Related papers: Two-local qubit Hamiltonians: when are they stoqua…

Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…

In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a…

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…

Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…

We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…

We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian. We present evidence that the answer is "yes" for generic local Hamiltonians, given either the ground state or an…

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…

A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge.…

A method is developed to determine the eigenvalues and eigenfunction of two-boson $2\times 2$ matrix Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable…

We study the complexity of local Hamiltonians in which the terms pairwise commute. Commuting local Hamiltonians (CLHs) provide a way to study the role of non-commutativity in the complexity of quantum systems and touch on many fundamental…

Any pure two-qubit state can be represented by six real angles, with a natural parameterization indicated by the bipartite structure. After explicitly identifying all of these angles for the first time, it is found that the parameters can…

In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On…

We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the…

This report compares two tests of second-order stationarity through simulation. It also provides several examples of localised autocovariances and their approximate confidence intervals on different real and simulated data sets. An…

We prove that 2-Local Hamiltonian (2-LH) with Low Complexity problem is QCMA-complete by combining the results from the QMA-completeness[4] of 2-LH and QCMA-completeness of 3-LH with Low Complexity[6]. The idea is straightforward. It has…

We study the computational complexity of the Local Hamiltonian problem under the promise that its ground state is succinctly represented. We show that the Succinct State 2-Local Hamiltonian problem, for qubit Hamiltonians, is (promise)…

An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum…

Classical hardness-of-sampling results are largely established for random quantum circuits, whereas analog simulators natively realize time evolutions under geometrically local Hamiltonians. Does a typical such Hamiltonian already yield…