Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and discuss the beneficial features of quantum annealing techniques and compare them with those of simulated annealing techniques. We then briefly discuss the quantum annealing studies of some model spin glass and kinetically constrained systems.
We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including a scaling of their number with the annealing rate and the system size. We prove that quantum correlations can accelerate computations and, at the end of the…
The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point could be understood based on physics, using the quantum Monte Carlo method. As a result, we found a phase transition detectable only by the divergence of fidelity susceptibility. The exponentially small gapless points of each instance are all located in the phase found in this study, which suggests that this phase transition is the physical cause of the failure…
In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on impleme…
Non-stoquastic drivers are known to improve the performance of quantum annealing by reducing first-order phase transitions into second-order ones in several mean-field-type model systems. Nevertheless, statistical-mechanical analysis shows that some target Hamiltonians still exhibit unavoidable first-order transitions even with non-stoquastic drivers, making them difficult for quantum annealing to solve. Recently, a mechanism called coherent catalysis was proposed by Durkin [Phys. Rev. A \textbf{99}, 032315 (2019)], in which he showed the existence of a particular point on the line of first-or…
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 state to a low energy state of a target Ising Hamiltonian of quantum spins, $H_I$. Here, we point to the existence of an analytical solution for such a problem for an arbitrary $H_I$ beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotoni…
Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well-suited for simulating the equilibrium properties of systems with rough free energy landscapes. In this work we seek to understand and improve the performance of population annealing. We derive several useful relations between quantities that describe the performance of population annealing and use these relations to suggest methods to optimize the algorithm. These optimization methods were tested by performing large-scale simulations of the 3D Edwards-Anderson (Ising) spin glass and measuring several…
