Fast quantum state discrimination with nonlinear PTP channels

TL;DR

This paper explores nonlinear quantum channels based on PTP maps, demonstrating their potential to exponentially speed up quantum state discrimination and proposing a noise-robust, fault-tolerant nonlinear discriminator using dissipation-induced bifurcation.

Contribution

It classifies nonlinear PTP channels, analyzes their computational power, and introduces a robust, fault-tolerant quantum state discrimination method leveraging dissipation.

Findings

Nonlinear PTP channels can increase state separation exponentially.

Dissipation induces bifurcations leading to fault-tolerant discrimination.

Channels support distortions that enhance quantum measurement speed.

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 $\phi$ on bounded linear operators $X$, there is an associated normalized PTP channel $ \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 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.