Related papers: Phase transitions and gaps in quantum random energ…
We propose an experimental method for evaluating the adiabatic condition during quantum annealing (QA), which will be essential for solving practical problems. The adiabatic condition consists of the transition matrix element and the energy…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
We study the nonequilibrium properties of a nonergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. The ground state and excited states of this…
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…
In this note we use ideas of Farhi, Goldstone, Gosset, Gutmann, Nagaj and Shor who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
We compare the critical behavior of the ground state and the thermal state of the XX model. We analyze the full energy spectrum and the eigenstates to reconstruct the ground state and the thermally excited state. With the solutions, we…
We consider a set of fully connected spins models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence,…
The quantum phase transition in an atom-molecule conversion system with atomic hopping between different hyperfine states is studied. In mean field approximation, we give the phase diagram whose phase boundary only depends on the atomic…
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for…
In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body…
The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems.…
Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. In the limit N >>1, where N is the number of states, we find that the survival probability of the initially…
This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann.Phys. 323, 1106 (2008). In many-body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel…