Gluon field digitization via group space decimation for quantum computers

Abstract

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use a smaller, fixed number of qubits at the cost of systematic errors. We systematize this approach by deriving the single plaquette action through matching the continuous group action to that of a discrete one via group character expansions modulo the field fluctuation contributions. We accompany this scheme by simulations of pure gauge over the largest discrete crystal-like subgroup of SU (3) up to the fifth-order in the coupling constant.

Quantum algorithms for transport coefficients in gauge theories

“…In order to reach the physical regime, this boundary must be crossed, and it is likely that a phase transition (associated with an exponentially small or even vanishing gap) is encountered. Even if there is no phase transition along the path to the desired coupling, the weak-coupling limit is inaccessible to many proposed truncation schemes for the gluon fields, including approximation by a finite subgroup [107,108] and momentum-space truncation [109].…”

The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory

“…In such case, systematic improvements are possible. Including additional terms in the action proportional to other characters [29,44,45] can allow for smaller a, while improved actions, in the spirit of the Symanzik program, can reduce the systemic error for fixed a [71][72][73]. The relative cost of these two improvements are left for future work.…”

“…Here, we will investigate the discrete subgroup approximation [27][28][29][30] using classical lattice simulations. While performed in imaginary time, this nonperturbative study of truncation errors is known to be related to those in real time [31][32][33], thus providing us access to much larger systems than with current quantum devices.…”

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…”