Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource

TL;DR

This paper introduces a fast, robust geometric quantum control scheme for logical qubits that simplifies control requirements and enhances error tolerance, demonstrated on superconducting circuits with high fidelity.

Contribution

It presents a new geometric control method combining decoherence-free subspace encoding and tunable couplings, improving robustness and fidelity over traditional approaches.

Findings

Numerical simulations show high gate fidelity and robustness.

The scheme effectively combines geometric phase and logical encoding error tolerance.

Experimental implementation on superconducting circuits is feasible.

Abstract

Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls, especially for logical qubits that involve more physical qubits, whose error tolerance is effective in principle though, their experimental demonstration is still demanding. Thus, how to best simplify the needed control and manifest its full advantage has become the key to widespread applications of geometric quantum computation. Here we propose a new fast and robust geometric scheme, with the decoherence-free-subspace encoding, and present its physical implementation on superconducting quantum circuits, where we only utilize the experimentally demonstrated parametrically tunable coupling to achieve high-fidelity geometric control over logical qubits. Numerical simulation verifies that it can efficiently combine the error tolerance from both the geometric phase and logical-qubit encoding, displaying our gate-performance superiority over the conventional dynamical one without encoding, in terms of both gate fidelity and robustness. Therefore, our scheme can consolidate both error suppression methods for logical-qubit control, which sheds light on the future large-scale quantum computation.