Improving Quantum Clocks via Semidefinite Programming

TL;DR

This paper introduces a numerical method using semidefinite programming to enhance the accuracy of quantum clocks by optimizing phase variance, leveraging control operations and prior knowledge.

Contribution

It presents a novel application of semidefinite programming to improve quantum clock precision through a greedy optimization approach.

Findings

The technique reduces phase variance in quantum clocks.

It accommodates arbitrary prior frequency knowledge.

Bounds on discretization errors are established.

Abstract

The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations or the probe times. We consider arbitrary prior frequency knowledge and compare clocks with varying numbers of ions and queries interlaced with unitary control. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.