Linear and integrable nonlinear evolution of the qutrit

Kowalski, Krzysztof

doi:10.1007/s11128-020-02640-6

Cited by 10 publications

(18 citation statements)

References 28 publications

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“…In this paper we investigate models of nonlinear quantum computation based on a category of PTP channels that take the form of a nonlinear positive channel rescaled to conserve trace [50,51,53,61]. Although normalized PTP channels do not provide an exhaustive clas-sification of nonlinear channels, they are sufficient to illustrate some of the different types of effective nonlinearity that are available or might become available in the near future.…”

Section: Ptp Modelsmentioning

confidence: 99%

“…The additional assumptions (i) and (ii) are sufficient to define, for any PTP channel, a Markovian master equation that extends linear Markovian CPTP evolution by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation [72,73]. Our approach follows a large body of work on nonlinear master equations [42][43][44][45][46][47][48][49][50][51][52][53]. Especially relevant are the recent papers by Kowalski and Rembieliński [50], Fernengel and Drossel [46], and Rembieliński and Caban [53].…”

Section: B Nino Channelsmentioning

confidence: 99%

“…Examples include mean field models for superfluids, superconductors, and laser fields. Beyond mean field theory, various forms of nonlinearity have been proposed to describe friction and dissipation in quantum mechanics [42,[45][46][47][48][49][50][51] and for open systems more generally [42,[45][46][47][48][49][50][51][52][53].…”

mentioning

confidence: 99%

“…Building on a growing body of similarly motivated work [42][43][44][45][46][47][48][49][50][51][52][53], we study a family of normalized PTP channels of the form φ(X)/tr[φ(X)], where φ(X) is a positive linear or nonlinear map on bounded linear operators X satisfying tr[φ(X)] = 0. Normalized PTP channels fall into 4 classes, yielding 3 distinct forms of nonlinearity.…”

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confidence: 99%

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Fast quantum state discrimination with nonlinear PTP channels

Geller¹

2021

Preprint

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We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and associated master equations. The models are defined in any finite Hilbert space, but the main results are for dimension 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)]. 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 4 types, yielding 3 distinct forms of nonlinearity whose computational power we explore. 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, resulting in an exponential speedup for state discrimination. Building on this idea, we argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a phase where a pair of stable fixed points create an intrinisically fault-tolerant nonlinear state discriminator.

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Section: Ptp Modelsmentioning

confidence: 99%

Section: B Nino Channelsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Fast quantum state discrimination with nonlinear PTP channels

Geller¹

2021

Preprint

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“…Several recent papers [1][2][3][4][5][6][7] have considered nonlinear generalizations of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation [8,9] for qudits. The superoperators resulting from these evolutions each take the form of a positive trace-preserving (PTP) channel [10,11] X → φ(X)/tr[φ(X)], with X a density matrix and φ a positive map.…”

mentioning

confidence: 99%

Lorenz qubit

Geller¹

2021

Preprint

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Nonlinear qubit master equations have recently been shown to exhibit rich dynamical phenomena such as period doubling, Hopf bifurcation, and strange attractors usually associated with classical nonlinear systems. Here we investigate nonlinear qubit models that support tunable Lorenz attractors. A Lorenz qubit could be realized experimentally by combining qubit torsion, generated by real or simulated mean field dynamics, with linear amplification and dissipation. This would extend engineered Lorenz systems to the quantum regime, allowing for their direct experimental study and possible application to quantum information processing.

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Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

Geller

2023

Adv Quantum Tech

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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. 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)]. 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.

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Linear and integrable nonlinear evolution of the qutrit

Cited by 10 publications

References 28 publications

Fast quantum state discrimination with nonlinear PTP channels

Fast quantum state discrimination with nonlinear PTP channels

Lorenz qubit

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

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