• Open Access

Quantum Computation as Gravity

Paweł Caputa and Javier M. Magan
Phys. Rev. Lett. 122, 231302 – Published 12 June 2019
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Abstract

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.

  • Received 6 September 2018
  • Revised 4 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.231302

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyParticles & Fields

Authors & Affiliations

Paweł Caputa1 and Javier M. Magan2

  • 1Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
  • 2Instituto Balseiro, Centro Atomico Bariloche S. C. de Bariloche, Rio Negro, R8402AGP, Argentina

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Issue

Vol. 122, Iss. 23 — 14 June 2019

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