Tensor-based phase difference estimation on time-series analysis

We propose a phase-difference-estimation algorithm based on tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy with a quantum-phase-estimation- (QPE) type algorithm. Using tensor networks, we construct circuits composed solely of nearest-neighbor gates and extract time-evolution data with four-type circuit measurements. In addition, to enhance the accuracy of the 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. Verification using a noiseless simulator for the eight-qubit one-dimensional Hubbard model using an ancilla qubit shows that the proposed algorithm achieves accuracies with 0.4%–4.7% error from a true energy gap with 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 4000 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.