Quantum Sensing Enhanced by Reservoir Computing in Trapped-Ion Systems*

Certain quantum sensing protocols, which involve repeatedly creating, perturbing, and destroying carefully designed states, are inherently slow and resource-intensive. While adaptive or Bayesian phase estimation algorithms offer some efficiency when trying to reach the Heisenberg limit in quantum sensing applications [1], these methods are challenging to implement due to the need for careful optimization of feedback, measurements, and state preparation. Quantum reservoir computing (QRC) addresses these challenges by leveraging the native complexity offered by quantum systems. Adapted from classical reservoir computing, QRC consists of a hybrid quantum system that evolves through interactions with an input signal, enabling efficient classification via classical post-processing [2]. In parallel, measurement-based evolution of quantum systems offers a new perspective into extracting the values of non-commuting observables [3]. As opposed to gate-based evolution, measurement-based evolution focuses on using quantum measurement as a control mechanism over quantum systems and offers increased flexibility in the design of quantum sensors.

In this work, we propose embedding a quantum reservoir computer within a trapped-ion quantum processor, focusing particularly on enabling highly sensitive and complex signal processing capabilities. To do this, we investigate the sequential measurement dynamics of signals interacting with the motional modes of a trapped ion and show that complex probability distributions can be uniquely mapped onto a bosonic mode. 

[1] C. L. Degen et al. Rev. Mod. Phys. 89, 035002 (2017)

[2] A. Senanian et al. Nat. Commun. 15, 7490 (2024)

[3] C. Flühmann et al. Phys. Rev. X 8, 021001 (2018)