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Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels Models of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension N=2$ N \! = \! 2$. For every normalizable linear or nonlinear positive map ϕ on bounded linear operators X, there is an associated normalized PTP channel ϕ(X)/tr[ϕ(X)]$ \phi (X) / {\rm tr}[\phi (X)]$. Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Quantum Technologies Wiley

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

Geller, Michael R.
Advanced Quantum Technologies , Volume 6 (6) – Jun 1, 2023
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References (114)

Publisher
Wiley
Copyright
© 2023 Wiley‐VCH GmbH
eISSN
2511-9044
DOI
10.1002/qute.202200156
Publisher site
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Abstract

Models of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension N=2$ N \! = \! 2$. For every normalizable linear or nonlinear positive map ϕ on bounded linear operators X, there is an associated normalized PTP channel ϕ(X)/tr[ϕ(X)]$ \phi (X) / {\rm tr}[\phi (X)]$. Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator.

Journal

Advanced Quantum Technologies – Wiley

Published: Jun 1, 2023

Keywords: nonlinear master equations; nonlinear quantum mechanics; quantum channels; quantum state discrimination

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