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Parallelization of the QC-lib Quantum Computer Simulator Library

I. Glendinning, Bernhard Ömer

Published Dec 28, 2009• 5 citations
OpenAlex

Abstract

Abstract. We report on work to parallelize QC-lib, a C++ library for the simulation of quantum computers at an abstract functional level. After a brief introduction to quantum computing, we give an outline of QClib, then describe its parallelization using MPI, and present performance measurements made on a Beowulf cluster. Using more processors allowed larger problems to be solved, and reasonable speedups were obtained for the Hadamard transform and Grover’s quantum search algorithm. 1

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Abstract. We report on work to parallelize QC-lib, a C++ library for the simulation of quantum computers at an abstract functional level. After a brief introduction to quantum computing, we give an outline of QClib, then describe its parallelization using MPI, and present performance measurements made on a Beowulf cluster. Using more processors allowed larger problems to be solved, and reasonable speedups were obtained for the Hadamard transform and Grover’s quantum search algorithm. 1
This paper reports on work to parallelize QC-lib, a C++ library for the simulation of quantum computers at an abstract functional level. After a brief introduction to quantum computing, we give an outline of QC-lib, then describe the parallelization using MPI of the general single qubit gate and the controlled-NOT gate (CNOT). Although QC-lib also implements other gates, this combination is already universal for quantum computing, and has allowed us to implement Grover's quantum search algorithm as a test case. We present some performance measurements made on a Beowulf cluster, which show reasonable speedups for Grover's algorithm.
Simulation of quantum computers using classical computers is a computationally hard problem, requiring a huge amount of operations and storage. Parallelization can alleviate this problem, allowing the simulation of more qubits at the same time or the same number of qubits to be simulated in less time. A promising approach is represented by executing these simulators in Grid systems that can provide access to high performance resources. In this paper we present a parallel implementation of the QC-lib quantum computer simulator deployed as a Grid service. Using a specific scheme for partitioning the terms describing quantum states and efficient parallelization of the general singe qubit operator and of the controlled operators, very good speed-ups were obtained for the simulation of the quantum search problem.
This thesis describes the design and implementation of an environment to allow quantum computation to be simulated on classical computers. Although it is believed that quantum computers cannot in general be efficiently simulated classically, it is nevertheless possible to simulate small but interesting systems, on the order of a few tens of quantum bits. Since the state of the art of physical implementations is less than 10 bits, simulation remains a useful tool for understanding the behavior of quantum algorithms. To create a suitable envrionment for simulation, we constructed a 32-node cluster of workstation class computers linked with a high speed (gigabit Ethernet) network. We then wrote an initial simulation environment based on parallel linear algebra libraries with a Matlab front end. These libraries operated on large matrices representing the problem being simulated. The parallel Matlab environment demonstrated a degree of parallel speedup as we added processors, but overall execution times were high, since the amount of data scaled exponentially with the size of the problem. This increased both the number of operations that had to be performed to compute the simulation, and the volume of data that had to be communicated between the nodes as they were computing. The scaling also affected memory utilization, limiting us to a maximum problem size of 14 qubits. In an attempt to increase simulation efficiency, we revisited the design of the simulation environment. Many quantum algorithms have a structure that can be described using the tensor product operator from linear algebra. We believed that a new simulation environment based on this tensor product structure would be substantially more efficient than one based on large matrices. We designed a new simulation envrionment that exploited this tensor product structure. Benchmarks that we performed on the new simulation environment confirmed that it was substantially more efficient, allowing us to perform simulations of the quantum Fourier transform and the discrete approximation to the solution of 3-SAT by adiabatic evolution up to 25 qubits in a reasonable time. Thesis Supervisor: Stephen A. Benton Title: Professor of Media Arts and Sciences
Quantum computing has been an attractive method adapted for increasing the computational speed and it is governed by the laws of quantum mechanics. Quantum computers are not limited to two states as compared with classical systems, but they encode information as quantum bits or qubits. A qubit represents atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and processors. The power of quantum computing lies in its multi-state representation which makes it million times more powerful than classical computer systems. Quantum computers also use another aspect of quantum mechanics known as entanglement, which is a property where multiple objects existing in the states that can be linked together. There exists a standard/specification of message passing library, known as message passing interface (MPI) that can be used for achieving high-performance computing. The goal of MPI is to provide a standardized framework for writing message-passing programs which can be used for programming systems that require distributed processing. The superposition principle used by the quantum algorithm can be simulated in the MPI environment with a cluster of computers or multi-CPU systems. This paper focuses on exposing the strength of quantum algorithm in high performance computing by using MPI, and also on comparing the sequential and parallel execution of programs on the basis of execution time and CPU utilization.
Simulation of quantum computers using classical computers is a hard problem with high memory and computational requirements. Parallelization can alleviate this problem, allowing the simulation of more qubits at the same time or the same number of qubits to be simulated in less time. A promising approach is to exploit the high performance computing capabilities provided by the latest graphical processing units. In this paper we present a parallel implementation of the QC-lib quantum computer simulator on the GPU using the CUDA programming model. The proposed scheme for partitioning the terms that describe the state of a quantum register takes advantage of the specific characteristics of the CUDA memory spaces and allows for an efficient parallelization of the general singe qubit operator. Experimental results indicate that very good speed-ups can be obtained in contrast with the sequential implementation.