Quantum computational complexity from quantum information to black holes and back

Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely different physical problem – that of information processing ins...

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Vydáno v:The European physical journal. C, Particles and fields Ročník 82; číslo 2; s. 1 - 40
Hlavní autoři: Chapman, Shira, Policastro, Giuseppe
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer
Springer Nature B.V
Springer Verlag (Germany)
SpringerOpen
Témata:
Astronomy
Astrophysics and Cosmology
Atoms
Black holes
Complexity
Data processing
Elementary Particles
Geometry
Hadrons
Heavy Ions
High Energy Physics - Theory
Holography
Measurement Science and Instrumentation
New Frontiers in Holographic Duality
Nuclear Energy
Nuclear Physics
Phase transitions
Physics
Physics and Astronomy
Quantum computing
Quantum Field Theories
Quantum Field Theory
Quantum phenomena
Regular Article - Theoretical Physics
Spacetime
String Theory
Theoretical physics
ISSN:1434-6044, 1434-6052
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Popis
Shrnutí:Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely different physical problem – that of information processing inside black holes. Quantum computational complexity was suggested as a new entry in the holographic dictionary, which extends the connection between geometry and information and resolves the puzzle of why black hole interiors keep growing for a very long time. In this pedagogical review, we present the geometric approach to complexity advocated by Nielsen and show how it can be used to define complexity for generic quantum systems; in particular, we focus on Gaussian states in QFT, both pure and mixed, and on certain classes of CFT states. We then present the conjectured relation to gravitational quantities within the holographic correspondence and discuss several examples in which different versions of the conjectures have been tested. We highlight the relation between complexity, chaos and scrambling in chaotic systems. We conclude with a discussion of open problems and future directions. This article was written for the special issue of EPJ-C Frontiers in Holographic Duality.
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ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-022-10037-1