From asymptotic freedom to $θ$ vacua: Qubit embeddings of the O(3) nonlinear $σ$ model

Abstract

Conventional lattice formulations of θ vacua in the 1 + 1-dimensional O(3) nonlinear sigma model suffer from a sign problem. Here, we construct the first sign-problem-free regularization for arbitrary θ. Using efficient lattice Monte Carlo algorithms, we demonstrate how a Hamiltonian model of spin-1 2 degrees of freedom on a 2-dimensional spatial lattice reproduces both the infrared sector for arbitrary θ, as well as the ultraviolet physics of asymptotic freedom. Furthermore, as a model of qubits on a two-dimensional square lattice with only nearest-neighbor interactions, it is naturally suited for studying the physics of θ vacua and asymptotic freedom on near-term quantum devices. Our construction generalizes to θ vacua in all CP(N − 1) models, solving a long standing sign problem.

Quantum Simulation for High Energy Physics

“…The advantage of this method is that the Hamiltonian that needs to be simulated is local in this extended space, so the quantum circuits that implement it are potentially simpler. Recent work shows how the O(3) model with a theta vacuum can be studied in this framework [428]. It has also been shown that the extra dimension may not be unnecessary in some cases [139]: the low-energy sector of Hamiltonians tuned to a quantum critical point are described by the QFT.…”

State Preparation in the Heisenberg Model through Adiabatic Spiraling

“…While a quantum advantage has yet to be established for a scientific application, including quantum field theories, there are substantial efforts underway to perform quantum simulations that can be compared with experiment, or impact future experiments, and impressive progress has been made toward these objectives in the last decade. This includes the development of techniques to simulate abelian gauge theories , non-abelian gauge theories , fermionic field theories [98][99][100][101], and scalar field theories [102][103][104][105][106][107][108]. There has also been the development of techniques to extract observables of interest to nuclear physics [109][110][111][112][113][114][115], scattering processes in high energy physics [116][117][118][119][120][121][122][123] and methods to mitigate errors on noisy quantum hardware [124][125][126][127][128][129].…”

Floquet Engineering Heisenberg from Ising Using Constant Drive Fields for Quantum Simulation

“…One of the most studied spin systems is the Heisenberg model which is able to describe critical points and phase transitions in magnetic materials. In addition to condensed matter applications, the Heisenberg model also has an important role in high energy physics as, for example, it can be used to study the lattice O(3) non-linear σ model [55][56][57][58][59][72][73][74]. This theory is one of the "sandboxes" used to better understand quantum chromodynamics (QCD) as it shares a number of qualitative aspects such as asymptotic freedom and θ-vacua.…”