Effects of self-phase modulation on weak nonlinear optical quantum gates

TL;DR

This paper investigates how self-phase modulation affects weak nonlinear optical quantum gates, revealing that it can hinder the gate's ability to distinguish qubit parity, thus impacting quantum computing implementations.

Contribution

It introduces generating functions for the Wigner function of modulated coherent states and analyzes the impact of self-phase modulation on parity gate performance.

Findings

Self-phase modulation can prevent parity distinction in quadrature measurements.

Materials with negligible self-phase modulation are necessary for effective weak nonlinear parity gates.

The study provides a framework for assessing physical implementations of optical quantum gates.

Abstract

A possible two-qubit gate for optical quantum computing is the parity gate based on the weak Kerr effect. Two photonic qubits modulate the phase of a coherent state, and a quadrature measurement of the coherent state reveals the parity of the two qubits without destroying the photons. This can be used to create so-called cluster states, a universal resource for quantum computing. Here, the effect of self-phase modulation on the parity gate is studied, introducing generating functions for the Wigner function of a modulated coherent state. For materials with non-EIT-based Kerr nonlinearities, there is typically a self-phase modulation that is half the magnitude of the cross-phase modulation. Therefore, this effect cannot be ignored. It is shown that for a large class of physical implementations of the phase modulation, the quadrature measurement cannot distinguish between odd and even parity. Consequently, weak nonlinear parity gates must be implemented with physical systems where the self-phase modulation is negligable.