TL;DR
This paper introduces a universal probabilistic quantum circuit capable of inverting unknown $d$-dimensional unitaries with success probability increasing exponentially with the number of uses, and demonstrates advantages of indefinite causal order circuits.
Contribution
It presents the first universal quantum circuit for inverting unknown unitaries, establishes necessary use counts, and shows indefinite causal order circuits outperform causally ordered ones.
Findings
Success probability decays exponentially with number of uses
Indefinite causal order circuits outperform causally ordered circuits
Necessary number of uses is at least $d-1$ for exact inversion
Abstract
Given a quantum gate implementing a -dimensional unitary operation , without any specific description but , and permitted to use times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse , whose failure probability decays, exponentially in . The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires , proven necessary for exact implementation of with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, uses are required. We then present a finite set of linear and positive semidefinite constraints characterizing universal unitary inversion protocols and formulate a convex optimization problem whose solution is the maximum success probability for given and . The optimal values are…
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