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CLEI electronic journal

Expanding the VPE-qGM Environment Towards a Parallel Quantum Simulation of Quantum Processes Using GPUs

Adriano Maron, Renata Reiser, Mauricio Lima Pilla, Adenauer Yamin

Published Dec 1, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.19153/cleiej.16.3.3

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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.
The simulation of quantum algorithms in classic computers is a task which requires high processing and storing capabilities, limiting the size of quantum systems supported by the simulators. However, optimizations for reduction of temporal and spatial complexities are promising, expanding the capabilities of some simulators. The main contribution of this work consists in designing optimizations resulting from the description of quantum transformations using Quantum Processes and Partial Quantum Processes conceived in the qGM theoretical model. These processes, when computed on the VPE-qGM execution environment, require low execution time and result in the improvement of the performance, allowing the simulation of more complex quantum algorithms. The performance evaluation of this proposal was performed by benchmarks used in similar works and included the sequential simulation of quantum algorithms up to 24 qubits. The results are promising when compared to the state-of-art, indicating the possibilities of advances in this research.
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.
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.
The simulation of quantum algorithms in classic computers is a task which requires high processing and storing capabilities, limiting the size of quantum systems supported by the simulators. However, optimizations for reduction of temporal and spatial complexities are promising and expanding the capabilities of some simulators. The main contribution of this work consists in designing optimizations by the description of quantum transformations using Quantum Processes and Partial Quantum Processes conceived in the qGM theoretical model. These processes, when computed on the VPE-qGM execution environment, result in lower execution time and better performance, allowing the simulation of more complex quantum algorithms. The performance evaluation of this proposal was carried out by benchmarks used in similar works and included the sequential simulation of quantum algorithms up to 24 qubits. The results show a great improvement when compared to the previous version of the environment and indicate possibilities of advances in this research.
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.
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.