addition, we introduce shot-branching that reduces calculations and memory usage for multi-shot simulations. By using these techniques, we speed up x10 from previous implementations.