Error mitigation and circuit division for early fault-tolerant quantum phase estimation

TL;DR

This paper introduces a framework for early fault-tolerant quantum algorithms, focusing on quantum phase estimation, with new techniques that improve noise robustness and error mitigation, reducing resource requirements in near-term quantum computing.

Contribution

It proposes a novel error mitigation and circuit division framework for early fault-tolerant quantum phase estimation, including a robust QFT-based method and the EUMLE data processing technique.

Findings

QFT-based QPE outperforms previous methods at low/moderate noise levels.

EUMLE provides consistent, asymptotically normal error mitigation beyond expectation values.

Resource reduction of roughly 50% in qubits with 10x time overhead.

Abstract

As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of "early fault tolerance" where 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 depolarising noise and outperforms the previous state of the art at low and moderate noise rates. We further introduce the Explicitly Unbiased Maximum Likelihood Estimation (EUMLE), a data processing technique that mitigates arbitrary 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 we can roughly halve the number of physical qubits with a $\sim 10\times$ wall-clock time overhead, but further reduction causes a steep runtime 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.