Simulating Fermionic Systems Using Quantum Cellular Automata

Joshi, Shivansh (2021) Simulating Fermionic Systems Using Quantum Cellular Automata. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Shivansh Joshi (16MS145)) 16MS145_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Quantum Cellular Automata (QCA) is a quantum analog of classical cellular automata. It describes the evolution of a quantum system on a lattice by a global rule. We study the structure and dynamics of QCA's which are essentially multi particle versions of quantum walks for simulating fermionic systems. These works are found extensively in literature for one dimensional system because fermionic operators are easily mapped to qubit operators. All interactions that occur in linear systems are between geometric nearest neighbour that are also consecutive in ordering. The challenge is to preserve this structure while describing the dynamics for Fermions in D > 1 systems. The property of QCA being local in evolution gets compromised due to their anti-commutation relations as we now have more geometric neighbours that are non consecutive in linear ordering. We study qubit and fermions rela- tionship that allows us to model a truly local two dimensional QCA dynamics. The result of the model does give the required results in the single particle limit. However additional qubits with new mapping structure is needed to make this work for N-particle evolution that mimics the dynamics of Dirac Equation.

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