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 i...

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Bibliographic Details
Published in:Physical review letters Vol. 122; no. 23; p. 231302
Main Authors: Caputa, Paweł, Magan, Javier M.
Format: Journal Article
Language:English
Published: United States American Physical Society 14.06.2019
Subjects:
Complexity
Computation
Conformal mapping
Gates (circuits)
Gravitation
Tensors
ISSN:0031-9007, 1079-7114, 1079-7114
Online Access:Get full text
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Summary: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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ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.122.231302