Circuit Complexity from Supersymmetric Quantum Field Theory with Morse Function

Computation of circuit complexity has gained much attention in the theoretical physics community in recent times, to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from Nielsen’s geometric approac...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-08, Vol.14 (8), p.1656
Main Authors: Choudhury, Sayantan, Selvam, Sachin Panneer, Shirish, K.
Format: Article
Language:English
Subjects:
Black holes
Circuits
Complexity
Cost function
Eigenvalues
Harmonic oscillators
Optimization
Oscillators
Quantum field theory
Quantum physics
Quantum theory
Supersymmetry
Theoretical physics
Topology
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Summary:Computation of circuit complexity has gained much attention in the theoretical physics community in recent times, to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from Nielsen’s geometric approach, which is based on the idea of optimal quantum control in which a cost function is introduced for the various possible path to determine the optimum circuit. In this paper, we study the relationship between the circuit complexity and Morse theory within the framework of algebraic topology, which will then help us study circuit complexity in supersymmetric quantum field theory describing both simple and inverted harmonic oscillators up to higher orders of quantum corrections. We will restrict ourselves to N=1 supersymmetry with one fermionic generator Qα. The expression of circuit complexity in quantum regime would then be given by the Hessian of the Morse function in supersymmetric quantum field theory. We also provide technical proof of the well known universal connecting relation between quantum chaos and circuit complexity of the supersymmetric quantum field theories, using the general description of Morse theory.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081656