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Perturbed Hamming weight problems serve as examples of optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work we study the efficiency of the adiabatic algorithm for solving…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with…
The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
We consider the adiabatic quantum algorithm for systems with "no sign problem", such as the transverse field Ising mode, and analyze the equilibration time for quantum Monte Carlo (QMC) on these systems. We ask: if the spectral gap is only…
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…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We introduce an approach to scattering problems in theories with non-Hermitian Hamiltonian, usually known as PT-symmetric quantum theories, by means of the adiabatic switching of the interaction. The modifications of usual methods needed to…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model…
We construct a nearest-neighbor Hamiltonian whose ground states encode the solutions to the NP-complete problem INDEPENDENT SET in cubic planar graphs. The Hamiltonian can be easily simulated by Ising interactions between adjacent particles…
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial…
We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n…
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental…
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is…
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 illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…