A tensorial toolkit for quantum computing in lattice gauge theory

Abstract

In most lattice simulations, the variables of integration are compact and character expansion (for instance Fourier analysis for U(1) models) can be used to rewrite the partition function and average observables as discrete sums of contracted tensors. These reformulations have been used for RG blocking but they also naturally fit the needs of quantum computing. We discuss FAQ about tensorial reformulations: effects of truncations on symmetries, boundary conditions, Grassmann variables, and other recent aspects of quantum computing in the same context.

More about the Grassmann tensor renormalization group

“…(2.1) and (2.2) defined below generalize the results of section 3.3 of ref. [11]. 4 We assume that either of A and B is a commutative tensor whose coefficient tensor (a) (b) variables Ψ a (a = 1, • • • , K) as Ψ a = (η (a−1)m+1 , η (a−1)m+2 , • • • , η am ).…”