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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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
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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.
AbstractList 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.
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.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.
ArticleNumber 231302
Author Magan, Javier M.
Caputa, Paweł
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BackLink https://www.ncbi.nlm.nih.gov/pubmed/31298880$$D View this record in MEDLINE/PubMed
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Snippet We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal...
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StartPage 231302
SubjectTerms Complexity
Computation
Conformal mapping
Gates (circuits)
Gravitation
Tensors
Title Quantum Computation as Gravity
URI https://www.ncbi.nlm.nih.gov/pubmed/31298880
https://www.proquest.com/docview/2249190163
https://www.proquest.com/docview/2257718877
Volume 122
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