Encoding qubits into harmonic-oscillator modes via quantum walks in phase space

TL;DR

This paper introduces a theoretical framework for encoding qubits into harmonic oscillator modes using quantum walks in phase space, resulting in codewords that outperform traditional GKP states in error correction.

Contribution

It presents a novel quantum walk-based encoding scheme for qubits in continuous-variable systems, with a detailed analysis of its error correction performance and implementation architecture.

Findings

Quantum walks can generate GKP-like codewords from squeezed states.

The new codewords slightly outperform traditional GKP states in error correction.

A circuit architecture for implementing the encoding scheme is proposed.

Abstract

We provide a theoretical framework for encoding arbitrary logical states of a quantum bit (qubit) into a continuous-variable quantum mode through quantum walks. Starting with a squeezed-vacuum state of the quantum mode, we show that quantum walks of the state in phase space can generate output states that are variants of codeword states originally put forward by Gottesman, Kitaev, and Preskill (GKP) [Phys. Rev. A {\bf 64}, 012310 (2001)]. In particular, with a coin-toss transformation that projects the quantum coin onto the diagonal coin-state, we show that the resulting {\em dissipative} quantum walks can generate qubit encoding akin to the prototypical GKP encoding. We analyze the performance of these codewords for error corrections and find that even without optimization our codewords outperform the GKP ones by a narrow margin. Using the circuit representation, we provide a general architecture for the implementation of this encoding scheme and discuss its possible realization through circuit quantum-electrodynamics systems.