arXiv subjects

M. A. Martin-Delgado

Publications and source records attributed to M. A. Martin-Delgado.

At least 37 records · Page 2Linked to original sources

arXiv2016

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

quant-ph↗

arXiv2015

Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase -- an interaction-driven topological insulator -- using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest and next-to-nearest neighbor interactions, and derive the associated zero temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic as well as a topologically non-trivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access in particular the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques.

cond-mat.quant-gas↗

arXiv2015

Symmetry-protected Topological Phases at Finite Temperature

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT) phase under external thermal fluctuations in two-dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.

cond-mat.str-el↗

arXiv2014

Quantum Google Algorithm: Construction and Application to Complex Networks

We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks. The algorithm has been shown to identify unambiguously the underlying topology of the network and to be capable of clearly highlighting the structure of secondary hubs of networks. Furthermore, it can resolve the degeneracy in importance of the low-lying part of the list of rankings. Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks. The quantum algorithm has been shown to display an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance among the nodes, as compared to the classical algorithm.

quant-ph↗

arXiv2014

Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers

We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number ${\rm n}_{\rm U}$. With it, we study thermal topological phases in several two-dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature $T$ is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal-topological transitions between two non-trivial phases in a model with high Chern numbers. At small temperature we recover the standard topological phases as the Uhlmann number approaches to the Chern number.

cond-mat.str-el↗

arXiv2014

Efficient algorithm to compute the Berry conductivity

We propose and construct a numerical algorithm to calculate the Berry conductivity in topological band insulators. The method is applicable to cold atom systems as well as solid state setups, both for the insulating case where the Fermi energy lies in the gap between two bulk bands as well as in the metallic regime and interpolates smoothly between both regimes. The algorithm is gauge-invariant by construction, efficient and yields the Berry conductivity with known and controllable statistical error bars. We apply the algorithm to several paradigmatic models in the field of topological insulators, including Haldane's model on the honeycomb lattice, the multi-band Hofstadter model and the BHZ model, which describes the 2D spin Hall effect observed in CdTe/HgTe/CdTe quantum well heterostructures.

cond-mat.str-el↗

arXiv2014

Quantum Information Engines with Many-Body States attaining optimal Extractable Work with Quantum Control

We introduce quantum information engines that extract work from quantum states and a single thermal reservoir. They may operate under three general conditions: i/ Unitarily Steered evolution (US); ii/ Irreversible Thermalization (IT) and iii/ Isothermal Relaxation (IR), and hence are called USITIR machines. They include novel engines without traditional feedback control mechanisms, as well as versions which also include them. Explicit constructions of USITIR engines are presented for one- and two-qubit states and their maximum extractable work is computed, which is optimal. Optimality is achieved when the notions of controllable thermalizability and density matrix controllability are fullfilled. Then, many-body extensions of USITIR engines are also analyzed and conditions for optimal work extraction are identified. When they are not met, we measure their lack of optimality by means of newly defined uncontrollable entropies, that are explicitly computed for some selected examples. This includes cases of distinguishable and indistinguishable particles.

quant-ph↗

arXiv2014

Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems

We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in 1D fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature $T_c$ at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.

quant-ph↗

arXiv2013

Density Matrix Topological Insulators

Thermal noise can destroy topological insulators (TI). However we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its steady state. This is based on a generalization of the Chern number valid for general mixed states (referred to as density matrix Chern value), which witnesses topological order in a system coupled to external noise. Additionally, we study its relation with the electrical conductivity at finite temperature, which is not a topological property. Nonetheless, the density matrix Chern value represents the part of the conductivity which is topological due to the presence of quantum mixed edge states at finite temperature. To make our formalism concrete, we apply these concepts to the two-dimensional Haldane model in the presence of thermal dissipation, but our results hold for arbitrary dimensions and density matrices.

