Related papers: Phase transitions and gaps in quantum random energ…
We show, for quantum annealing, that a certain type of inhomogeneous driving of the transverse field erases first-order quantum phase transitions in the p-body interacting mean-field-type model with and without longitudinal random field.…
We argue the feasibility to study the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a novel method and successfully test it in application to the Schwinger model in the…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the $J_x$ and $J_z$ coupling constants of the model, we…
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the…
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of…
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of…
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…
Quantum sensors based on critical many-body systems are known to exhibit enhanced sensing capability. Such enhancements typically scale algebraically with the probe size. Going beyond algebraic advantage and reaching exponential scaling has…
First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…
We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In…
Quantum phase transitions have been the subject of intense investigations in the last two decades [1]. Among other problems, these phase transitions are relevant in the study of heavy fermion systems, high temperature superconductors and…
What correlations are present in the ground state of a many-body Hamiltonian? We study the relationship between ground-state correlations, especially entanglement, and the energy gap between the ground and first excited states. We prove…
We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a…
We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the…