SU(2) lattice gauge theory on a quantum annealer

Abstract

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.

Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer

“…In recent years, there have been significant advances in quantum simulation of various quantum field theories (QFTs), such as scalar field theory, nuclear effective field theory, and LGTs. On the experimental front, a plethora of proof-of-concept simulations of QFTs have been implemented on currently available quantum devices, using approaches including analog quantum simulation [42][43][44][45], variational quantum simulation [46][47][48][49][50][51][52][53][54], quantum frequency processing [55], quantum annealing [56], and digital quantum simulation [57][58][59][60]. On the theoretical front, there exists a host of methods to realize QFTs on quantum hardware [17,25,26,29,30,.…”

Standard model physics and the digital quantum revolution: thoughts about the interface

“…The right-side panels show results obtained for the Schwinger model: (top) the vector current after a θ-quench obtained using IBM's classical simulators (2020) [449], and pair-production on a four-site (staggered) lattice obtained using (middle) Innsbruck's trapped ion systems (2016) [40], and (bottom) IBM's quantum devices (2018) [448]. The lower-left panels show, for two-plaquette systems in SU(2), (right) the time dependence of the local electric energy obtained using IBM's quantum devices (2019) [327], and (left) the strong-coupling vacuum persistence probability obtained using D-wave's quantum annealing systems (2021) [469]. The upper-left panel shows the electric energy of two plaquettes of SU(3) obtained using IBM's quantum devices (2021) [328].…”

GPU-accelerated simulations of quantum annealing and the quantum approximate optimization algorithm

“…Special devices built to perform QA are the D-Wave quantum annealers. The largest existing quantum annealer is the D-Wave Advantage, which has 5000+ physical qubits [33] and has been used for quantum support vector machines [34] (see also [35]), in studies of stock markets [36], for computer vision [37], and for lattice gauge theory [38]. It has recently been benchmarked with 3D spin glass prob-In this paper, we scrutinize the overlapping region between QA and the QAOA.…”