Kerr-effect-based quantum logical gates in decoherence-free subspace

TL;DR

This paper introduces a set of quantum logical gates within decoherence-free subspaces using Kerr nonlinearities, achieving high success probabilities and robustness, without complex circuits or auxiliary photons, enhancing practical quantum computing.

Contribution

It proposes a novel scheme for implementing key quantum gates in DFS using Kerr effects, simplifying the setup and improving robustness and feasibility.

Findings

Logical gates have success probabilities close to 1.

Gates are robust against photon loss with current technology.

The scheme avoids complex circuits and auxiliary photons.

Abstract

The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.