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arXiv:2607.17202

Multi-level Random-Telegraph Noise Mitigation using a Single Spectator Qubit

Yanan Liu, Hongting Song, Areeya Chantasri, Howard M. Wiseman

quant-phSubmitted Jul 19, 2026• Announced Jul 21, 2026• 0 citations
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Abstract

Preserving quantum coherence in the presence of environmental noise is one of the principal challenges for quantum technologies. Noise mitigation using spectator qubits (SQs) has recently emerged as a promising approach, enabling indirect probing of the noise without disturbing the data qubit (DQ). However, existing analyses that probe ultimate performance have been restricted to two-state random telegraph process noise, which does not capture more complex noise processes that may arise in the environment. Therefore, we here develop a SQ-based noise mitigation for DQs subject to general multi-level fluctuator noise. We first derive the coherence dynamics of the DQ under such noise, then develop a mitigation scheme in which information about the noise is inferred from sequential SQ measurements and used for phase correction. A memory-efficient heuristic adaptive protocol is proposed to dynamically select the SQ measurement time and angle based on the current noise estimate. Numerical simulations demonstrate that the proposed strategy significantly suppresses decoherence under multi-level noise, achieving performance comparable to that in the two-level case despite the increased complexity of the noise process.

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11 pages, 2 figures

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Preserving quantum coherence in the presence of environmental noise is one of the principal challenges for quantum technologies. Noise mitigation using spectator qubits (SQs) has recently emerged as a promising approach, enabling indirect probing of the noise without disturbing the data qubit (DQ). However, existing analyses that probe ultimate performance have been restricted to two-state random telegraph process noise, which does not capture more complex noise processes that may arise in the environment. Therefore, we here develop a SQ-based noise mitigation for DQs subject to general multi-level fluctuator noise. We first derive the coherence dynamics of the DQ under such noise, then develop a mitigation scheme in which information about the noise is inferred from sequential SQ measurements and used for phase correction. A memory-efficient heuristic adaptive protocol is proposed to dynamically select the SQ measurement time and angle based on the current noise estimate. Numerical simulations demonstrate that the proposed strategy significantly suppresses decoherence under multi-level noise, achieving performance comparable to that in the two-level case despite the increased complexity of the noise process.
Spectator qubits (SQs) for random-telegraph noise mitigation have been proposed by Song et al., Phys. Rev. A, 107, L030601 (2023), where an SQ operates as a noise probe to estimate optimal noise-correction control on the hard-to-access data qubits. It was shown that a protocol with adaptive measurement on the SQs and a Bayesian estimation-based control can suppress the data qubits' decoherence rate by a large factor with quadratic scaling in the SQ sensitivity. However, the protocol's practicality in real-world scenarios remained in question, due to various sources of imperfection that could affect the performance. We therefore analyze here the proposed adaptive protocol under non-ideal conditions, including parameter uncertainties in the system, efficiency and time delay in readout and reset processes of the SQs, and additional decoherence on the SQs. We also explore analytical methods of Bayesian estimation in the time domain and generalize the map-based formalism to non-ideal scenarios. This allows us to derive imperfection bounds at which the decoherence suppression remains approximately the same as under ideal conditions.
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 ($\mathrm{\ensuremath{\Theta}}$) family of algorithms. In the asymptotic regime of high noise sensitivity of the SQ, we show analytically that this $\mathrm{\ensuremath{\Theta}}$ family of algorithms reduces the data qubit decoherence rate by a divisor scaling as the square of this sensitivity. Setting $\mathrm{\ensuremath{\Theta}}$ equal to its optimal value, ${\mathrm{\ensuremath{\Theta}}}^{★}$, 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.
Protecting quantum coherence against realistic environmental noise remains one of the fundamental obstacles to scalable quantum technologies. We develop a noise-adaptive dynamical decoupling framework that combines analytical open-quantum-system modeling with machine-learning-based forecasting for a qubit interacting with random telegraph noise. Unlike conventional dynamical decoupling protocols based on fixed pulse schedules, the proposed approach continuously forecasts short-time coherence evolution and adaptively applies control pulses according to the instantaneous noise dynamics. We investigate stationary and non-stationary environments spanning both Markovian and non-Markovian regimes. Numerical simulations demonstrate that the machine-learning-assisted adaptive control strategy substantially outperforms conventional periodic dynamical decoupling while using a comparable number of control pulses. The improvement becomes particularly pronounced in non-Markovian and non-stationary regimes, where memory effects, coherence revivals, and temporally evolving noise strongly limit the effectiveness of static pulse protocols. These results establish predictive machine-learning-assisted dynamical decoupling as a promising and scalable framework for adaptive quantum control in realistic noisy quantum devices.
Abstract We consider a system of qubits affected by an environmental random-telegraph process (RTP) noise and investigate the recently proposed idea of using a spectator qubit (SQ) as a noise probe to remove noise effects from a data qubit (DQ). By measuring the SQ at various times with particular measurement bases, their measurement readouts can be used to extract the information of the noise effects. In this work, we propose the use of recurrent neural network (RNN), with the Long short-term memory (LSTM) layers, to process the SQ’s readouts and train the model to estimate the errors occurred in the DQ. We present numerical results of the DQ’s and SQ’s phases and show that the LSTM can estimate the unknown DQ’s phase with the estimation accuracy depending on the SQ’s noise sensitivity.
Abstract We investigate the recently proposed theoretical models and algorithms in Song et al. [1] for mitigating decoherence in solid-state qubit systems, where qubits are affected by charge (random telegraph) noises. The model includes a setup of a logical qubit (data qubit) and a spectator qubit, where the latter is used as a probe of the noise. The probe results can be used in correcting the phase error in order to improve the decoherence of the data qubit. In this work, we apply the proposed model with parameters extracted from recent solid-state qubit experiments. We extract parameters such as the noise switching rates, the qubit sensitivities to noise, and the measurement dead time. Using these parameters, we then numerically simulate the data qubit’s phase and the qubit decoherence. We also show that the proposed phase-correction technique using Bayesian estimation can improve the data qubit decoherence significantly.