Circuit Complexity in Z2 EEFT

Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in Z2 Even Effective Field Theories (Z2 EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as ϕ4, ϕ6, and ϕ8. To facil...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-01, Vol.15 (1), p.31
Main Authors: Adhikari, Kiran, Choudhury, Sayantan, Kumar, Sourabh, Mandal, Saptarshi, Pandey, Nilesh, Roy, Abhishek, Sarkar, Soumya, Sarker, Partha, Shariff, Saadat Salman
Format: Article
Language:English
Subjects:
AdS/CFT correspondence
circuit complexity
Circuits
Complexity
Computation
effective field theory
Entangled states
Field theory
Geometry
Operators (mathematics)
Oscillators
Physics
Quantum computing
Quantum field theory
Scalars
Spacetime
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Summary:Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in Z2 Even Effective Field Theories (Z2 EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as ϕ4, ϕ6, and ϕ8. To facilitate our computation, we regularize the theory by putting it on a lattice. First, we consider a simple case of two oscillators and later generalize the results to N oscillators. This study was carried out for nearly Gaussian states. In our computation, the reference state is an approximately Gaussian unentangled state, and the corresponding target state, calculated from our theory, is an approximately Gaussian entangled state. We compute the complexity using the geometric approach developed by Nielsen, parameterizing the path-ordered unitary transformation and minimizing the geodesic in the space of unitaries. The contribution of higher-order operators to the circuit complexity in our theory is discussed. We also explore the dependency of complexity on other parameters in our theory for various cases.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15010031