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arXiv:2308.14756 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Adaptive mitigation of time-varying quantum noise

Samudra Dasgupta, Travis S. Humble, Arshag Danageozian

Published Sep 17, 2023• 9 citations
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Abstract

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.

DOI
10.1109/qce57702.2023.00020

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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.
Estimates of noise channels for quantum gates are required for most error-mitigation techniques and are desirable for informing quantum error-correction decoders. These estimates can be obtained by resource-intensive offline characterization techniques, but can become stale due to device drift and fluctuations. We propose a method to address this issue by performing real-time adaptation of noise channel estimates during the execution of a quantum algorithmic circuit using extended flag gadgets, midcircuit measurements, and Bayesian inference. We carry out analytical calculations and numerical simulations employing a Dirichlet prior distribution for the error rates in a Pauli channel to demonstrate and evaluate the technique, which can be seen as a protocol for real-time calibration of high-level gate error information.
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise that is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates is critical to these models. We use a Bayesian inference approach to identify posterior distributions of these parameters such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM’s quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in some scenarios.
Error mitigation in a noisy quantum device requires a very good estimate of the noise channel. The accuracy of probabilistic error cancellation is often limited by the high sample complexity of channel tomography. In principle, optimal sample complexity is attained by maximum likelihood estimation (MLE), but MLE is computationally challenging. We show that MLE can be made computationally tractable in certain cases of interest. For the common case of a 1D-local sparse Pauli-Lindblad channel, the likelihood function reduces to an efficiently-evaluable Bayesian network. We show that the resulting computation leads to substantially improved tomography. In addition, we demonstrate by simulation that this can lead to meaningful improvements to the overhead of error mitigation. We also discuss possible extensions of our algorithm to more general settings, such as non-1D circuits and non-Pauli errors.
Conventional computers have evolved to device components that demonstrate failure rates of 1e-17 or less, while current quantum computing devices typically exhibit error rates of 1e-2 or greater. This raises concerns about the reliability and reproducibility of the results obtained from quantum computers. The problem is highlighted by experimental observation that today's NISQ devices are inherently unstable. Remote quantum cloud servers typically do not provide users with the ability to calibrate the device themselves. Using inaccurate characterization data for error mitigation can have devastating impact on reproducibility. In this study, we investigate if one can infer the critical channel parameters dynamically from the noisy binary output of the executed quantum circuit and use it to improve program stability. An open question however is how well does this methodology scale. We discuss the efficacy and efficiency of our adaptive algorithm using canonical quantum circuits such as the uniform superposition circuit. Our metric of performance is the Hellinger distance between the post-stabilization observations and the reference (ideal) distribution.
Quantum error mitigation (QEM) is a crucial technique for enhancing the reliability of quantum computations. Current methods, however, often rely on fixed noise levels, which can be computationally demanding and limit efficiency. This paper introduces a novel QEM algorithm utilizing a Bayesian neural network to dynamically adjust the probabilistic noise applied during error correction. Our design systematically learns the optimal noise level for each quantum state, continuously adapting to the evolving error profile. This adaptive approach promises to significantly improve both error suppression and computational efficiency compared to existing methods. The proposed algorithm offers a fundamentally new way to optimize error mitigation, paving the way for more robust and practical quantum computations.
Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC. Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER. We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.