Quantum random circuits

Quantum random circuits (QRC) is a concept of incorporating an element of randomness into the local unitary operations and measurements of a quantum circuit. The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable, hard-to-solve problems by averaging over an ensemble of outcomes. This incorporation of randomness into the circuits has many possible advantages, some of which are (i) the validation of quantum computers, which is the method that Google used when they claimed quantum supremacy in 2019,^[1] and (ii) understanding the universal structure of non-equilibrium and thermalization processes in quantum many-body dynamics.^[2]

^ Arute, Frank; Arya, Kunal; Bacon, Dave; et al. (2019-10-23). "Quantum supremacy using a programmable superconducting processor". Nature. 574 (7779): 505–510. arXiv:1910.11333. Bibcode:2019Natur.574..505A. doi:10.1038/s41586-019-1666-5. PMID 31645734. S2CID 204836822.
^ Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haan, Jeongwan (2017-07-24). "Quantum Entanglement Growth under Random Unitary Dynamics". Phys. Rev. X. 7 (3): 031016. arXiv:1608.06950. Bibcode:2017PhRvX...7c1016N. doi:10.1103/PhysRevX.7.031016. S2CID 118619617 – via American Physical Society.

[1] Arute, Frank; Arya, Kunal; Bacon, Dave; et al. (2019-10-23). "Quantum supremacy using a programmable superconducting processor". Nature. 574 (7779): 505–510. arXiv:1910.11333. Bibcode:2019Natur.574..505A. doi:10.1038/s41586-019-1666-5. PMID 31645734. S2CID 204836822.

[:0-2] Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haan, Jeongwan (2017-07-24). "Quantum Entanglement Growth under Random Unitary Dynamics". Phys. Rev. X. 7 (3): 031016. arXiv:1608.06950. Bibcode:2017PhRvX...7c1016N. doi:10.1103/PhysRevX.7.031016. S2CID 118619617 – via American Physical Society.

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