Related papers: Adiabatic optimization without local minima
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…
We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. 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…
According to the adiabatic theorem of quantum mechanics, a system initially in the ground state of a Hamiltonian remains in the ground state if one slowly changes the Hamiltonian. This can be used in principle to solve hard problems on…
Current quantum annealing experiments often suffer from restrictions in connectivity in the sense that only certain qubits can be coupled to each other. The most common strategy to overcome connectivity restrictions so far is by combining…
We propose a protocol for quantum adiabatic optimization, whereby an intermediary Hamiltonian that is diagonal in the computational basis is turned on and off during the interpolation. This `diagonal catalyst' serves to bias the energy…
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…
We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
In Phys. Rev. A {\bf 71}, 060312(R) (2005) the robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian was examined. We expand this analysis to include the case of the global…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
A particle-in-a-box model of continuous space quantum annealing is proposed and studied numerically by solving the Schr\"odinger wave equation directly. Three types of energy landscapes with multiple local minima are considered, namely a…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…