Fast quantum state discrimination with nonlinear PTP channels

Abstract

We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution 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 $\varphi$ on bounded linear operators $X$, there is an associated normalized PTP channel $\varphi (X)/\mathrm{tr}[\varphi (X)]$. 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, suggesting 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 novel phase where a pair of attracting fixed points create an intrinsically fault-tolerant nonlinear state discriminator.

References in corpus (10)

• Quantum state discrimination and its applications
• Mixed-state evolution in the presence of gain and loss
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• A Causal Framework for Non-Linear Quantum Mechanics
• Quantum Dynamics with Mean Field Interactions: a New Approach
• Stability of the Grabert master equation
• Self-organized PT-symmetry of exciton-polariton condensate in a double-well potential
• Nonlinear quantum gates for a Bose-Einstein condensate
• Nonlinear speed-ups in ultracold quantum gases

Cited by in corpus (7)

• Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians
• Quantum simulation of dissipation for Maxwell equations in dispersive media
• Nonlinear and non-CP gates for Bloch vector amplification
• Proposal for a Lorenz qubit
• Suppressing excitations in the nonlinear Landau-Zener model
• Quantum thermodynamics of Gross-Pitaevskii qubits
• The universe as a nonlinear quantum simulation: Large $n$ limit of the central spin model