Related papers: On the Approximation of the Quantum Gates using La…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
We construct a quantum mechanical matrix model that approximates $\mathcal{N}=1$ super-Yang-Mills on $S^3\times\mathbb{R}$. We do so by pulling back the set of left-invariant connections of the gauge bundle onto the real superspace, with…
In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…
The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of…
Computing the vacuum and energy spectrum in non-Abelian, interacting lattice gauge theories remains an open challenge, in part because approximating the continuum limit requires large lattices and huge Hilbert spaces. To address this…
In the framework of a non-compact lattice regularization of nonabelian gauge theories we look, in the SU(2) case, for the scaling window through the analysis of the ratio of two masses of hadronic states. In the two-dimensional parameter…
In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…
The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
An approximate dual representation for non-Abelian lattice gauge theories in terms of a new set of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still…
In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
Using quantum Monte Carlo simulations, we compute the participation (Shannon-R\'enyi) entropies for groundstate wave functions of Heisenberg antiferromagnets for one-dimensional (line) subsystems of length $L$ embedded in two-dimensional…
We discuss an algorithm for the approximate solution of Schrodinger's equation for lattice gauge theory, using lattice SU(3) as an example. A basis is generated by repeatedly applying an effective Hamiltonian to a ``starting state.'' The…
In this paper we study the topological susceptibility of two-dimensional $U(N)$ gauge theories. We provide explicit expressions for the partition function and the topological susceptibility at finite lattice spacing and finite volume. We…