Hidden Quantum Markov Models and non-adaptive read-out of many-body states

A Monras, A Beige, K Wiesner

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)]. These are based on repeated von Neumann measurements on a quantum dynamical system. Here we generalise the quantum finite-state generators by replacing the von Neumann pro jections by stochastic quantum operations. In this way we assure that any time series with a stochastic compressed description has a compressed quantum description. Moreover, we establish a link between our stochastic generators and the sequential readout of many-body states with translationally-invariant matrix product state representations. As an example, we consider the non-adaptive read-out of 1D cluster states. This is shown to be equivalent to a Hidden Quantum Model with two internal states, providing insight on the inherent complexity of the process. Finally, it is proven by example that the quantum description can have a higher degree of compression than the classical stochastic one.
Translated title of the contributionHidden Quantum Markov Models and non-adaptive read-out of many-body states
Original languageEnglish
Pages (from-to)93 - 122
Number of pages30
JournalApplied Mathematical and Computational Sciences
Volume3, issue 1
Publication statusPublished - Aug 2011

Bibliographical note

Publisher: MiLi Publications

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