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Measuring distance between quantum states on a quantum computer

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Abstract

We propose protocols for determining the distances in Hilbert space between pure and mixed quantum states prepared on a quantum computer. In the case of pure quantum states, the protocol is based on measuring the square of modulus of scalar product between certain states. Determination of the distance between mixed quantum states is reduced to measuring the squares of modules of scalar products between all pure states included in the mixed states. In addition, we develop a protocol that allows one to determine the speed of evolution of the spin system simulated by a quantum computer. We apply these protocols to measure distances and speeds of evolution of different quantum systems implemented on the ibmq-santiago quantum computer.

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Acknowledgements

This work was partly supported by Project 77/02.2020 (No. 0120U104801) from National Research Foundation of Ukraine. We are grateful to Profs. Volodymyr Tkachuk and Andrij Rovenchak for helpful advices.

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  1. Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., Lviv, UA, 79005, Ukraine

    A. R. Kuzmak

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Kuzmak, A.R. Measuring distance between quantum states on a quantum computer. Quantum Inf Process 20, 269 (2021). https://doi.org/10.1007/s11128-021-03196-9

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