Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem

TL;DR

This paper introduces a new quantum algorithm with indefinite causal order for generalized Deutsch's problem, reducing query complexity and gate count, and demonstrates it experimentally with high success probability.

Contribution

It generalizes Deutsch's problem to multiple functions and proposes an innovative indefinite causal order quantum algorithm, experimentally validated with high fidelity.

Findings

Achieved ~99.7% success probability in experiments.

Reduced the number of queries and gates compared to classical and previous quantum algorithms.

Demonstrated robustness and stability of the implementation in a Sagnac loop interferometer.

Abstract

Deutsch's algorithm is the first quantum algorithm to show the advantage over the classical algorithm. Here we generalize Deutsch's problem to $n$ functions and propose a new quantum algorithm with indefinite causal order to solve this problem. The new algorithm not only reduces the number of queries to the black-box by half over the classical algorithm, but also significantly reduces the number of required quantum gates over the Deutsch's algorithm. We experimentally demonstrate the algorithm in a stable Sagnac loop interferometer with common path, which overcomes the obstacles of both phase instability and low fidelity of Mach-Zehnder interferometer. The experimental results have shown both an ultra-high and robust success probability $\sim 99.7\%$. Our work opens up a new path towards solving the practical problems with indefinite casual order quantum circuits.