Optimal Universal Quantum Circuits for Unitary Complex Conjugation - INSPIRE

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Optimal Universal Quantum Circuits for Unitary Complex Conjugation

Daniel Ebler
(
- Unlisted, CN
)
,
Michał Horodecki
(
- Gdansk U.
)
,
Marcin Marciniak
(
- Gdansk U.
)
,
Tomasz Młynik
(
- Gdansk U.
)
,
Marco Túlio Quintino
(
- LIP6, Paris and
- IQOQI, Vienna and
- Vienna U.
)

May 31, 2022

20 pages

Published in:

IEEE Trans.Info.Theor. 69 (2023) 8, 5069-5082,
IEEE Trans.Info.Theor. 69 (2023) 8

Published: Aug, 2023

e-Print:

2206.00107 [quant-ph]

DOI:

10.1109/TIT.2023.3263771

View in:

ADS Abstract Service

reference search12 citations

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Abstract: (IEEE)

Let

U_{d}

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

U_{d}

into its complex conjugate

\overline {U_{d}}

. Our circuits admit a parallel implementation and are proven to be optimal for any

k

and

d

with an average fidelity of

\left \langle{ {F}}\right \rangle =\frac {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

U_{d}

, and the special case of

k=d-1

calls. We then show that our results encompass optimal transformations from

k

calls of

U_{d}

to

f(U_{d})

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.

Note:

20 pages, 5 figures. Improved presentation, typos corrected, and some proofs are now clearer. Close to the published version

Quantum circuit
Quantum channels
Transforms
Task analysis
Logic gates
Quantum state
Decoding
optimisation
probability
quantum computing

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