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Quantum Computation as Gravity.

08:00 EDT 14th June 2019 | BioPortfolio

Summary of "Quantum Computation as Gravity."

We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.

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This article was published in the following journal.

Name: Physical review letters
ISSN: 1079-7114
Pages: 231302

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