Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation

TL;DR

This paper introduces faster, simpler quantum algorithms for phase, energy, and amplitude estimation that operate coherently with minimal resources, avoiding complex transforms and median computations.

Contribution

The authors develop novel quantum estimation algorithms that are more efficient and resource-friendly than traditional methods, suitable for single-copy, non-eigenstate inputs.

Findings

Reduced query complexity compared to textbook methods

Elimination of quantum Fourier transform and median computation

Enhanced performance in quantum Metropolis sampling and Bayesian inference

Abstract

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algorithms make assumptions that make them unsuitable for this 'coherent' setting, leaving only the textbook approach. We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint. They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates. Instead, they use block-encoding techniques to compute the estimate one bit at a time, performing all amplification via singular value transformation. These improved subroutines accelerate the performance of quantum Metropolis sampling and quantum Bayesian inference.