cond-mat.mes-hall↗

arXiv2013

Quantum Google in a Complex Network

We investigate the behavior of the recently proposed quantum Google algorithm, or quantum PageRank, in large complex networks. Applying the quantum algorithm to a part of the real World Wide Web, we find that the algorithm is able to univocally reveal the underlying scale-free topology of the network and to clearly identify and order the most relevant nodes (hubs) of the graph according to their importance in the network structure. Moreover, our results show that the quantum PageRank algorithm generically leads to changes in the hierarchy of nodes. In addition, as compared to its classical counterpart, the quantum algorithm is capable to clearly highlight the structure of secondary hubs of the network, and to partially resolve the degeneracy in importance of the low lying part of the list of rankings, which represents a typical shortcoming of the classical PageRank algorithm. Complementary to this study, our analysis shows that the algorithm is able to clearly distinguish scale-free networks from other widespread and important classes of complex networks, such as Erdős-Rényi networks and hierarchical graphs. We show that the ranking capabilities of the quantum PageRank algorithm are related to an increased stability with respect to a variation of the damping parameter $α$ that appears in the Google algorithm, and to a more clearly pronounced power-law behavior in the distribution of importance among the nodes, as compared to the classical algorithm. Finally, we study to which extent the increased sensitivity of the quantum algorithm persists under coordinated attacks of the most important nodes in scale-free and Erdős-Rényi random graphs.

quant-ph↗

arXiv2012

Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator

In this work we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. To this end, we first derive the zero-temperature phase diagram of the interacting model within a mean-field theory treatment. We show that besides a semi-metallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e. purely as a result of the repulsive fermionic interactions and in the absence of any external gauge fields. We establish the topological nature of this dynamically created Mott insulating phase by the numerical calculation of a Chern number. Based on the knowledge of the mean-field phase diagram, we then discuss in detail how the interacting Hamiltonian can be engineered effectively by state-of-the-art experimental techniques for laser-dressing of cold fermionic ground-state atoms with electronically excited Rydberg states that exhibit strong dipolar interactions.

cond-mat.str-el↗

arXiv2012

Thermal Instability of Protected End States in a 1-D Topological Insulator

We have studied the dynamical thermal effects on the protected end states of a topological insula- tor (TI) when it is considered as an open quantum system in interaction with a noisy environment at a certain temperature T . As a result, we find that protected end states in a TI become unstable and decay with time. Very remarkably, the interaction with the thermal environment (fermion-boson) respects chiral symmetry, which is the symmetry responsible for the protection (robustness) of the end states in this TI when it is isolated from the environment. Therefore, this mechanism makes end states unstable while preserving their protecting symmetry. Our results have immediate practical implications in recently proposed simulations of TI using cold atoms in optical lattices. Accordingly, we have computed lifetimes of topological end states for these physical implementations that are useful to make those experiments realistic.

cond-mat.mes-hall↗

arXiv2012

Self-Correcting Quantum Computers

Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we first give a sufficient condition on the connect- edness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting capabilities. Also, we address the transversality properties of topological color codes, showing that 6D color codes provide a self-correcting model that allows the transversal and local implementation of a universal set of operations in seven spatial dimensions. Finally, we give a procedure to initialize such quantum memories at finite temperature.

quant-ph↗

arXiv2012

Google in a Quantum Network

We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class represents a quantization of the PageRank protocol currently employed to list web pages according to their importance. We have found an instance of this class of quantum protocols that outperforms its classical counterpart and may break the classical hierarchy of web pages depending on the topology of the web.

quant-ph↗

arXiv2012

Optimal error correction in topological subsystem codes

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing for error syndrome recovery with only 2-local measurements in a two-dimensional array of qubits. We study the error threshold for topological subsystem color codes under very general external noise conditions. By transforming the problem into a classical disordered spin model, we estimate using Monte Carlo simulations that topological subsystem codes have an optimal error tolerance of 5.5(2)%. This means there is ample space for improvement in existing error-correcting algorithms that typically find a threshold of approximately 2%.

quant-ph↗

arXiv2012

Strong Resilience of Topological Codes to Depolarization

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase both via large-scale Monte Carlo simulations and via the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this agrees within error bars with the result for a different class of codes-topological color codes-where the mapping yields interesting new types of interacting eight-vertex models.

quant-ph↗

arXiv2012

Generalized Toric Codes Coupled to Thermal Baths

We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system relax to the Gibbs state for arbitrary qudits, we also prove that above a certain crossing temperature, qutrits initial decay rate is smaller than the original case for qubits. Surprisingly this behavior only happens with qutrits and not with other qudits with $d>3$.

quant-ph↗

arXiv2011

On Quantum Effects in a Theory of Biological Evolution

We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for evolution to take place. However, in more natural scenarios, the rate of evolution depends on the degree of entanglement present in quantum organisms with respect to classical organisms. If the entanglement is maximal, classical evolution turns out to be more favorable.

quant-ph↗