The SWITCH test for discriminating quantum evolutions

We study different quantum circuits that can discriminate between two arbitrary quantum evolution operators. These circuits can be used to check whether two quantum operators are equal or not and to estimate a fidelity measure telling how close the operators are. This operator comparison is related to the SWAP test for discriminating two quantum states. In terms of their practical realization, we comment possible laboratory implementations with light along the same lines of recent experimental realizations of quantum superpositions of causal orders exploiting the different degrees of freedom of photons. We also discuss hardware efficient realizations for noisy intermediate scale quantum computers. Finally, we comment potential applications to the discrimination of quantum communication channels and to the search for simpler quantum circuits in quantum compilers.

Automated summary

We study different quantum circuits for discriminating between two arbitrary quantum evolution operators. These circuits can be used to check whether two quantum operators are equal and estimate the fidelity measure of their closeness. The operator comparison is related to the SWAP test for discriminating two quantum states. We discuss possible laboratory implementations with light using recent experimental realizations of quantum superpositions of causal orders and hardware efficient realizations for noisy intermediate scale quantum computers. We also comment on potential applications in discriminating quantum communication channels and searching for simpler quantum circuits in quantum compilers.