Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective, low energy, symmetry, or as an "exact" symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to new type of (table-top) experiments, that shall be used to study various QCD phenomena, as the confinement of dynamical quarks, phase transitions, and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing quantum simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1 dimensions using ultracold atoms in optical lattices.
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background 2representative citing papers
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
citing papers explorer
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Ether of Orbifolds
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.