Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits

TL;DR

This paper proposes a method for implementing universal holonomic quantum gates in superconducting circuits using only two-level transmon qubits within a decoherence-free subspace, overcoming previous limitations and enabling high-fidelity, robust quantum computation.

Contribution

It introduces a scheme for non-adiabatic holonomic quantum computation in superconducting circuits using minimal resources and only two levels per qubit, simplifying implementation.

Findings

Achieves high-fidelity quantum gates in superconducting circuits.

Overcomes previous challenges requiring multi-level systems.

Demonstrates robustness of the proposed holonomic scheme.

Abstract

To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is a conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfil for superconducting qubits, appearing to be a main reason why only single qubit gates was implemented in a recent experiment [A. A. Abdumalikov Jr \emph{et al}., Nature 496, 482 (2013)]. Here we propose to realize non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies, but also can still achieve considerably large effective coupling strength, such that high fidelity quantum gates can be achieved. Therefore, the present scheme makes it very promising way to realize robust holonomic quantum computation with superconducting circuits.