Quantum simulation of quantum mechanical system with spatial noncommutativity

• URL: http://arxiv.org/abs/2211.08338v4
• Date: Sun, 30 Jul 2023 04:44:33 GMT
• Title: Quantum simulation of quantum mechanical system with spatial noncommutativity
• Authors: S. Hasibul Hassan Chowdhury, Talal Ahmed Chowdhury, Salah Nasri, Omar Ibna Nazim and Shaikh Saad
• Abstract summary: We demonstrate the quantum simulation of a quantum mechanical system with spatial noncommutativity. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate the quantum simulation of such a model, a quantum mechanical system with spatial noncommutativity, which is inspired by the works in Noncommutative Geometry and Noncommutative Field theory for a universal quantum computer. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian and then carry out the quantum simulation using the Trotter-Suzuki product formula. Furthermore, we distinguish the impact of the noncommutativity parameter on the quantum simulation, especially on the Trotter error, and point out how its sizable value affects the simulation.

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