Roman Orus

Entanglement entropy in the Lipkin-Meshkov-Glick model

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one- dimensional XY chain.

Universality of Entanglement and Quantum Computation Complexity

We study the universality of scaling of entanglement in Shors factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete exact cover problem as well as Grovers problem. The analytic result for Shors algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore making it hard to generate 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 near which the system evolves. On the other hand, entanglement in Grovers adiabatic algorithm remains a bounded quantity even at the critical point. The classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.

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 energy 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 Grovers algorithm is bounded by a constant.

Half the entanglement in critical systems is distillable from a single specimen

We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as

Systematic analysis of majorization in quantum algorithms

{E}_{1}({ensuremath{rho}}_{L})=(c∕6)mathrm{ln}phantom{rule{0.2em}{0ex}}Lensuremath{-}(c∕6)({ensuremath{pi}}^{2}∕mathrm{ln}phantom{rule{0.2em}{0ex}}L)+O(1∕L)

Simulation of many-qubit quantum computation with matrix product states

, where

Weakly entangled states are dense and robust

L

Quantum phase transitions in antiferromagnetic planar cubic lattices

is the number of constituents in a block of an infinite chain and

Natural Majorization of the Quantum Fourier Transformation in Phase-Estimation Algorithms

c

Entanglement and majorization in (1+1)-dimensional quantum systems

denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the