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Parallelization of the General Single Qubit Gate and CNOT for the QC-lib Quantum Computer Simulator Library

I. Glendinning, Bernhard Ömer

Published Jun 1, 2003• 4 citations
OpenAlex

Abstract

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.

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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.
Simulation of quantum computers using classical computers is a computationally hard problem, requiring a huge amount of operations and storage. Grid systems are a good choice for simulating quantum algorithms, since they provide access to high-performance computer clusters. In this paper we present the design of a message passing parallel version of the quantum computer simulator, QCL, deployed as a grid service. After describing the architecture of our grid service and the parallelization strategy for the general single qubit operator, we present the performance measurements for some test cases, showing the speedups obtained.
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.
Models of Grover’s search algorithm is reviewed to build the foundation for the other algorithms. Thereafter, some preliminary modifications of the original algorithms by others are stated, that increases the applicability of the search procedure. A general quantum computation on an isolated system can be represented by a unitary matrix. In order to execute such a computation on a quantum computer, it is common to decompose the unitary into a quantum circuit, i.e., a sequence of quantum gates that can be physically implemented on a given architecture. There are different universal gate sets for quantum computation. Here we choose the universal gate set consisting of CNOT and single-qubit gates. We measure the cost of a circuit by the number of CNOT gates as they are usually more difficult to implement than single qubit gates and since the number of single-qubit gates is bounded by about twice the number of CNOT’s.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.