arXiv subjects

M. A. Martin-Delgado

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

At least 55 records · Page 3Linked to original sources

arXiv2011

Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes

We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a statistical-mechanical three-dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories.

quant-ph↗

arXiv2011

Quantum algorithms for classical lattice models

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.

quant-ph↗

arXiv2011

Universality in phase boundary slopes for spin glasses on self dual lattices

We study the effects of disorder on the slope of the disorder--temperature phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase-boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.

cond-mat.dis-nn↗

arXiv2010

Localization of phonons in ion traps with controlled quantum disorder

We show that the vibrations of a chain of trapped ions offer an interesting route to explore the physics of disordered quantum systems. By preparing the internal state of the ions in a quantum superposition, we show how the local vibrational energy becomes a stochastic variable, being its statistical properties inherited from the underlying quantum parallelism of the internal state. We describe a minimally-perturbing measurement of the resonance fluorescence, which allows us to study effects like Anderson localization without the need of ground-state cooling or individual addressing, and thus paves the way towards high-temperature ion experiments.

quant-ph↗

arXiv2010

Wilson Fermions and Axion Electrodynamics in Optical Lattices

The formulation of massless relativistic fermions in lattice gauge theories is hampered by the fundamental problem of species doubling, namely, the rise of spurious fermions modifying the underlying physics. A suitable tailoring of the fermion masses prevents such abundance of species, and leads to the so-called Wilson fermions. Here we show that ultracold atoms provide us with the first controllable realization of these paradigmatic fermions, thus generating a quantum simulator of fermionic lattice gauge theories. We describe a novel scheme that exploits laser-assisted tunneling in a cubic optical superlattice to design the Wilson fermion masses. The high versatility of this proposal allows us to explore a variety of interesting phases in three-dimensional topological insulators, and to test the remarkable predictions of axion electrodynamics.

cond-mat.quant-gas↗

arXiv2010

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point

We study the adiabatic dynamics of Majorana fermions across a quantum phase transition. We show that the Kibble-Zurek scaling, which describes the density of bulk defects produced during the critical point crossing, is not valid for edge Majorana fermions. Therefore, the dynamics governing an edge state quench is nonuniversal and depends on the topological features of the system. Besides, we show that the localization of Majorana fermions is a necessary ingredient to guaranty robustness against defect production.

cond-mat.str-el↗

arXiv2010

Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.

cond-mat.quant-gas↗

arXiv2010

Mapping all classical spin models to a lattice gauge theory

In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all possible k-body Ising-type interactions, for all k, which we also prove. Here, we elaborate on the proof of the result, and we illustrate it by computing quantities of a specific model as a function of the partition function of the 4D Z_2 LGT. The result also allows one to establish a new method to compute the mean-field theory of Z_2 LGTs with d > 3, and to show that computing the partition function of the 4D Z_2 LGT is computationally hard (#P hard). The proof uses techniques from quantum information.

quant-ph↗

arXiv2010

Topological phase transitions in the non-Abelian honeycomb lattice

Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics can be tested. Here, we generalize this system to non-Abelian quantum electrodynamics, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly-interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.

cond-mat.mes-hall↗

arXiv2010

Topological Color Codes and Two-Body Quantum Lattice Hamiltonians

Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a four-valent lattice, the so called ruby lattice, governed by a 2-body Hamiltonian. In a particular regime of coupling constants, degenerate perturbation theory implies that the low energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. The gauge symmetry $\mathbf{Z}_{2}\times\mathbf{Z}_{2}$ of color code could already be realized by identifying three distinct plaquette operators on the lattice. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other giving rise to exact topological degeneracy of the model. Connection to 2-colexes can be established at the non-perturbative level. The particular structure of the 2-body Hamiltonian provides a fruitful interpretation in terms of mapping to bosons coupled to effective spins. We show that high energy excitations of the model have fermionic statistics. They form three families of high energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. Also, we use Jordan-Wigner transformation in order to test the integrability of the model via introducing of Majorana fermions. The four-valent structure of the lattice prevents to reduce the fermionized Hamiltonian into a quadratic form due to interacting gauge fields. We also propose another construction for 2-body Hamiltonian based on the connection between color codes and cluster states. We discuss this latter approach along the construction based on the ruby lattice.

cond-mat.str-el↗

arXiv2010

Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code demonstrate the inherent robustness of this implementation.

quant-ph↗

arXiv2009

Interacting Anyonic Fermions in a Two-Body Color Code Model

We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2 gauge group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.

cond-mat.str-el↗

arXiv2009

Error Threshold for Color Codes and Random 3-Body Ising Models

We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random 3-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p_c = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities does not necessarily imply lower resistance to noise.

cond-mat.dis-nn↗

arXiv2009

Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.

cond-mat.mes-hall↗

arXiv2009

Quantum 2-Body Hamiltonian for Topological Color Codes

We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect. The model has a $\Z_2\times \Z_2$ gauge group symmetry and string-net integrals of motion. There exists a gapped phase in which the low-energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.

quant-ph↗

arXiv2009

Unifying all classical spin models in a Lattice Gauge Theory

We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d>3, and we show that the computation of the partition function of the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z_2 LGT. All results are proven using quantum information techniques.

hep-lat↗

arXiv2009

Competing many-body interactions in systems of trapped ions

We propose and theoretically analyse an experimental configuration in which lasers induce 3-spin interactions between trapped ions.By properly choosing the intensities and frequencies of the lasers, 3-spin couplings may be dominant or comparable to 2-spin terms and magnetic fields. In this way, trapped ions can be used to study exotic quantum phases which do not have a counterpart in nature. We study the conditions for the validity of the effective 3-spin Hamiltonian, and predict qualitatively the quantum phase diagram of the system.

quant-ph↗

arXiv2009

Topology induced anomalous defect production by crossing a quantum critical point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterise the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the non-universal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.

cond-mat.str-el↗