A Very Small Logical Qubit

TL;DR

This paper proposes a simple superconducting circuit design that passively protects against quantum errors, significantly enhancing logical qubit coherence times by leveraging continuous driving and engineered dissipation.

Contribution

It introduces a novel circuit blueprint combining transmon and lossy qubits with continuous driving and dissipation for passive error protection in superconducting qubits.

Findings

Logical state coherence could be improved by a factor of forty or more.

The proposed method offers substantial headroom for coherence improvement.

The design is compatible with existing superconducting qubit technologies.

Abstract

Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven SQUID couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multi-qubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of forty or more compared to the individual qubit $T_1$ and $T_2$ using this technique. We thus demonstrate that there is substantial headroom for improving the coherence of modern superconducting qubits with a fairly modest increase in device complexity.