Single-loop multiple-pulse nonadiabatic holonomic quantum gates

TL;DR

This paper introduces a single-loop approach for nonadiabatic holonomic quantum gates, simplifying previous multi-loop methods and enabling efficient, robust quantum computation with potential experimental implementation in atomic systems.

Contribution

It proposes a novel single-loop scheme for nonadiabatic holonomic one-qubit gates, reducing complexity and maintaining universality for quantum computation.

Findings

Single-loop gates are sufficient for arbitrary one-qubit holonomic operations.

The scheme can be implemented using laser pulses in atomic systems with a three-level structure.

The approach enhances efficiency and robustness of quantum gates.

Abstract

Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. {\bf 14}, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\Lambda$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\Lambda$-coupling structure, by utilizing carefully chosen laser pulses.