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Physical Review A

Experimental characterization of a non-Markovian quantum process

Kaumudibikash Goswami, Christina Giarmatzi, Christopher Pineda Monterola, Sally Shrapnel, Jacquiline Romero, Fabio Costa

Published Aug 26, 2021• 34 citations
Publisher

Abstract

Most noise-characterization methods for quantum technologies assume Markovianity, meaning that the environment and the system have no memory of their interactions with each other, because it is inefficient and computationally demanding to take temporal correlations into account. Here, the authors propose a more efficient machine learning method for estimating non-Markovian noise and implement it in a proof-of-principle quantum optics experiment.

DOI
10.1103/physreva.104.022432

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Most noise-characterization methods for quantum technologies assume Markovianity, meaning that the environment and the system have no memory of their interactions with each other, because it is inefficient and computationally demanding to take temporal correlations into account. Here, the authors propose a more efficient machine learning method for estimating non-Markovian noise and implement it in a proof-of-principle quantum optics experiment.
Every quantum system is coupled to an environment. Such system-environment interaction leads to temporal correlation between quantum operations at different times, resulting in non-Markovian noise. In principle, a full characterisation of non-Markovian noise requires tomography of a multi-time processes matrix, which is both computationally and experimentally demanding. In this paper, we propose a more efficient solution. We employ machine learning models to estimate the amount of non-Markovianity, as quantified by an information-theoretic measure, with tomographically incomplete measurement. We test our model on a quantum optical experiment, and we are able to predict the non-Markovianity measure with 90%90\%90% accuracy. Our experiment paves the way for efficient detection of non-Markovian noise appearing in large scale quantum computers.
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of projective single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of projective single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.
We show how a tensor-network-based machine learning algorithm can learn the structures of generic, non-Markovian, quantum stochastic processes. First, a process is represented as a matrix product operator (MPO) and trained with a database of local input states at different times and the corresponding time-nonlocal output state. We then apply the algorithm to predict the output state of a process at different times for a system that is coupled to a spin-chain environment. We then reconstruct the full process, and we quantify the non-Markovian memory by means of the bond dimension of the MPO for various properties of the system, of the environment, and of their interaction. Our study paves the way for a possible experimental investigation into the process tensor and its properties, and an effective characterization of noise in quantum devices.
The development of fault-tolerant quantum processors relies on the ability to control noise. A particularly insidious form of noise is temporally correlated or non-Markovian noise. By combining randomized benchmarking with supervised machine learning algorithms, we develop a method to learn the details of temporally correlated noise. In particular, we can learn the time-independent evolution operator of system plus bath and this leads to (i) the ability to characterize the degree of non-Markovianity of the dynamics and (ii) the ability to predict the dynamics of the system even beyond the times we have used to train our model. We exemplify this by implementing our method on a superconducting quantum processor. Our experimental results show a drastic change between the Markovian and non-Markovian regimes for the learning accuracies.