arXiv subjects

Artur Garcia-Saez

Publications and source records attributed to Artur Garcia-Saez.

28 records · Page 2Linked to original sources

arXiv2019

Quantum Observables for continuous control of the Quantum Approximate Optimization Algorithm via Reinforcement Learning

We present a classical control mechanism for Quantum devices using Reinforcement Learning. Our strategy is applied to the Quantum Approximate Optimization Algorithm (QAOA) in order to optimize an objective function that encodes a solution to a hard combinatorial problem. This method provides optimal control of the Quantum device following a reformulation of QAOA as an environment where an autonomous classical agent interacts and performs actions to achieve higher rewards. This formulation allows a hybrid classical-Quantum device to train itself from previous executions using a continuous formulation of deep Q-learning to control the continuous degrees of freedom of QAOA. Our approach makes a selective use of Quantum measurements to complete the observations of the Quantum state available to the agent. We run tests of this approach on MAXCUT instances of size up to N = 21 obtaining optimal results. We show how this formulation can be used to transfer the knowledge from shorter training episodes to reach a regime of longer executions where QAOA delivers higher results.

quant-ph↗

arXiv2015

Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above and at the critical temperature. Application of the tensor-network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q=3,4,5,6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

cond-mat.str-el↗

arXiv2015

Efficient evaluation of high-order moments and cumulants in tensor network states

We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several applications for such quantities. For example, the second cumulant of the energy of a state, $\langle ΔH^2 \rangle$, gives a straightforward method to check the convergence of numerical ground-state approximation algorithms. Additionally, we discuss the use of moments and cumulants in the study of phase transitions. Of particular interest is the application of our method to calculate the so-called Binder's cumulant, which we use to detect critical points and study the critical exponent of the correlation length with only small finite numerical calculations. We apply these methods to study the behavior of a family of one-dimensional models (the transverse Ising model, the spin-1 Ising model, and the spin-1 Ising model in a crystal field), as well as the two-dimensional Ising model on a square lattice. Our results show that in one dimension, cumulant-based methods can produce precise estimates of the critical points at a low computational cost, and show promise for two-dimensional systems as well.

cond-mat.stat-mech↗

arXiv2014

Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows to extract the critical exponent of the correlation length, and shows that there is no continuous entanglement-loss along renormalization group flows in topological phases.

cond-mat.str-el↗

arXiv2014

Topological Minimally Entangled States via Geometric Measure

Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O. Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.

cond-mat.str-el↗

arXiv2013

Spectral gaps of AKLT Hamiltonians using Tensor Network methods

Using exact diagonalization and tensor network techniques we compute the gap for the AKLT Hamiltonian in 1D and 2D spatial dimensions. Tensor Network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies e_0<0, which is a quantum critical point. With the Tensor Network Renormalization Group methods we provide evidence of a finite gap in the thermodynamic limit for the AKLT models in the 1D chain and 2D hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model.

cond-mat.str-el↗

arXiv2012

Intensive temperature and quantum correlations for refined quantum measurements

We consider the concept of temperature in a setting beyond the standard thermodynamics prescriptions. Namely, rather than restricting to standard coarse-grained measurements, we consider observers able to master any possible quantum measurement--a scenario that might be relevant at nanoscopic scales. In this setting, we focus on quantum systems of coupled harmonic oscillators and study the question of whether the temperature is an intensive quantity, in the sense that a block of a thermal state can be approximated by an effective thermal state at the same temperature as the whole system. Using the quantum fidelity as figure of merit, we identify instances in which this approximation is not valid, as the block state and the reference thermal state are distinguishable for refined measurements. Actually, there are situation in which this distinguishability even increases with the block size. However, we also show that the two states do become less distinguishable with the block size for coarse-grained measurements--thus recovering the standard picture. We then go further and construct an effective thermal state which provides a good approximation of the block state for any observables and sizes. Finally, we point out the role entanglement plays in this scenario by showing that, in general, the thermodynamic paradigm of local intensive temperature applies whenever entanglement is not present in the system.

quant-ph↗

arXiv2009

Strong cooperativity and inhibitory effects in DNA multi-looping processes

We show the existence of a high interrelation between the different loops that may appear in a DNA segment. Conformational changes in a chain segment caused by the formation of a particular loop may either promote or prevent the appearance of another. The underlying loop selection mechanism is analyzed by means of a Hamiltonian model from which the looping free energy and the corresponding repression level can be computed. We show significant differences between the probability of single and multiple loop formation. The consequences that these collective effects might have on gene regulation processes are outlined.

q-bio.BM↗

arXiv2008

Area laws and entanglement distillability of thermal states

We study the entanglement distillability properties of thermal states of many-body systems. Following the ideas presented in [D.Cavalcanti et al., arxiv:0705.3762], we first discuss the appearance of bound entanglement in those systems satisfying an entanglement area law. Then, we extend these results to other topologies, not necessarily satisfying an entanglement area law. We also study whether bound entanglement survives in the macroscopic limit of an infinite number of particles.

quant-ph↗

arXiv2007

Monogamy and ground-state entanglement in highly connected systems

We consider the ground-state entanglement in highly connected many-body systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their degree of connectivity, we investigate the interplay between the enhancement of entanglement, due to connections, and its frustration, due to monogamy constraints. Remarkably, we see that in many situations the degree of entanglement in a highly connected system is essentially of the same order as in a low connected one. We also identify instances in which the entanglement decreases as the degree of connectivity increases.

quant-ph↗