Greedy versus Map-based Optimized Adaptive Algorithms for random-telegraph-noise mitigation by spectator qubits

TL;DR

This paper develops and compares adaptive algorithms, including a novel map-based method, for mitigating dephasing noise in solid-state qubits using spectator qubits, demonstrating superior performance in high noise sensitivity regimes.

Contribution

The paper introduces the MOAAAR algorithm, a map-based adaptive strategy that outperforms greedy methods for noise mitigation in qubits with spectator probes, especially at high noise sensitivities.

Findings

MOAAAR reduces decoherence rate more effectively than greedy algorithms.

High noise sensitivity enhances the performance gap between MOAAAR and greedy strategies.

Analytical and numerical results confirm MOAAAR's superiority in asymptotic regimes.

Abstract

In a scenario where data-storage qubits are kept in isolation as far as possible, with minimal measurements and controls, noise mitigation can still be done using additional noise probes, with corrections applied only when needed. Motivated by the case of solid-state qubits, we consider dephasing noise arising from a two-state fluctuator, described by random telegraph process, and a noise probe which is also a qubit, a so-called spectator qubit (SQ). We construct the theoretical model assuming projective measurements on the SQ, and derive the performance of different measurement and control strategies in the regime where the noise mitigation works well. We start with the Greedy algorithm; that is, the strategy that always maximizes the data qubit coherence in the immediate future. We show numerically that this algorithm works very well, and find that its adaptive strategy can be well approximated by a simpler algorithm with just a few parameters. Based on this, and an analytical construction using Bayesian maps, we design a one-parameter ($\Theta$) family of algorithms. In the asymptotic regime of high noise-sensitivity of the SQ, we show analytically that this $\Theta$-family of algorithms reduces the data qubit decoherence rate by a divisor scaling as the square of this sensitivity. Setting $\Theta$ equal to its optimal value, $\Theta^\star$, yields the Map-based Optimized Adaptive Algorithm for Asymptotic Regime (MOAAAR). We show, analytically and numerically, that MOAAAR outperforms the Greedy algorithm, especially in the regime of high noise sensitivity of SQ.