Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits

TL;DR

This paper proposes a practical method for implementing Clifford gates and read-out in superconducting GKP qubits, reducing error spread and achieving high-fidelity measurements with realistic hardware constraints.

Contribution

It introduces a hardware-efficient scheme for Clifford gates and state read-out in superconducting GKP codes, with error mitigation techniques and analytical models for loss and dephasing effects.

Findings

Clifford gates can be performed without single-qubit gates, reducing error spread.

Error mitigation via decoder modification significantly improves gate fidelity.

High-fidelity logical state read-out achievable with 75% efficiency in under a microsecond.

Abstract

The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. In this work, we provide a practical proposal to perform Clifford gates and state read-out in GKP codes implemented with active error correction in superconducting circuits. We present a method of performing Clifford circuits without physically implementing any single-qubit gates, reducing the potential for them to spread errors in the system. In superconducting circuits, all the required two-qubit gates can be implemented with a single piece of hardware. We analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Moreover, we develop a simple analytical technique to estimate the effect of loss and dephasing on GKP codes that matches well with numerics. Finally, we consider the effect of homodyne measurement inefficiencies on logical state read-out and present a scheme that implements a measurement with a $0.1\%$ error rate in $630$ ns assuming an efficiency of just~$75\%$.