Gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

“…This is a hard requirement when investigating both LGT descending from high-energy quantum field theories [87][88][89][90] , and condensed matter models with emergent gauge fields 91,92 . While other pathways have been developed [93][94][95][96] , in this work we adopted the well-known approach of truncating the gauge field space based on an energy density cutoff. In this section, we present the construction of the QED gauge-invariant configurations for the local sites that we exploit as a computational basis in our TN algorithm.…”

Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods

“…The other way to lift the redundancy is to change to a dual formulation of gauge theories, with magnetic variables, where there is no local symmetry anymore. Such formulations were introduced in the pure gauge case [63][64][65] as well as in the presence of dynamical fermionic matter, using translational invariant, Green's function-based approach [66] or a maximal tree approach [67].…”

“…Such a stroboscopic scheme, in which the time evolution is trotterized and the plaquette interaction is generated through sequences of two-body interactions with ancillary degrees of freedom, and matter may be simulated as well, was introduced in [53,54], based on objects called stators [75]. One of the advantages of this scheme is that the stroboscopic evolution does not affect the gauge symmetry, and it is completely protected [54,66].…”

“…There, the magnetic Hamiltonian becomes local, and the electric Hamiltonian becomes interacting-and only with two-body interactions [63,64]. This can be very useful for quantum simulation of pure gauge theories [65], but when dynamical matter is introduced [66,67,76], other parts of the Hamiltonian become complicated and non-local, but tradeoffs have always been and will most likely always be central to quantum simulation.…”

Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis

“…Considerable effort has been devoted to developing quantum algorithms for the design and time evolution of lattice gauge theories on quantum devices , often through the Kogut-Susskind Hamiltonian formulation [59][60][61][62][63][64]. Consequently, there has been a wide range of explorations of quantum simulation basis design for fields from the scalar field to gauge theories e.g., on a position-space lattice in the eigenbasis of the field operator [11,12], in a basis of the local free-field eigenstates [65], on a lattice of momentum modes [66], in the magnetic basis [43,44], through gauge field integration in low-dimensional spaces [23,24], on an orbifold lattice [45,67], in a prepotential framework or basis of gauge-invariant loop, string, and hadron excitations [33,36,49,[68][69][70][71][72][73], through the use of a spin system producing the desired continuous fields approaching a critical point [74][75][76][77][78][79][80], through discrete subgroups and group space decimation [19,25,37,81], through mesh digitization [82], using light-front formulations of lattice field theory [83,84], and in hybrid and analog approaches leveraging natural properties of trapped ions or ultracold atoms in optical lattices…”