Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience

Abstract

We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation algorithm to reduce a circuit depth from the original HHL algorithm. In this paper, we show that this hybrid algorithm is functionally identical to the HHL algorithm under the assumption that the number of qubits used in algorithms is large enough. In addition, it is experimentally examined with four qubits in the IBM Quantum Experience setups, and the experimental results of our algorithm show higher accurate performance on specific systems of linear equations than that of the HHL algorithm.

arXiv comment12 pages, 6 figures

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• Depth analysis of variational quantum algorithms for heat equation
• Robustness of quantum algorithms against coherent control errors
• Quantum algorithms for scientific computing
• Large-scale quantum hybrid solution for linear systems of equations
• Non-Markovian memory in IBMQX4
• Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm
• Noise-Resilient and Reduced Depth Approximate Adders for NISQ Quantum Computing
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• Identifying Bottlenecks of NISQ-friendly HHL algorithms
• A new error-modeling of Hardy's paradox for superconducting qubits and its experimental verification
• Protection of noisy multipartite entangled states of superconducting qubits via universally robust dynamical decoupling schemes
• Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks