Related papers: Anderson localization casts clouds over adiabatic …
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
Adiabatic quantum annealers encounter scalability challenges due to exponentially fast diminishing energy gaps between ground and excited states with qubit-count increase. This introduces errors in identifying ground states compounded by a…
Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final…
We prove an adiabatic theorem that applies at timescales short of the typical adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of…
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here…
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation…
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required…
We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the…
Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and…
In this report, we explore the use of a quantum optimization algorithm for obtaining low energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of…
Since the discovery of adiabatic quantum computing, a need has arisen for rigorously proven bounds for the error in the adiabatic approximation. We present in this paper, a rigorous and elementary derivation of upper and lower bounds on the…
Adiabatic elimination is a standard tool in quantum optics, which produces an effective Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher unperturbed energy. It shares with…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial…
We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an…
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state.…