Self-correcting GKP qubit in a superconducting circuit with an oscillating voltage bias

TL;DR

This paper introduces a superconducting circuit with an oscillating voltage bias that passively stabilizes GKP qubits against noise, significantly enhancing coherence times through dissipative error correction.

Contribution

The authors propose a novel circuit architecture that implements dissipative error correction for GKP qubits using a Josephson junction with oscillating voltage bias, enabling passive stabilization.

Findings

Dissipative stabilization enhances coherence time by ~1000 times.

The scheme works for both square and hexagonal GKP codes.

Proposes a Josephson current-based readout and Clifford gates.

Abstract

We propose a simple circuit architecture for a dissipatively error corrected Gottesman-Kitaev-Preskill (GKP) qubit. The device consists of a electromagnetic resonator with impedance $h/2e^2\approx 12.91\,{\rm k}\Omega$ connected to a Josephson junction with a voltage bias oscillating at twice the resonator frequency. For large drive amplitudes, the circuit is effectively described by the GKP stabilizer Hamiltonian, whose low-energy subspace forms the code space for a qubit protected against phase-space local noise. The GKP states in the codespace can be dissipatively stabilized and error corrected by coupling the resonator to a bath through a bandpass filter; a resulting side-band cooling effect stabilizes the system in the GKP code space, dissipatively correcting it against both bit and phase flip errors. Simulations show that this dissipative error correction can enhance coherence time by factor $\sim 1000$ with NbN-based junctions, for operating temperatures in the $\sim 100\,{\rm mK}$ range. The scheme can be used to stabilize both square- and hexagonal-lattice GKP codes. Finally, a Josephson current based readout scheme, and dissipatively corrected single-qubit Clifford gates are proposed.