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IEEE Transactions on Communications

On Estimating Time-Varying Pauli Noise

Junaid ur Rehman, Hayder Al-Hraishawi, Trung Q. Duong, Symeon Chatzinotas, Hyundong Shin

Published Dec 12, 2023• 3 citations
Publisher

Abstract

We consider the problem of estimating time-varying quantum noise. Specifically, we focus on Pauli qubit noise with time-variations and attempt to construct the most accurate instantaneous channel description. To this end, we propose an adaptive framework of simultaneous communication and parameter estimation (SCAPE) that efficiently and accurately estimates the time-varying Pauli channel while communicating reliably over the channel being estimated. This adaptive framework gives the informed control of communication rate–parameter estimation tradeoff to communicating parties. Interestingly, this adaptive SCAPE requires post-processing entirely on the receiver’s end and minimal feedback to the sender to increase, decrease, or continue with the same code rate of employed error correcting code. This procedure can be particularly useful in time-varying quantum channels with natural periodic deviations in channel conditions, e.g., in satellite communication channels.

DOI
10.1109/tcomm.2023.3341886

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•Sep 2, 2026•0 citations
We consider the problem of estimating time-varying quantum noise. Specifically, we focus on Pauli qubit noise with time-variations and attempt to construct the most accurate instantaneous channel description. To this end, we propose an adaptive framework of simultaneous communication and parameter estimation (SCAPE) that efficiently and accurately estimates the time-varying Pauli channel while communicating reliably over the channel being estimated. This adaptive framework gives the informed control of communication rate–parameter estimation tradeoff to communicating parties. Interestingly, this adaptive SCAPE requires post-processing entirely on the receiver’s end and minimal feedback to the sender to increase, decrease, or continue with the same code rate of employed error correcting code. This procedure can be particularly useful in time-varying quantum channels with natural periodic deviations in channel conditions, e.g., in satellite communication channels.
We propose a scheme for simultaneous classical communication and parameter estimation of generalized Pauli channels. This framework relies on the facts that i) under certain conditions, Pauli channels act as classical symmetric channel, and ii) a recently proposed parameter estimation method of Pauli channels can be executed while satisfying the conditions of i). The performance of the parameter estimation part in this simultaneous scheme relies on the symbol error rate of the communication module. This reliance gives rise to a natural tradeoff between the communication rate and the performance of parameter estimation in this simultaneous scheme. We exemplify our protocol by utilizing repetition codes for communication and the aforementioned parameter estimation scheme for the characterization of the channel at hand. We explore the tradeoff behavior between the communication rate and the performance of parameter estimation in the numerical examples. Our proposal paves the way for practical methods in simultaneous communication and channel estimation over unknown quantum channels.
To capture the problem of joint communication and sensing in the quantum regime, we consider the problem of reliably communicating over a Classical-Quantum (c-q) channel that depends on a random parameter while simultaneously estimating the random parameter at the transmitter through a noisy feedback channel. Specifically, for non-adaptive estimation strategies, we obtain an exact characterization of the optimal tradeoffs between the rate of communication and the error exponent of parameter estimation. As in the classical setting, the tradeoff is governed by the empirical distribution of the codewords, which simultaneously controls the rate of reliable communication and the error exponent.
Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference based adaptive algorithm that can learn and mitigate quantum noise in response to changing channel conditions. Our study emphasizes the need for dynamic inference of critical channel parameters to improve program accuracy. We use the Dirichlet distribution to model the stochasticity of the Pauli channel. This allows us to perform Bayesian inference, which can improve the performance of probabilistic error cancellation (PEC) under time-varying noise. Our work demonstrates the importance of characterizing and mitigating temporal variations in quantum noise, which is crucial for developing more accurate and reliable quantum technologies. Our results demonstrate that Bayesian PEC can outperform non-adaptive approaches by a factor of 4.5x when measured using Hellinger distance from the ideal distribution.
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome measurements done anyway during quantum error correction. While these measurements preserve the encoded quantum state, it is currently not clear how much information about the noise can be extracted in this way. So far, apart from the limit of vanishing error rates, rigorous results have only been established for some specific codes. In this work, we rigorously resolve the question for arbitrary stabilizer codes. The main result is that a stabilizer code can be used to estimate Pauli channels with correlations across a number of qubits given by the pure distance. This result does not rely on the limit of vanishing error rates, and applies even if high weight errors occur frequently. Moreover, it also allows for measurement errors within the framework of quantum data-syndrome codes. Our proof combines Boolean Fourier analysis, combinatorics and elementary algebraic geometry. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.
This article explores the performance of quantum communication systems in the presence of noise and focuses on finding the optimal encoding for maximizing the classical communication rate, approaching the classical capacity in some scenarios. Instead of theoretically bounding the ultimate capacity of the channel, we adopt a signal processing perspective to estimate the achievable performance of a physically available but otherwise unknown quantum channel. By employing a variational algorithm to estimate the trace distance between quantum states, we numerically determine the optimal encoding protocol for the amplitude damping and Pauli channels. Our simulations demonstrate the convergence and accuracy of the method with a few iterations, confirming that optimal conditions for binary quantum communication systems can be variationally determined with minimal computation. Furthermore, since the channel knowledge is not required at the transmitter or at the receiver, these results can be employed in arbitrary quantum communication systems, including satellite-based communication systems, a particularly relevant platform for the quantum Internet.
This paper investigates adaptive optimization techniques for quantum error correction (QEC) codes. The core claim is that dynamic adjustment of QEC parameters, guided by estimates of decoherence probabilities, can significantly enhance the efficiency of quantum information transmission. The proposed mechanism utilizes real-time adjustments to the code's redundancy, encoding scheme, and error correction protocols, adapting to varying noise environments and qubit states. Traditional QEC approaches typically employ fixed parameters, lacking the crucial element of adaptability. This research addresses this limitation by introducing a framework for continuous optimization based on accurate decoherence probability assessment. The framework involves estimating the decoherence probability (Pd) of individual qubits, which is then used to dynamically modify key parameters of the QEC code. Specifically, we explore adjusting the code rate (R), the minimum distance (d) of the code, and the choice of error correction scheme. The optimization algorithm aims to minimize the overall error rate while maintaining a desired level of performance. This work presents a novel approach to QEC, promising improved robustness and efficiency in quantum communication and computation. The key mathematical components of this work are presented below.