Engineering Bosonic Codes with Quantum Lattice Gates

TL;DR

This paper introduces a universal quantum gate set called quantum lattice gates for engineering bosonic code states, enabling fault-tolerant quantum computing with continuous-variable systems, especially suited for superconducting circuits.

Contribution

It presents a systematic Floquet Hamiltonian engineering framework for bosonic code state preparation and transformation using a novel quantum lattice gate set.

Findings

Demonstrates code state engineering for single states, code space embedding, and transformations.

Shows application to automatic quantum error correction with four-legged cat codes.

Proposes implementation in superconducting circuits with fast gate times.

Abstract

Bosonic codes offer a hardware-efficient approach to encoding and protecting quantum information with a single continuous-variable bosonic system. In this paper, we introduce a new universal quantum gate set composed of only one type of gate element, which we call the quantum lattice gate, to engineer bosonic code states for fault-tolerant quantum computing. We develop a systematic framework for code state engineering based on the Floquet Hamiltonian engineering, where the target Hamiltonian is constructed directly from the given target state(s). We apply our method to three basic code state engineering processes, including single code state preparation, code space embedding and code space transformation. We explore the application of our method to automatic quantum error correction against single-photon loss with four-legged cat codes. Our proposal is particularly well-suited for superconducting circuit architectures with Josephson junctions, where the full nonlinearity of Josephson junction potential is harnessed as a quantum resource and the quantum lattice gate can be implemented on a sub-nanosecond timescale.