Circuit Complexity in Z2 EEFT

Symmetry, vol. 15, pp. 31

Abstract

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.

Authors 7

1. Kiran Adhikari Aachen Department of Physics

   RWTH Aachen University

   Affiliation as printed

   Department of Physics, RWTH Aachen University, Otto-Blumenthal-Straße, 52074 Aachen, Germany

2. Sayantan Choudhury corresponding

   National Institute of Science Education and Research · Homi Bhabha National Institute · Shree Guru Gobind Singh Tricentenary University

   Affiliation as printed

   Centre For Cosmology and Science Popularization (CCSP), SGT University, Delhi-NCR, Gurugram 122505, India

   Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India

   National Institute of Science Education and Research, Bhubaneswar 752050, India

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, India

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, India

   Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600025, India