Experimentally undoing an unknown single-qubit unitary

TL;DR

This paper demonstrates experimentally reversing unknown single-qubit unitaries using linear optical elements, achieving high fidelity and confirming the feasibility of universal quantum circuit-based undoing schemes.

Contribution

It provides the first experimental implementation of reversing unknown single-qubit unitaries, validating a theoretical universal undoing scheme.

Findings

Average fidelity of inverse unitaries is 0.9767

Experimental results match theoretical predictions

Feasibility of reversing unknown unitaries confirmed

Abstract

Undoing a unitary operation, $i.e$. reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any specific description, however, it is a hard and challenging task to realize the inverse operation. Recently, a universal quantum circuit has been proposed [Phys.Rev.Lett. 123, 210502 (2019)] to undo an arbitrary unknown $d$-dimensional unitary $U$ by implementing its inverse with a certain probability. In this letter, we report the experimental reversing of three single-qubit unitaries $(d = 2)$ by linear optical elements. The experimental results prove the feasibility of the reversing scheme, showing that the average fidelity of inverse unitaries is $F=0.9767\pm0.0048$, in close agreement with the theoretical prediction.