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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-order phase transitions where the energy gap scales polynomially as expected for a second-order transition. We show by extensive numerical computations that this phenomenon is observed in a few additional mean-field-type optimization problems where non-stoquastic drivers fail to change the order of phase transition in the thermodynamic limit. This opens up the possibility of using coherent catalysis to search for exponential speedups in systems previously thought to be exponentially slow for quantum annealing to solve.
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary pha
I study the universal finite-size scaling function for the lowest gap of the quantum Ising chain with a one-parameter family of ``defect boundary conditions, which includes periodic, open, and antiperiodic boundary conditions as special cases. The un
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system wit
The energy dissipation rate in a nonequilibirum reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for react
We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which consists of