We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.

arXiv:1403.5238Physical Review ADec 1, 201441 citations

Improved Hamiltonians for Quantum Simulations of Gauge Theories

Marcela S. Carena, Henry Lamm, Ying-Ying Li +1 more

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 discretization errors will reduce quantum resources, i.e., require ≳2^{d} fewer qubits in quantum simulations for lattices with d-spatial dimensions. In this work, we consider O(a^{2})-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. An explicit demonstration for Z_{2} gauge theory is presented including exploratory tests using the ibm_perth device.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 discretization errors will reduce quantum resources, i.e., require ≳2^{d} fewer qubits in quantum simulations for lattices with d-spatial dimensions. In this work, we consider O(a^{2})-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. An explicit demonstration for Z_{2} gauge theory is presented including exploratory tests using the ibm_perth device.

arXiv:2203.02823Physical Review LettersJul 29, 202249 citations

Simulation of non-Abelian gauge theories with optical lattices

Luca Tagliacozzo, Alessio Celi, Peter Orland A. B. C +2 more

arXiv:1211.2704Nature CommunicationsOct 28, 2013235 citations

We connect explicitly the classical

\text{O}(2)

model in

1+1

dimensions, a model sharing important features with

\text{U}(1)

lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a

^{87}\mathrm{Rb}

and

^{41}\mathrm{K}

Bose-Bose mixture.