Tensor-based phase difference estimation on time series analysis

TL;DR

This paper introduces a tensor-network based phase difference estimation algorithm for quantum phase estimation, improving accuracy and scalability on near-term quantum devices through circuit optimization and error mitigation.

Contribution

It presents a novel tensor-network circuit compression method for quantum phase estimation, incorporating error mitigation and iterative optimization techniques for enhanced performance.

Findings

Achieved 0.4-4.7% error from true energy gap in simulations.

Demonstrated the algorithm on IBM quantum devices with over 4,000 gates.

Showed improved overlap with matrix product states through optimization.

Abstract

We propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor networks, we construct circuits composed solely of nearest-neighbor gates and extract time-evolution data by four-type circuit measurements. In addition, to enhance the accuracy of time-evolution and state-preparation circuits, we propose techniques based on algorithmic error mitigation and on iterative circuit optimization combined with merging into matrix product states, respectively. Verifications using a noiseless simulator for the 8-qubit one-dimensional Hubbard model using an ancilla qubit show that the proposed algorithm achieves accuracies with 0.4--4.7\% error from a true energy gap on an appropriate time-step size, and that accuracy improvements due to the algorithmic error mitigation are observed. We also confirm the enhancement of the overlap with matrix product states through iterative optimization. Finally, the proposed algorithm is demonstrated on IBM Heron devices with Q-CTRL error suppression for 8-, 36-, and 52-qubit models using more than 4,000 2-qubit gates. These largest-scale demonstrations for the QPE-type algorithm represent significant progress not only toward practical applications of near-term quantum computing but also toward preparation for the era of error-corrected quantum devices.