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International Conference on Software, Telecommunications and Computer Networks (SoftCOM)

The GR2 Algorithm for Subgraph Isomorphism. A Study from Parallelism to Quantum Computing

Radu-Iulian Gheorghica

Published Sep 23, 2021• 2 citations
Publisher

Abstract

In this paper is presented the GR2 Algorithm in the context of a study that encompassed elements of Parallel Programming and pruning techniques. Also there were executed circuits having 5, 10 and 15 qubits on quantum computers. For these circuits were used classical and quantum gates along with oracles and Grover’s Algorithm. The original contribution consists in highlighting the importance of Parallel Programming in classiscal computing as well as in quantum computing.

DOI
10.23919/softcom52868.2021.9559130

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In this paper is presented the GR2 Algorithm in the context of a study that encompassed elements of Parallel Programming and pruning techniques. Also there were executed circuits having 5, 10 and 15 qubits on quantum computers. For these circuits were used classical and quantum gates along with oracles and Grover’s Algorithm. The original contribution consists in highlighting the importance of Parallel Programming in classiscal computing as well as in quantum computing.
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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.
Quantum parallelism arises from the ability of quantum qubits to exist in multiple states simultaneously due to superposition. It enables quantum computers to explore a vast number of possibilities in parallel, potentially solving complex problems exponentially faster than classical computers. Recently, there has been an increasing demand for skilled professionals with expertise in quantum computing and programming. This paper presents a practical approach to teaching quantum computing to Electrical Engineering & Computer Science (EECS) students through dedicated hands-on programming labs. The labs cover a diverse range of topics, encompassing fundamental elements, such as quantum gates and circuits, as well as quantum algorithms. As educators, we aim to share our teaching insights and resources with fellow instructors in the field. This article elucidates the rationale behind the design of each experiment, enabling a deeper understanding of quantum computing.
Quantum computing offers an accelerated mechanism for solving combinatorial optimization problems that could be hardly solvable with classical tools, in this context, this paper highlights the utility of quantum computing in solving NP-complete problems efficiently and shows up the importance of employing quantum algorithms achieving parallel calculation in the purpose of reducing the algorithmic complexity and simplifying the development of optimization applications. Within this publication, an optimized version of quantum circuit conception for developing the oracle of the Grover's search algorithm is introduced for solving the vertex cover problem, and it was also tested using the Qiskit library and applied to a set of instances to evaluate its performance.
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Quantum computers have already shown high potential in solving complex computational problems much more efficiently compared to the typical conventional supercomputers. One major challenge in the field of quantum computing is to implement the major operations of the conventional computers using the available quantum hardware (quantum gates). Such operations are the arithmetic operations as well as decoding and multiplexing. An obvious burden is the absence of quantum gates that directly implement the fundamental Boolean operations like AND and OR. Moreover, care should be taken in order to reduce the costs involved when implementing a quantum circuit. In this paper, we present an oracle-based approach to implement quantum decoding and multiplexing in a joint circuit. The use of oracles necessarily implies that some type of quantum programming will be used. A quantum program is a process organized in a sequence of computations whose data elements are selected from the set of the known quantum gates. In our approach, the oracles are used as pre-programmed black boxes that determine if a datum should be directed from the input to the output. The important idea behind our scheme is that the oracles operate in parallel, therefore their selection decisions are taken simultaneously, while the approaches found in the literature implement sequential circuits with feedbacks from the outputs to inputs that burden the overall performance. We have used Qiskit open-source software development kit to verify the correctness of our design through extensive simulations.