Protected gates for superconducting qubits

TL;DR

This paper demonstrates that quantum phase gates on superconducting qubits, protected by continuous-variable quantum error correction, can achieve exponentially small errors with high oscillator impedance, enabling fault-tolerant quantum computation.

Contribution

It introduces a scheme for protected quantum gates on superconducting qubits using tunable Josephson coupling and analyzes their error suppression capabilities.

Findings

Gate errors are exponentially small with large oscillator impedance.

Protected gates are not universal alone but can be combined with unprotected operations for universal computation.

Numerical simulations validate the analytical error estimates.

Abstract

We analyze the accuracy of quantum phase gates acting on "0-$\pi$ qubits" in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an $LC$ oscillator and a qubit or pair of quits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance $\sqrt{L/C}$ is large compared to $\hbar/4e^2 \approx 1\, k\Omega$. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.