The Jones polynomial, discovered in 1984 [18], is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten [32]) to… (More)

We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings’ famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed… (More)

Radu Balan a, Peter G. Casazza b,∗, Christopher Heil c,∗∗, and Zeph Landau d a Siemens Corporate Research, Princeton, New Jersey 08540 E-mail: rvbalan@scr.siemens.com b Department of Mathematics,… (More)

The quantum analogue of the constraint satisfaction problem is the fundamental physics question of finding the minimal energy state of a local Hamiltonian --- each term of the Hamiltonian specifies a… (More)

In the first part of this paper, we provide polynomial quantum algorithms for additive approximations of the Tutte polynomial, at any point in the Tutte plane, for any planar graph. This includes an… (More)

We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastingsâ 1D area law and which is tight to within a… (More)

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept… (More)

In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over Z q , which is considered the most " quantum " part of Shor's algorithm, can in fact be… (More)

Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics and is the quantum analog of constraint satisfaction problems. The problem is known to be… (More)