Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order

TL;DR

This paper presents a practical protocol for implementing arbitrary nonlocal controlled-unitary gates using indefinite causal order, enhancing scalability and flexibility in distributed quantum computation.

Contribution

It introduces an ICO-based method for programmable nonlocal gates that reduces circuit complexity and improves experimental feasibility.

Findings

Protocol enables arbitrary CU gate implementation via ICO.

Optical setup using Sagnac interferometer demonstrates practical realization.

Method offers scalable and flexible distributed quantum computation.

Abstract

Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orders of single-qubit gates, our protocol circumvents the drawback of complex local two-qubit operations. This ICO-based approach enables full programmability of CU gates by adjusting the inherent single-qubit operations, offering advantages over conventional fixed causal-order methods in terms of reduced circuit complexity and improved experimental flexibility. Furthermore, we develop an optical construction to implement the polarization CU gate using a stable and reciprocal Sagnac interferometer. Our work establishes a practical framework for scalable distributed quantum computation with flexible operations.