Related papers: Quantum algorithm of a set of quantum 2-sat proble…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
We outline an algorithm for the Quantum Counting problem using Adiabatic Quantum Computation (AQC). We show that using local adiabatic evolution, a process in which the adiabatic procedure is performed at a variable rate, the problem is…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
The Quantum k-SAT problem is the quantum generalization of the k-SAT problem. It is the problem whether a given local Hamiltonian is frustration-free. Frustration-free means that the ground state of the k-local Hamiltonian minimizes the…
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…
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…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time…
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 present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of…
We propose a circuit-model quantum algorithm for eigenpath traversal that is based on a combination of concepts from Grover's search and adiabatic quantum computation. Our algorithm deploys a sequence of reflections determined from…
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…
We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to…
Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a…
Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. Here, we design a new scheme which employs an arbitrary two-body source…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…