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International Conference on Information and Communication Technology Convergence (ICTC)

Symmetry Verification and Circuit Implementation using Qiskit

Youshin Chung, Jinyoung Ha, Yujin Kang, Jun Heo

Published Oct 11, 2023• 0 citations
Publisher

Abstract

For near-term quantum computer, Quantum Error Mitigation (QEM) has recently attracted attention as a solution to reduce errors in quantum computers. In this paper, we introduce one of the QEM protocols, symmetry verification, and implement it using Qiskit. To check the performance, we use the VQE (Variational Quantum Eigensolver) to find the ground-state energy of hydrogen molecule (H2) on two qubits.

DOI
10.1109/ictc58733.2023.10392960

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For near-term quantum computer, Quantum Error Mitigation (QEM) has recently attracted attention as a solution to reduce errors in quantum computers. In this paper, we introduce one of the QEM protocols, symmetry verification, and implement it using Qiskit. To check the performance, we use the VQE (Variational Quantum Eigensolver) to find the ground-state energy of hydrogen molecule (H2) on two qubits.
Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy.
Abstract Solving the electronic structure for multi-electronic systems is a hard problem. Even for small atoms and molecules, approximations have to be made in order to solve numerically the Schrödinger equation. Although different methods have been developed to take into account electron correlations, their computational cost reduces their feasibility. Quantum simulation provides an alternative to traditional computational methods for enquiring the electronic structure of molecules. Specifically, the Variational Quantum Eigensolver (VQE) algorithm provides a hybrid quantum-classical algorithm for the implementation on current near term quantum devices. In this work, we explore the implementation of VQE on Qiskit for calculating the ground-state energy of diatomic Hydrogen molecule.
Quantum computers are anticipated to transcend classical supercomputers for computationally intensive tasks by exploiting the principles of quantum mechanics. However, the capabilities of the current generation of quantum devices are limited due to noise or errors, and therefore implementation of error mitigation and/or correction techniques is pivotal to reliably process quantum algorithms. In this work, we have performed a comparative analysis of the error mitigation capability of the [[4,2,2]] quantum error-detecting code (QEC method), duplicate circuit technique, and the Bayesian read-out error mitigation (BREM) approach in the context of proof-of-concept implementations of variational quantum eigensolver (VQE) algorithm for determining the ground state energy of H2_22​ molecule. Based on experiments on IBM quantum device, our results show that the duplicate circuit approach performs superior to the QEC method in the presence of the hardware noise. A significant impact of cross-talk noise was observed when multiple mappings of the duplicate circuit and the QEC method were implemented simultaneously −-− again the duplicate circuit approach overall performed better than the QEC method. To gain further insights into the performance of the studied error mitigation techniques, we also performed quantum simulations on IBM system with varying strengths of depolarising circuit noise and read-out errors which further supported the main finding of our work that the duplicate circuit offer superior performance towards mitigating of errors when compared to the QEC method. Our work reports a first assessment of the duplicate circuit approach for a quantum algorithm implementation and the documented evidence will pave the way for future scalable implementations of the duplicated circuit techniques for the error-mitigated practical applications of near-term quantum computers.
Feynmans ideas to employ quantum systems for simulating other quantum systems gave rise to quantum simulation. While current quantum computers are still prone to decoherence and rely on error correction, the development of hybrid algorithms that employ both quantumand classical computation allow to perform quantum simulation. Among these algorithms, the Variational Quantum Eigensolver algorithm has permitted to explore the electronic structure of simple atoms and molecules by exploiting the Rayleigh Ritz variational principle. In this work we provide the implementation of the VQE algorithm for finding the ground state energy of the hydrogen molecule on Qiskit library for python.
molecule, emphasizing practical implementation and performance on current quantum hardware. Our research presents a comparative study of HEA and UCCSD ansätze on noiseless and noisy simulations and implements VQE on recent IBM quantum computer noise models and a real quantum computer, IBM Fez, providing a fully functional code employing Qiskit 1.2. Our experiments confirm UCCSD's reliability in ideal conditions, while the HEA demonstrates greater robustness to hardware noise, achieving chemical accuracy on state-vector simulation (SVS). The results reveal that achieving ground-state energy within chemical accuracy is feasible without error mitigation during VQE convergence. We demonstrate that current quantum devices effectively optimize circuit parameters despite misestimating simulated energies. The SVS-evaluated energies provide a more accurate representation of the solution quality compared to QPU-estimated energy values, indicating that VQE converges to the correct ground state despite quantum noise. Our study also applies noise mitigation as a postprocessing technique, using zero-noise extrapolation (ZNE) on a real quantum computer. The detailed methodologies presented in this study, including Hamiltonian construction and Fermionic-to-qubit transformations, facilitate flexible adaptation of the VQE approach for various algorithm variants and across different levels of algorithmic implementation.
Quantum computing has emerged as a promising technology for solving problems that are intractable for classical computers. In this study, we introduce quantum computing and implement the Variational Quantum Eigensolver (VQE) algorithm using Qiskit on the IBM Quantum platform to calculate the ground state energy of a hydrogen molecule. We provide a theoretical framework of quantum mechanics, qubits, quantum gates, and the VQE algorithm. Our implementation process is described, and we simulate the results. Additionally, experiments are conducted on the IBM Quantum platform, and the results are analyzed. Our fi ndings demonstrate that VQE can effi ciently calculate molecular properties with high accuracy. However, limitations and challenges in scaling the algorithm for larger molecules are also identifi ed. This work contributes to the growing body of research on quantum computing and highlights the potential applications of VQE for real-world problem-solving.