Nonlinear and non-CP gates for Bloch vector amplification

TL;DR

This paper explores nonlinear and non-CP quantum gates that rapidly amplify the Bloch vector of a qubit, enabling efficient state preparation and demonstrating non-CP dynamics with potential experimental applications.

Contribution

It introduces nonlinear Markovian PTP channels for fast Bloch vector amplification, overcoming limitations of linear CPTP channels near fixed points.

Findings

Nonlinear channels enable rapid Bloch vector amplification.

Non-CP dynamics can be simulated with these channels.

Fast amplification without critical slowing down.

Abstract

Any state r = (x,y,z) of a qubit, written in the Pauli basis and initialized in the pure state r = (0,0,1), can be prepared by composing three quantum operations: two unitary rotation gates to reach a pure state on the Bloch sphere, followed by a depolarization gate to decrease |r|. Here we discuss the complementary state-preparation protocol for qubits initialized at the center of the Bloch ball, r=0, based on increasing or amplifying |r| to its desired value, then rotating. Bloch vector amplification may or may not increase qubit energy, but it necessarily increases purity and decreases entropy. Amplification can be achieved with a linear Markovian CPTP channel by placing the channel's fixed point away from r=0, making it nonunital, but the resulting gate suffers from a critical slowing down as that fixed point is approached. Here we consider alternative designs based on linear and nonlinear Markovian PTP channels, which offer benefits relative to linear CPTP channels, namely fast Bloch vector amplification without deceleration. These operations simulate a reversal of the thermodynamic arrow of time for the qubit and would provide striking experimental demonstrations of non-CP dynamics.