Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models

Luchnikov, I. A.; Kiktenko, E. O.; Gavreev, M. A.; Ouerdane, H.; Filippov, S. N.; Fedorov, A. K.

doi:10.48550/arxiv.2103.14490

Cited by 3 publications

(4 citation statements)

References 73 publications

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“…The data driven approach for predictive dynamics used here and, for instance, in references [19,20] has some clear similarities to both the projection and the collision methods. One defines r t i as the Bloch vector for the i-th qubit at the time t, which is then discretised into t n = n∆ with n an integer and some fundamental time ∆, and sets…”

Section: B Data-driven Methodsmentioning

confidence: 98%

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Data-Driven Time Propagation of Quantum Systems with Neural Networks

Nelson,

Coopmans,

Kells

et al. 2022

Preprint

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We investigate the potential of supervised machine learning to propagate a quantum system in time. While Markovian dynamics can be learned easily, given a sufficient amount of data, non-Markovian systems are non-trivial and their description requires the memory knowledge of past states. Here we analyse the feature of such memory by taking a simple 1D Heisenberg model as manybody Hamiltonian, and construct a non-Markovian description by representing the system over the single-particle reduced density matrix. The number of past states required for this representation to reproduce the time-dependent dynamics is found to grow exponentially with the number of spins and with the density of the system spectrum. Most importantly, we demonstrate that neural networks can work as time propagators at any time in the future and that they can be concatenated in time forming an autoregression. Such neural-network autoregression can be used to generate long-time and arbitrary dense time trajectories. Finally, we investigate the time resolution needed to represent the system memory. We find two regimes: for fine memory samplings the memory needed remains constant, while longer memories are required for coarse samplings, although the total number of time steps remains constant. The boundary between these two regimes is set by the period corresponding to the highest frequency in the system spectrum, demonstrating that neural network can overcome the limitation set by the Shannon-Nyquist sampling theorem.

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Section: B Data-driven Methodsmentioning

confidence: 98%

“…For instance, in reference [19] this data-driven method was applied to learn time-local generators of the dynamics of open quantum systems. Similarly, in [20] a related approach was used to find an effective Markovian embedding from which several important properties and the exact dynamics of the reduced system could be extracted.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Time Propagation of Quantum Systems with Neural Networks

Nelson,

Coopmans,

Kells

et al. 2022

Preprint

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“…The mentioned adjustments and enhancements with multiple small QRs are essential for realistic experimental implementations of QRC based on modern quantum technology 23 . Additionally, QRC may be interpreted as the 'inverse' to recently proposed methods that apply machine learning techniques to learn non-Markovian quantum dynamics of a qubit system in a complex environment 24,25 .…”

Section: Introductionmentioning

confidence: 99%

Computing with two quantum reservoirs connected via optimized two-qubit nonselective measurements

Vintskevich¹,

Grigoriev²

2022

Preprint

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At the present level of technology, quantum reservoir computing is one of the most promising and experimentally available techniques of hybrid quantum-classical machine learning. However, quantum reservoirs' practical applications are limited due to technological restrictions in the size of quantum systems, issues with gates control, and the affection of noise. Here we proposed a novel approach to connect quantum reservoirs in a network to overcome these issues and enhance quantum reservoir computing performance. This approach is based on an optimized two-qubit nonselective measurements channel. We also introduce an optimized single qubit purification channel for further quantum reservoir computing enhancements. We validate our approach via numerical simulations. We demonstrate that the optimized channels applied to a seven-qubits network can effectively transfer information between its parts. The resulting overall performance is comparable with networks of twenty-five qubits in total connected via a classical information link.

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“…Here, we propose a different approach to a class of problems where a sufficiently small subsystem S of a many-body system is subject to time-dependent controls. Focusing on time evolution of degrees of freedom in S, we represent the rest of the many-body system E by its lower-dimensional "twin", or a reduced-order [10][11][12][13] model. Such a reduction effectively keeps track of the relevant degrees of freedom in E, discarding the ones which have little or no influence on dynamics of S. The reduced-order model may involve effective Hilbert space dimension that is orders of magnitude smaller than the one in the original problem.…”

Section: Introductionmentioning

confidence: 99%

Controlling quantum many-body systems using reduced-order modelling

Luchnikov¹,

Gavreev²,

Fedorov³

2022

Preprint

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Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum systems, where time-dependent controls are applied to a sufficiently small subsystem. The approach is based on a tensor-networks-based scheme to build a low-dimensional reduced-order model of the subsystem's non-Markovian dynamics. Simulating dynamics of such a reduced-order model, viewed as a "digital twin" of the original subsystem, is significantly more efficient, which enables the use of gradient-based optimization toolbox in the control parameter space. We validate the proposed method by solving control problems for quantum spin chains. In particular, the approach automatically identifies sequences for exciting the quasiparticles and guiding their dynamics to recover and transmit information. Additionally, when disorder is induced and the system is in the many-body localized phase, we find generalized spin-echo sequences for dynamics inversion, which show improved performance compared to standard ones. Our approach by design takes advantage of non-Markovian dynamics of a subsystem to make control protocols more efficient, and, under certain conditions can store information in the rest of the many-body system and subsequently retrieve it at a desired moment of time. We expect that our results will find direct applications in the study of many-body systems, in probing non-trivial quasiparticle properties, as well as in development control tools for quantum computing devices.

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Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models

Cited by 3 publications

References 73 publications

Data-Driven Time Propagation of Quantum Systems with Neural Networks

Data-Driven Time Propagation of Quantum Systems with Neural Networks

Computing with two quantum reservoirs connected via optimized two-qubit nonselective measurements

Controlling quantum many-body systems using reduced-order modelling

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