The paper derives optimal success probabilities and no-go thresholds for probabilistically transforming unknown unitary operations into their transpose, complex conjugate, or inverse, and proves adaptive circuits give exponential improvements over parallel ones.
Optimal processing of reversible quantum channels
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abstract
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully parallelized, consisting in a preprocessing channel followed by a parallel action of all the N unitaries and a final postprocessing channel. Our techniques allow to achieve an exponential reduction in the number of the free parameters of the optimization problem making it amenable to an efficient numerical treatment. Finally, we apply our general results to find the analytical solution for special cases of interest like the cloning of qubit phase gates.
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Probabilistic exact universal quantum circuits for transforming unitary operations
The paper derives optimal success probabilities and no-go thresholds for probabilistically transforming unknown unitary operations into their transpose, complex conjugate, or inverse, and proves adaptive circuits give exponential improvements over parallel ones.