Related papers: Circuit Complexity in $\mathcal{Z}

Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$

URL: http://arxiv.org/abs/2109.09759v5
Date: Fri, 16 Dec 2022 10:38:24 GMT
Title: Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$
Authors: Kiran Adhikari, Sayantan Choudhury, Sourabh Kumar, Saptarshi Mandal, Nilesh Pandey, Abhishek Roy, Soumya Sarkar, Partha Sarker, Saadat Salman Shariff
Abstract summary: We computation circuit complexity in $mathcalZ$ Even Effective Field Theories. We consider a massive free field theory with higher-order Wilsonian operators. The study has been carried out for nearly Gaussian states.
Score: 1.3177888879666482
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as $\phi^{4}$, $\phi^{6}$ and $\phi^8.$ 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. The study has been 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 has been discussed. We also explore the dependency of complexity with other parameters in our theory for various cases.

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