Related papers: First-order transitions and the performance of qua…
We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…
We study first-order quantum phase transitions in models where the mean-field traitment is exact, and the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
We point out that, when an optimization problem has more than one solution, the quantum adiabatic algorithms (QAA) encounter topological obstructions leading to adiabatic spectral flows where spectral branches unavoidably traverse the…
Quantum optimization algorithms (QOAs) have the potential to fundamentally transform the application of optimization methods in decision making. For certain classes of optimization problems, it is widely believed that QOA enables…
In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…
We study quantum fluctuation driven first-order phase transitions of a two-species bosonic system in a three-dimensional optical lattice. Using effective potential method we find that the superfluid-Mott insulator phase transition of one…
We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian,…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by…
We prove that lattice quantum systems may undergo a first-order quantum phase transition through a general mechanism which consists in an infinite dilution of the states associated to (or, more in general, near to) the lowest energy levels.…
Motivated by the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain…
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…
Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$…