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Impact of various IBM Quantum architectures with different properties on Grover's algorithm

Mohd Harith Akmal Zulfaizal Fadillah, Bahari Idrus, Mohammad Khatim Hasan, Siti Munirah Mohd

Published Oct 12, 2021• 4 citations
Publisher

Abstract

Quantum computing and quantum algorithms have been said to be able to provide significant speed-up over classical computation with classical algorithms by exploiting the nature of quantum mechanical systems. In this work, we will study the qubit architecture of quantum systems available at IBM Quantum (IBM-Q) such as the properties of the qubit system, the qubit layout and connectivity as well as the transpilation process of circuits and its effects to the circuits. We investigate the correspondence between limited and sparse connectivity and connected physical qubits to Grover's algorithm implementation of 2 and 3 qubits. We will also test Grover's algorithm on the different connectivity available on four IBM-Q systems for 2, 3, 4 and 5 qubits using optimization level of 0, 1, 2 and 3 to compare the circuit depth of the transpiled circuits as well as their execution times. This work will provide guidance for researchers on the important factors to consider before implementing a quantum algorithm on a real quantum system.

DOI
10.1109/iceei52609.2021.9611142

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Quantum computing and quantum algorithms have been said to be able to provide significant speed-up over classical computation with classical algorithms by exploiting the nature of quantum mechanical systems. In this work, we will study the qubit architecture of quantum systems available at IBM Quantum (IBM-Q) such as the properties of the qubit system, the qubit layout and connectivity as well as the transpilation process of circuits and its effects to the circuits. We investigate the correspondence between limited and sparse connectivity and connected physical qubits to Grover's algorithm implementation of 2 and 3 qubits. We will also test Grover's algorithm on the different connectivity available on four IBM-Q systems for 2, 3, 4 and 5 qubits using optimization level of 0, 1, 2 and 3 to compare the circuit depth of the transpiled circuits as well as their execution times. This work will provide guidance for researchers on the important factors to consider before implementing a quantum algorithm on a real quantum system.
Quantum computing is a quickly growing field of research thanks to recent hardware advances. The quantum mechanical properties of quantum computers allow them to solve certain families of problems faster than classical computers. A quantum algorithm solving such a problem is Grover's algorithm, which finds an element in an unordered set faster than any classical search algorithm. In this paper an implementation of a 4-qubit Grover's algorithm for the IBM Q computer ibmqx5 is presented. Executing the implementation on an ibmqx5 simulator yield results in line with the theoretically optimal results. The accuracy of the ibmqx5 simulation results compared to the ibmqx5 execution results suggests that current hardware is not yet suitable,due to required complexity of the circuits for a 4-qubit Grover implementation.
This paper focuses on testing the current viability of using quantum computers for the processing of data-driven tasks fueled by emerging data science applications. We test the publicly available IBM quantum computers using Grover's algorithm, a well-known quantum search algorithm, to obtain a baseline for the general evaluations of these quantum devices and to investigate the impacts of various factors such as number of quantum bits (or qubits), qubit choice, and device choice. The main contributions of this paper include a new 4-qubit implementation of Grover's algorithm and test results showing the current capabilities of quantum computers. Our study indicates that quantum computers can currently only be used accurately for solving simple problems with very small amounts of data. There are also notable differences between different selections of the qubits in the implementation design and between different quantum devices that execute the algorithm.
Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression algorithm that can efficiently compress unknown quantum information. We restricted ourselves to compression of three pure qubits into two qubits, as the complexity of even such a simple implementation is barely within the reach of today's quantum processors. We implemented the algorithm on IBM quantum processors with two different topological layouts-a fully connected triangle processor and a partially connected line processor. It turns out that the incomplete connectivity of the line processor affects the performance only minimally. On the other hand, it turns out that the transpilation, i.e. compilation of the circuit into gates physically available to the quantum processor, crucially influences the result. We also have seen that the compression followed by immediate decompression is, even for such a simple case, on the edge or even beyond the capabilities of currently available quantum processors.
Cloud-accessible quantum processors enable direct execution of quantum algorithms on heterogeneous hardware platforms. Unlike classical systems, however, identical quantum circuits may exhibit substantially different behavior across devices due to architectural variations in qubit connectivity, gate fidelity, and coherence times. In this work, we systematically benchmark five representative quantum algorithms - Bell state preparation, GHZ state generation, Quantum Fourier Transform (QFT), Grover's Search, and the Quantum Approximate Optimization Algorithm (QAOA) - across trapped-ion, superconducting, and simulator backends using Amazon Braket. Performance metrics including fidelity, CHSH violation, success probability, circuit depth, and gate counts are evaluated. Our results demonstrate a strong dependence of algorithmic performance on hardware topology and noise characteristics. For example, 10-qubit GHZ states achieved fidelities above 0.8 on trapped-ion hardware, while superconducting platforms dropped below 0.15 due to routing overhead and accumulated two-qubit gate errors. These findings highlight the importance of hardware-aware algorithm selection and provide practical guidance for benchmarking in the NISQ era.
In the context of actual information technology, data processing and storage have increased exponentially. Searching through large databases is considered an important problem, with multiple applications, where the properties of quantum computing could be used to find a potential solution. In this paper, the authors present an implementation for Grover’s search algorithm, a fast quantum algorithm for database search, and analyze the results for various graph topologies used in some of the real quantum devices provided by IBM. The algorithm provides a quadratic speedup over its classical counterpart (linear complexity). The code used in the implementation is possible with the help of the Qiskit framework and IBM Q Experience platform. Multiple tests with their results are presented. The experiments include three implementations of Grover’s search algorithm for different input register sizes: 2, 3 and 4 qubits, and exploration of multiple running configurations. We focus on the performance impact of selecting different groups of qubits on various real quantum devices, such as the probability to find the desired state and the execution time. For each experiment, we present the motivation, the results and their analysis.
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www. RESEARCH: ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.