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Annals of Telecommunications

Quantum signal processing for quantum phase estimation: Fourier transform versus maximum likelihood approaches

François Chapeau‐Blondeau, Étienne Belin

Published Sep 5, 2020• 7 citations
Publisher
DOI
10.1007/s12243-020-00803-1

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As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of during which limited error correction is available. We propose a framework for designing early fault-tolerant algorithms by trading between error-correction overhead and residual logical noise, and apply it to quantum phase estimation (QPE). We develop a quantum-Fourier-transform- (QFT) based QPE technique that is robust to global depolarizing noise and outperforms the previous state of the art at low and moderate noise rates. We further introduce the explicitly unbiased maximum-likelihood estimator (EUMLE), a data-processing technique that mitigates errors in QFT-based QPE schemes. EUMLE provides consistent asymptotically normal error-mitigated estimates, addressing the open problem of extending error mitigation beyond expectation-value estimation. Applying this scheme to the ground-state problem of the two-dimensional Hubbard model and various molecular Hamiltonians, we find that we can roughly halve the number of physical qubits with a ∼ 10 times wall-clock time overhead, but that further reduction causes a steep run-time increase. This work provides an end-to-end analysis of early fault-tolerance cost reductions and space-time trade-offs, and identifies which areas can be improved in the future.