Quantum simulation of quantum mechanical system with spatial noncommutativity
arXiv:2211.08338 · doi:10.1142/S0219749923500284
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.
Discussion on entanglement entropy and noisy simulation added, accepted version
References in corpus (47)
- Probing many-body dynamics on a 51-atom quantum simulator
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
- Simulating Lattice Gauge Theories within Quantum Technologies
- Tools for quantum simulation with ultracold atoms in optical lattices
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
- Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
- Quantum Algorithms for Simulating the Lattice Schwinger Model
- Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
- Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
- A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
- Observation of a symmetry-protected topological time crystal with superconducting qubits
- Quantum simulation of the Schwinger model: A study of feasibility
- Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
- Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model
- Simulating sparse Hamiltonians with star decompositions
- Realizing a dynamical topological phase in a trapped-ion quantum simulator
- Quantum simulation of open quantum systems in heavy-ion collisions
- Magnetic fields in noncommutative quantum mechanics
- Partonic collinear structure by quantum computing
- Determining the proton content with a quantum computer
- Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term
- Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
- Light-Front Field Theory on Current Quantum Computers
- Improved Hamiltonians for Quantum Simulations
- Toward Quantum Simulations of Gauge Theory Without State Preparation
- Quantum simulation of quantum field theories as quantum chemistry
- Quantum Simulation of Light-Front Parton Correlators
- Digital Simulation of Topological Matter on Programmable Quantum Processors
- Towards a Quantum Computing Algorithm for Helicity Amplitudes and Parton Showers
- Lattice Renormalization of Quantum Simulations
- Quantum Simulation of Chiral Phase Transitions
- Particle Track Reconstruction with Quantum Algorithms
- Quantum algorithm for Feynman loop integrals
- Quantum tomography for collider physics: Illustrations with lepton pair production
- Simulating Effective QED on Quantum Computers
- State preparation and measurement in a quantum simulation of the O(3) sigma model
- Quantum Computation of Phase Transition in the Massive Schwinger Model
- Floquet Prethermal Phase Protected by U(1) Symmetry on a Superconducting Quantum Processor
- Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding
- Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics