Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks

TL;DR

This paper introduces a linear-optical scheme for encoding grid-state qubits into bosonic modes using cat states and quantum walks, enabling high-fidelity qubit preparation suitable for optical and microwave platforms.

Contribution

It presents a novel linear-optical implementation of quantum-walk encoding for GKP qubits using cat states and post-selection, advancing bosonic qubit encoding methods.

Findings

High-fidelity encoding achievable with proper parameter tuning

Feasible with current optical and superconducting-circuit technologies

Conditional phase-space displacement implemented via Mach-Zehnder interferometer

Abstract

We propose a linear-optical scheme that allows encoding grid-state quantum bits (qubits) into a bosonic mode using cat state and post-selection as sources of non-Gaussianity in the encoding. As a linear-optical realization of the quantum-walk encoding scheme in [Lin {\em et al.}, Quantum Info. Processing {\bf 19}, 272 (2020)], we employ the cat state as a quantum coin that enables encoding approximate Gottesman-Kitaev-Preskill (GKP) qubits through quantum walk of a squeezed vacuum state in phase space. We show that the conditional phase-space displacement necessary for the encoding can be realized through a Mach-Zehnder interferometer (MZI) assisted with ancillary cat-state input under appropriate parameter regimes. By analyzing the fidelity of the MZI-based displacement operation, we identify the region of parameter space over which the proposed linear-optical scheme can generate grid-state qubits with high fidelity. With adequate parameter setting, our proposal should be accessible to current optical and superconducting-circuit platforms in preparing grid-state qubits for bosonic modes in the, respectively, optical and microwave domains.