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International Journal of Computers Communications & Control

Parallel Simulation of Quantum Search

Simona Caraiman, Vasile Manta

Published Dec 1, 2010• 5 citations
Publisher

Abstract

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.

DOI
10.15837/ijccc.2010.5.2219

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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.
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
Recent technological advancements show promise in leveraging quantum mechanical phenomena for computation. This brings substantial speed-ups to problems that are once considered to be intractable in the classical world. However, the physical realization of quantum computers is still far away from us, and a majority of research work is done using quantum simulators running on classical computers. Classical computers face a critical obstacle in simulating quantum algorithms. Quantum states reside in a Hilbert space whose size grows exponentially to the number of subsystems, i.e., qubits. As a result, the straightforward statevector approach does not scale due to the exponential growth of the memory requirement. Decision diagrams have gained attention in recent years for representing quantum states and operations in quantum simulations. The main advantage of this approach is its ability to exploit redundancy. However, mainstream quantum simulators still rely on statevectors or tensor networks. We consider the absence of decision diagrams due to the lack of parallelization strategies. This work explores several strategies for parallelizing decision diagram operations, specifically for quantum simulations. We propose optimal parallelization strategies. Based on the experiment results, our parallelization strategy achieves a 2-3 times faster simulation of Grover’s algorithm and random circuits than the state-of-the-art single-thread DD-based simulator DDSIM.
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups, e.g., for integer factorization or database search. However, since physical realizations of quantum computers are in their infancy, a significant amount of research in this domain still relies on simulations of quantum computations on conventional machines. This causes a significant complexity which current state-of-the-art simulators try to tackle with a rather straight forward array-based representation and by applying massive hardware power. There also exist solutions based on decision diagrams (i.e., graph-based approaches) that try to tackle the exponential complexity by exploiting redundancies in quantum states and operations. However, these existing approaches do not fully exploit redundancies that are actually present. In this paper, we revisit the basics of quantum computation, investigate how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion. This leads to a new graph-based simulation approach which outperforms state-of-the-art simulators (array-based as well as graph-based). Experimental evaluations show that the proposed solution is capable of simulating quantum computations for more qubits than before, and in significantly less run-time (several magnitudes faster compared to previously proposed simulators). An implementation of the proposed simulator is publicly available online at http://iic.jku.at/eda/research/quantum_simulation.