Related papers: Primitive Quantum Gates for Dihedral Gauge Theorie…
We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$) group on two quantum architectures. This nonabelian discrete group serves as a crude approximation to $SU(2)$ lattice gauge…
We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral ($\mathbb{BO}$) group. This nonabelian discrete group better approximates $SU(2)$ lattice gauge theory than previous work on the binary…
We study lattice gauge theory with discrete, non-Abelian gauge groups. We extend the formalism of previous studies on D-Wave's quantum annealer as a computing platform to finite, simply reducible gauge groups. As an example, we use the…
We construct the primitive gate set for the digital quantum simulation of the 108-element $\Sigma(36\times3)$ group. This is the first time a nonabelian crystal-like subgroup of $SU(3)$ has been constructed for quantum simulation. The gauge…
Non-abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation.…
We develop qutrit circuit models for discrete-time three-state quantum walks on Cayley graphs corresponding to Dihedral groups $D_N$ and the additive groups of integers modulo any positive integer $N$. The proposed circuits comprise of…
In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes…
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…
Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo…
Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in…
Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories…
We discuss the implementation of lattice gauge theories on digital quantum computers, focusing primarily on the number of quantum gates required to simulate their time evolution. We find that to compile quantum circuits, using available…
We construct a primitive gate set for the digital quantum simulation of a discrete subgroup of $SU(3)$: the 216-element $\Sigma(72\times3)$. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and…
Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved…
In this article, we review some of the recent developments towards the future goal of quantum computing or quantum simulating lattice QCD. This includes a novel theoretical framework developed for non-Abelian gauge theories that is the…
We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the…
Gauge theories represent a fundamental framework underlying modern physics, constituting the basis of the Standard Model and also providing useful descriptions of various phenomena in condensed matter. Realizing gauge theories on accessible…
In this work, we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: SNAP &…
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD,…
Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this…