Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm

Abstract

We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus on lower-order phase components, and the punctured method removes qubits corresponding to known phase bits, thereby streamlining the circuit. To demonstrate the effectiveness of the two variations, we integrate them into a hybrid quantum-classical implementation of the Harrow--Hassidim--Lloyd algorithm for solving linear systems. The hybrid method leverages both quantum and classical processors to identify and remove unnecessary qubits and gates. As a result, our method reduces qubit and gate counts compared to previous implementations, leading to lower overall circuit error rates on current hardware. Experimental demonstrations on IBM superconducting hardware confirm the error-mitigation effectiveness of the proposed hybrid method.

20 pages, 11 figures

References in corpus (23)

• Quantum Computing in the NISQ era and beyond
• Quantum algorithm for solving linear systems of equations
• Surface codes: Towards practical large-scale quantum computation
• Quantum information with Rydberg atoms
• Quantum metrology
• Quantum support vector machine for big data classification
• Simulated Quantum Computation of Molecular Energies
• Quantum principal component analysis
• Error mitigation for short-depth quantum circuits
• Optical Quantum Computing
• Extending the computational reach of a noisy superconducting quantum processor
• Quantum Computational Supremacy
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Entanglement-free Heisenberg-limited phase estimation
• Quantum Data Fitting
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Quantum Metropolis Sampling
• Search via Quantum Walk
• High-order quantum algorithm for solving linear differential equations
• Efficient quantum algorithm for dissipative nonlinear differential equations
• A quantum linear system algorithm for dense matrices
• Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience