Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces

TL;DR

This paper proposes efficient non-adiabatic holonomic quantum gates within decoherence-free subspaces, enabling robust two- and three-qubit controlled operations with minimal resource requirements for fault-tolerant quantum computing.

Contribution

It introduces compact schemes for implementing multi-qubit controlled gates using non-adiabatic holonomy in decoherence-free subspaces with minimal encoding resources.

Findings

Successful implementation of two- and three-qubit controlled gates.

Minimal resource encoding using only two neighboring physical qubits.

Enhanced fault tolerance and coherence stability in quantum gates.

Abstract

Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented using non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.