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IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI)

An Algorithm for Concurrent Use of Quantum Simulators and Computers in the Context of Subgraph Isomorphism

Radu-Iulian Gheorghica

Published May 23, 2023• 0 citations
Publisher

Abstract

Quantum computers represent the new generation of computing. But despite this, they have a limit which consists of the number of qubits, or quantum bits, that each computer has at its disposal. The purpose of this research is the ability to use multiple quantum simulators and computers in order to achieve calculations made by a unified number of qubits. The design for this algorithm makes use of parallel and distributed programming. The key results are amplified amplitudes obtained for large quantum circuits that would otherwise be impossible to execute on a single quantum computer whose available number of qubits is exceeded by the one of such circuits. Thus the algorithm presented in the current paper has been designed and tested, showing favorable results. A 25 qubit circuit was used for the test cases. It was partitioned in multiple smaller circuits that were sent for execution from a laptop, directly to the quantum devices. The circuit number of qubits can be increased as considered necessary by the user.

DOI
10.1109/saci58269.2023.10158547

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Quantum computers represent the new generation of computing. But despite this, they have a limit which consists of the number of qubits, or quantum bits, that each computer has at its disposal. The purpose of this research is the ability to use multiple quantum simulators and computers in order to achieve calculations made by a unified number of qubits. The design for this algorithm makes use of parallel and distributed programming. The key results are amplified amplitudes obtained for large quantum circuits that would otherwise be impossible to execute on a single quantum computer whose available number of qubits is exceeded by the one of such circuits. Thus the algorithm presented in the current paper has been designed and tested, showing favorable results. A 25 qubit circuit was used for the test cases. It was partitioned in multiple smaller circuits that were sent for execution from a laptop, directly to the quantum devices. The circuit number of qubits can be increased as considered necessary by the user.
The purpose of the research presented in this paper is finding the best execution times for searching subgraph isomorphisms. For this was created the GR3 Algorithm, its design consisting of a combination of Parallel Programming and Quantum Computing. The obtained execution times are significantly small. Thus can be deduced that an approach such as this is superior in obtaining the required results. The original contribution consists in studying a Parallel Programming approach combined with Quantum Computing Circuits and Grover’s Algorithm for searching subgraph isomorphisms using a laptop and real quantum computers [16].
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This paper explores the potential of quantum parallelism to dramatically reduce the computational complexity of a specific problem. We introduce a novel quantum algorithm designed to exploit quantum circuits and distributed parallelism to achieve significant performance gains compared to classical approaches. The core mechanism centers on the execution of independent quantum circuits on multiple qubits, effectively increasing the overall number of operations performed. This research investigates the feasibility of this approach and presents a preliminary design with a focus on demonstrating a substantial reduction in computational steps. The paper concludes with a discussion of future research directions and the potential impact of this technology.
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, simulation methods for parallel processors are required. We have developed a general-purpose simulator for quantum algorithms/circuits on the parallel computer (Sun Enterprise4500). It can simulate algorithms/circuits with up to 30 qubits. In order to test efficiency of our proposed methods, we have simulated Shor's factorization algorithm and Grover's database search, and we have analyzed robustness of the corresponding quantum circuits in the presence of both decoherence and operational errors. The corresponding results, statistics, and analyses are presented in this paper.
Recently quantum computing has achieved significant results both in theoretical and experimental areas and quantum algorithms have drawn the attention of many scientists. At the present there exist several experiments that realized some parts of certain important quantum algorithms. While those experiments work with only up to seven qubits, quantum simulators allow scientists to design algorithms with many more qubits. The existing simulators have one or more of the following restrictions: either they require powerful computers and additional computation packages such as Matlab or Mathematica or they don't provide an easy method for interacting between the classical and quantum parts of an algorithm. More importantly, none of them can simulate a generic 64-qubit circuit. It is important at this stage of quantum computing development to investigate technological improvements in simulating quantum circuit design. In this thesis we developed a specialized data structure, QSV, for quantum simulators along with new method for calculation of the new state vector after application of a quantum gate in a quantum simulator. We also developed a technique that speeds up the simulation time with our QSV vectors. With those results we built a quantum simulator that overcomes many shortcomings in other simulators and it has many advanced features. Our simulator can simulate many 64-qubit circuits and it can directly simulate multiple qubit gates as well as allows users to define gates with up to 10 qubits. The simulation time is much less in comparison with other simulators we tested. The simulator defines specifications so that users can easily design and test quantum circuits. With the simulator we also developed some new quantum circuits and verified many designs and constructions.