Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations

Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao
Phys. Rev. Lett. 123, 210502 – Published 21 November 2019

Abstract

Given a quantum gate implementing a d-dimensional unitary operation Ud, without any specific description but d, and permitted to use k times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse Ud1, whose failure probability decays exponentially in k. The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires that kd1, proven necessary for the exact implementation of Ud1 with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, kd1 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 k and d. The optimal values are computed using semidefinite programing solvers for k3 when d=2 and k2 for d=3. With this numerical approach we show for the first time that indefinite causal order circuits provide an advantage over causally ordered ones in a task involving multiple uses of the same unitary operation.

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  • Received 22 October 2018
  • Revised 2 September 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.210502

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao

  • Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

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Issue

Vol. 123, Iss. 21 — 22 November 2019

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