Logical measurement-based quantum computation in circuit-QED

TL;DR

This paper introduces a measurement-based quantum computing scheme in circuit-QED that uses error-correcting codes and continuous-variable qubits, enabling scalable, fault-tolerant quantum computation with microwave cavities.

Contribution

It presents a novel protocol for logical MBQC using CV qubits and a method to create cluster states via cross-Kerr interactions in circuit-QED.

Findings

Proposes a scalable scheme for logical MBQC in superconducting circuits.

Demonstrates how to generate CV-qudit cluster states with cross-Kerr interactions.

Lays groundwork for fault-tolerant quantum computing in circuit-QED systems.

Abstract

We propose a new scheme of measurement-based quantum computation (MBQC) using an error-correcting code against photon-loss in circuit quantum electrodynamics. We describe a specific protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schr\"odinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a readout resonator coupled with an ancillary superconducting qubit. We then examine a practical approach of how to create the CV-qudit cluster state via a cross-Kerr interaction induced by intermediary superconducting qubits between neighbouring cavities under the Jaynes-Cummings Hamiltonian. This approach could be scalable for building 2D logical cluster states and therefore will pave a new pathway of logical MBQC in superconducting circuits toward fault-tolerant quantum computing.