Optimal purification of a spin ensemble by quantum-algorithmic feedback

TL;DR

This paper introduces a quantum feedback algorithm that actively stabilizes a large ensemble of nuclear spins from a high-temperature state to a near-pure macrostate, demonstrating significant reduction in fluctuations and potential for quantum state engineering.

Contribution

The authors develop and experimentally implement a novel quantum feedback algorithm for ensemble purification, achieving stabilization from infinite temperature to a single quantum state in a large nuclear spin ensemble.

Findings

Reduced nuclear-spin fluctuations by 83-fold

Achieved stabilization of ~50,000 nuclei to a single macrostate

Engineered classically correlated ensemble states with macrostate tuning

Abstract

Purifying a high-temperature ensemble of quantum particles towards a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is based on feedback to stabilise the system actively around a target state. This alternative, if realised, offers additional control capabilities for the design of quantum states. Here we present a quantum feedback algorithm capable of stabilising the collective state of an ensemble from an infinite-temperature state to the limit of single quanta. We implement this on ~50,000 nuclei in a semiconductor quantum dot, and show that the nuclear-spin fluctuations are reduced 83-fold down to 10 spin macrostates. While our algorithm can purify a single macrostate, system-specific inhomogeneities prevent reaching this limit. Our feedback algorithm further engineers classically correlated ensemble states via macrostate tuning, weighted bimodality, and latticed multistability, constituting a pre-cursor towards quantum-correlated macrostates.