Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Simple proof of equivalence between adiabatic quantum computation and the circuit model

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.Comment: 5 pages, 2 figures. v2: improved gap estimates and added some more detail

Universality of Entanglement and Quantum Computation Complexity

We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The analytic result for Shor's algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore difficulting the possibility of an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution Exact Cover algorithm, which also shows universality of the quantum phase transition the system evolves nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains a bounded quantity even at the critical point. A classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure

Regularization of Brane Induced Gravity

We study the regularization of theories of ``brane induced'' gravity in codimension $N>1$. The brane can be interpreted as a thin dielectric with a large dielectric constant, embedded in a higher dimensional space. The kinetic term for the higher dimensional graviton is enhanced over the brane. A four dimensional gravitation is found on the brane at distances smaller than a critical distance $r<r_c$, and is due to the exchange of a massive resonant graviton. The crossover scale $r_c$ is determined by the mass of the resonance. The suppression of the couplings of light Kaluza-Klein modes to brane matter results in a higher dimensional force law at large distances. We show that the resulting theory is free of ghosts or tachyons.Comment: One reference added. To appear in PRD. 20 pages, 3 figure

Entanglement and non-locality are different resources

Bell's theorem states that, to simulate the correlations created by measurement on pure entangled quantum states, shared randomness is not enough: some "non-local" resources are required. It has been demonstrated recently that all projective measurements on the maximally entangled state of two qubits can be simulated with a single use of a "non-local machine". We prove that a strictly larger amount of this non-local resource is required for the simulation of pure non-maximally entangled states of two qubits $\ket{\psi(\alpha)}= \cos\alpha\ket{00}+\sin\alpha\ket{11}$ with $0<\alpha\lesssim\frac{\pi}{7.8}$.Comment: 8 pages, 3 figure

Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity

In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S'=\sum_{h \epsilon \{h_1,h_2,...\} } \lambda_h V_h$ is added to the gravitational action, where $\{h_1,h_2,...\}$ is a subset of the hinges and $\{\lambda_h\}$ are positive constants, one expects that the volumes $V_{h_1}$, $V_{h_2}$, ... tend to collapse and that the excitations of the lattice propagating through the hinges $\{h_1,h_2,...\}$ are damped. We study the continuum analogue of this effect. The additional term $S'$ may represent the coupling of the gravitational field to an external Bose condensate.Comment: LaTex, 18 page

Spherically symmetric spacetimes in massive gravity

We explore spherically symmetric stationary solutions, generated by ``stars'' with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically exploring the inward continuation of the class of asymptotically flat solutions, we find that, when m is ``small'', they all end up in a singularity at a finite radius, well outside the source, instead of joining some conjectured ``continuous'' solution near the source. We reopen, however, the possibility of reconciling massive gravity with phenomenology by exhibiting a special class of solutions, with ``spontaneous symmetry breaking'' features, which are close, near the source, to general relativistic solutions and asymptote, for large radii, a de Sitter solution of curvature ~m^2.Comment: 57 pages, references addde

Effects of epitaxial strain on the growth mechanism of YBa2Cu3O7-x thin films in [YBa2Cu3O7-x / PrBa2Cu3O7-x] superlattices

We report on the growth mechanism of YBa2Cu3O7-x (YBCO). Our study is based on the analysis of ultrathin, YBa2Cu3O7-x layers in c-axis oriented YBa2Cu3O7-x / PrBa2Cu3O7-x superlattices. We have found that the release of epitaxial strain in very thin YBCO layers triggers a change in the dimensionality of the growth mode. Ultrathin, epitaxially strained, YBCO layers with thickness below 3 unit cells grow in a block by block two dimensional mode coherent over large lateral distances. Meanwhile, when thickness increases, and the strain relaxes, layer growth turns into three dimensional, resulting in rougher layers and interfaces.Comment: 10 pages + 9 figures, accepted in Phys. Rev.