Related papers: Constrained quantum annealing of graph coloring
Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal…
The goal of this work is to define a notion of a quantum neural network to classify data, which exploits the low energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…
Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave…
Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic…
Quantum devices are affected by intrinsic and environmental noises. An in-depth characterization of noise effects is essential for exploiting noisy quantum computing. To this end, we studied the energy dissipative behavior of a quantum…
The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
Quantum annealing is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale…
We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied. Hypergraph coloring is a constraint satisfaction problem where…
Graph partitioning has many applications in powersystems from decentralized state estimation to parallel simulation. Focusing on parallel simulation, optimal grid partitioning minimizes the idle time caused by different simulation times for…
Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…