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Journal of Physics Conference Series

Random-telegraph noise mitigation and qubit decoherence in solid-state experiments

Nattawut kamjam, Poramet Pathumsoot, Areeya Chantasri

Published Jan 1, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/2431/1/012102

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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.
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.
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.
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.
With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example are charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modelled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a {\em single} fluctuator, we theoretically implement an elementary bang-bang control protocol. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of the stochastic Schrödinger equation and compare it with an analytical saddle point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period and the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of 1/f1/f1/f-noise ubiquitous to the solid state world can be reduced.
With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example is charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modeled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a single fluctuator, we theoretically implement an elementary bang-bang control protocol, a protocol based on sudden pulses. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of a stochastic Schr\"odinger equation and compare it with an analytical saddle-point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period to the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of 1∕f1∕f1∕f noise ubiquitous to the solid-state world can be reduced.