Optimal Universal Quantum Circuits for Unitary Complex Conjugation

Autor(en)

Daniel Ebler, Michal Horodecki, Marcin Marciniak, Tomasz Młynik, Marco Túlio Quintino, Michał Studziński

Abstrakt

Let Ud be a unitary operator representing an arbitrary d-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number k of calls of Ud into its complex conjugate Ud. Our circuits admit a parallel implementation and are proven to be optimal for any k and d with an average fidelity of {F}=k+1/d(d-k). Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call ( k=1) of the operation Ud, and the special case of k=d-1 calls. We then show that our results encompass optimal transformations from k calls of Ud to f(Ud) for any arbitrary homomorphism f from the group of d-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphism on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Huawei Technologies Co., Ltd., University of Gdańsk, Österreichische Akademie der Wissenschaften (ÖAW), Icm & Sorbonne University

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

Band

69

Seiten

5069-5082

Anzahl der Seiten

14

ISSN

0018-9448

DOI

https://doi.org/10.48550/arXiv.2206.00107

Publikationsdatum

08-2023

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 102015 Informationssysteme

Schlagwörter

ASJC Scopus Sachgebiete

Information systems, Computer Science Applications, Library and Information Sciences

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/e8c6a60f-5c07-4215-9868-c392b2e075e4