Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction

TL;DR

This paper introduces a unified framework for encoding qubits in bosonic modes using lattice structures in number-phase space, enabling efficient error correction and improved performance against dephasing noise.

Contribution

It presents a novel number-phase lattice encoding scheme for bosonic modes, expanding beyond quadrature-based codes and demonstrating new vortex effects for quantum error correction.

Findings

Oblique and diamond codes exhibit a number-phase vortex effect.

Codes outperform traditional quadrature codes against dephasing noise.

Potential applications in fault-tolerant quantum computation and quantum communication.

Abstract

Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in the quadrature phase space. Here we introduce a unified framework for encoding a qubit utilizing the symmetries in the phase space of number and phase variables of a bosonic mode. The logical codewords form lattice structures in the number-phase space, resulting in rectangular, oblique, and diamond-shaped lattice codes. Notably, oblique and diamond codes exhibit a number-phase vortex effect, where number-shift errors induce discrete phase rotations as syndromes, enabling efficient correction via phase measurements. These codes show significant performance advantages over conventional quadrature codes against dephasing noise in the potential one-way quantum communication applications. Our generalized number-phase codes open up new possibilities for fault-tolerant quantum computation and extending the quantum communication range with bosonic systems.