Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms

Abstract

The 1+1D O(3) non-linear σ-model is a model system for future quantum lattice simulations of other asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use of two-dimensional layouts presently available on cold atom quantum simulators. A new definition of the renormalized coupling is introduced, which is applicable to systems with open boundary conditions and can be measured using analog quantum simulators. Monte Carlo and tensor network calculations are performed to determine the quantum resources required to reproduce perturbative short-distance observables. In particular, we show that a rectangular array of 48 Rydberg atoms with existing quantum hardware capabilities should be able to adiabatically prepare low-energy states of the perturbatively-matched theory. These states can then be used to simulate non-perturbative observables in the continuum limit that lie beyond the reach of classical computers.

12 pages, 5 figures, 2 tables, published version

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• SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
• Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Toward quantum computations of the $O(3)$ model using qumodes
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations