Trade-off between complexity and energy in quantum phase estimation

TL;DR

This paper introduces a framework to analyze the trade-off between energy cost and complexity in quantum phase estimation, optimizing resource use for precise measurements.

Contribution

The authors develop a new framework to quantify and optimize the energy-complexity trade-off in quantum processes, specifically applied to quantum phase estimation protocols.

Findings

Established a trade-off relation between energy cost and number of channel applications.

Identified a co-optimization point where energy and complexity are balanced.

Framework adaptable for benchmarking other quantum protocols and devices.

Abstract

Quantifying the energetic cost of implementing quantum operations is essential for assessing the efficiency and scalability of quantum sensing and information-processing technologies. Here, we introduce a framework for analysing the interplay between complexity and energy cost of quantum processes. In particular, we apply our framework to a sequential quantum phase estimation protocol, where a phase of physical significance is encoded in a quantum channel. The channel is applied to a probe state repeatedly until the probe is measured and the outcome leads to an estimate on the phase. We establish a trade-off relation between the total energy cost of the protocol and the number of times the channel is applied (complexity), while reaching a desired estimation precision. A sweet spot is located where the two quantities are co-optimised. The principles of our analysis can be adapted to benchmark the energetic requirements in other quantum protocols and devices.