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.Comment: 12 pages, 5 figures, 1 tabl

Quantum Measurements and Gates by Code Deformation

The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in which a single code layer is used for the entire computation, in particular a surface code. Qubits can be created, manipulated and non-destructively measured by code deformations that amount to `cut and paste' operations in the surface. All the interactions between qubits remain purely local in a two-dimensional setting.Comment: Revtex4, 6 figure

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.Comment: 21 pages, 21 figures; published versio

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 $d>3$.Comment: Revtex4 file, color figures. New Journal of Physics' versio

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.Comment: 56 pages, 16 figures, published version

Digital Quantum Simulation with Rydberg Atoms

We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaev's toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for controlled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.Comment: submitted to special issue "Quantum Information with Neutral Particles" of "Quantum Information Processing

A Rydberg Quantum Simulator

Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (QS) is a controlled quantum device which reproduces the dynamics of any other many particle quantum system with short range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. We investigate how laser excited Rydberg atoms in large spacing optical or magnetic lattices can provide an efficient implementation of a universal QS for spin models involving (high order) n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such as the Kitaev toric code, color code, and lattice gauge theories with spin liquid phases. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates.Comment: 8 pages, 4 figure

A systematic review and meta-analysis of neurological soft signs in relatives of people with schizophrenia

<p>Abstract</p> <p>Background</p> <p>Neurological soft signs are subtle but observable impairments in motor and sensory functions that are not localized to a specific area of the brain. Neurological soft signs are common in schizophrenia. It has been established that soft signs meet two of five criteria for an endophenotype, namely: association with the illness, and state independence. This review investigated whether soft signs met a further criterion for an endophenotype, namely familial association. It was hypothesized that if familial association were present then neurological soft signs would be: (a) more common in first-degree relatives of people with schizophrenia than in controls; and (b) more common in people with schizophrenia than in their first-degree relatives.</p> <p>Method</p> <p>A systematic search identified potentially eligible studies in the EMBASE (1980-2011), OVID - MEDLINE (1950-2011) and PsycINFO (1806-2011) databases. Studies were included if they carried out a three-way comparison of levels of soft signs between people with schizophrenia, their first-degree relatives, and normal controls. Data were extracted independently by two reviewers and cross-checked by double entry.</p> <p>Results</p> <p>After screening 8678 abstracts, seven studies with 1553 participants were identified. Neurological soft signs were significantly more common in first-degree relatives of people with schizophrenia than in controls (pooled standardised mean difference (SMD) 1.24, 95% confidence interval (c.i) 0.59-1.89). Neurological soft signs were also significantly more common in people with schizophrenia than in their first-degree relatives (SMD 0.92, 95% c.i 0.64-1.20). Sensitivity analyses examining the effects of age and group blinding did not significantly alter the main findings.</p> <p>Conclusions</p> <p>Both hypotheses were confirmed, suggesting that the distribution of neurological soft signs in people with schizophrenia and their first-degree relatives is consistent with the endophenotype criterion of familial association.</p

The Functional DRD3 Ser9Gly Polymorphism (rs6280) Is Pleiotropic, Affecting Reward as Well as Movement

Abnormalities of motivation and behavior in the context of reward are a fundamental component of addiction and mood disorders. Here we test the effect of a functional missense mutation in the dopamine 3 receptor (DRD3) gene (ser9gly, rs6280) on reward-associated dopamine (DA) release in the striatum. Twenty-six healthy controls (HCs) and 10 unmedicated subjects with major depressive disorder (MDD) completed two positron emission tomography (PET) scans with [11C]raclopride using the bolus plus constant infusion method. On one occasion subjects completed a sensorimotor task (control condition) and on another occasion subjects completed a gambling task (reward condition). A linear regression analysis controlling for age, sex, diagnosis, and self-reported anhedonia indicated that during receipt of unpredictable monetary reward the glycine allele was associated with a greater reduction in D2/3 receptor binding (i.e., increased reward-related DA release) in the middle (anterior) caudate (p<0.01) and the ventral striatum (p<0.05). The possible functional effect of the ser9gly polymorphism on DA release is consistent with previous work demonstrating that the glycine allele yields D3 autoreceptors that have a higher affinity for DA and display more robust intracellular signaling. Preclinical evidence indicates that chronic stress and aversive stimulation induce activation of the DA system, raising the possibility that the glycine allele, by virtue of its facilitatory effect on striatal DA release, increases susceptibility to hyperdopaminergic responses that have previously been associated with stress, addiction, and psychosis

EPA-0882 - Prediction of diagnosis of early-onset schizophrenia spectrum disorders using support vector machines

To develop a Support Vector Machine (SVM) algorithm as a predictive tool for diagnostic outcome in patients with FE-EOP, based on clinical and biomedical data at the emergence of the illness