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

arXiv (Cornell University)

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 $ϕ^{4}$, $ϕ^{6}$ and $ϕ^8.$ 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.

Authors 7

1. Kiran Adhikari Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Aachen , Germany

2. Sayantan Choudhury
3. Sourabh Kumar

   University of Calgary

   Affiliation as printed

   Department of Physics and Astronomy , University of Calgary , Calgary , AB T2N 1N4 , Canada

   Institute for Quantum Science and Technology , University of Calgary , Calgary , AB T2N 1N4 , Canada

4. Saptarshi Mandal

   Indian Institute of Technology Kharagpur · Jadavpur University

   Affiliation as printed

   Department of Physics , Indian Institute of Technology Kharagpur , Kharagpur - 721302 , India

   Department of Physics , Jadavpur University , Kolkata - 700032

5. Nilesh Pandey

   Delhi Technological University

   Affiliation as printed

   Department of Applied Physics , Delhi Technological University , Delhi- 110042 , India

6. Abhishek Roy

   Indian Institute of Technology Jodhpur

   Affiliation as printed

   Department of Physics , Indian Institute of Technology Jodhpur , Karwar , Jodhpur - 342037 , India

7. Saadat Salman Shariff

   University of Madras · Indian Institute of Science Education and Research Berhampur

   Affiliation as printed

   Department of Physics , Indian Institute of Science and Educational Research , Behrampur-760010

   Department of Theoretical Physics , University of Madras , Guindy Campus , Chennai - 600025 . and