Quantum Error Correction with the Semion Code

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string operators that implement the basic logical operations for information processing. Physically, the new open string operators provide a detailed microscopic description of the creation of semions at their endpoints. Remarkably, topological properties of the string operators are determined using fundamental properties of the Hamiltonian, namely the fact that it is composed of commuting local terms squaring to the identity. In all, the semion code is a topological code that, unlike previously studied topological codes, it is of non-CSS type and fits into the stabilizer formalism. This is in sharp contrast with previous attempts yielding non-commutative codes.Comment: REVTeX 4 file, color figure

La correction d'erreur pour les anyons non abéliens

Bien que le calcul quantique topologique soit tolérant aux fautes de manière intrinsèque à température nulle, cette protection topologique est perdue à toute température plus élevée. L'utilisation de méthodes servant à contrecarrer les effets délétères des excitations thermiques sera donc nécessaire pour construire un ordinateur quantique basé sur ces principes. Dans cette thèse, nous développons des outils de simulation numérique permettant l'analyse de systèmes donnant lieu à des anyons d’Ising. Nous présentons également une méthode de correction d'erreur pouvant être appliquée pour tout modèle anyonique non cyclique, abélien ou non. Cette procédure est fondée sur les travaux de Gács et de Harrington et est basée sur l'utilisation d'automates cellulaires. Une analyse détaillée démontre l'existence d'un taux de création d'excitations critique en deçà duquel l'information peut être protégée. Des simulations numériques permettent d’estimer ce dernier entre $10^{-4}$ et $10^{-3}$

Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a misstatement about the detailed balance condition of our Metropolis simulations. All conclusions from v1 are unaffected by this correctio

Stabilizer Formalism for Operator Algebra Quantum Error Correction

We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction and subsystem codes (OQEC). The construction generates hybrid classical-quantum stabilizer codes and we formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code, generalizing the fundamental theorems for the QEC and OQEC stabilizer formalisms. We discover hybrid versions of the Bacon-Shor subsystem codes motivated by the formalism, and we apply the theorem to derive a result that gives the distance of such codes. We show how some recent hybrid subspace code constructions are captured by the formalism, and we also indicate how it extends to qudits

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable and fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional hybrid resource states comprising both bosonic qubits and squeezed vacuum states. The proposal enables exploiting state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.Comment: 38 pages, many figures. Comments welcom

Fabrication, structural relaxation, and flow in solid-state nanopores

Single solid-stat nanopores have been fabricated in free-standing layers of amorphous silicon nitride. Using a focused electron beam and a focused ion beam, diameters ranging from about 0.7 nm to a few hundred nanometerswere achieved. Structural relaxation of nanopores fabricated by focused electron beam was observed. Depending on the initial diameter and on the length of the nanopores, two distinct phases for the relaxation process were found. An experimental setup for themeasurement of pressure-driven mass flow of helium through a single nanopore was built. The conductance of nanopores with diameters ranging from 25 nm to 315 nm was measured. A semi-phenomenological model was developed and it was shown to quantitatively describe the conductance of fluid through a short cylindrical nanopore.Des nanopores ont été fabriqués dans de minces couches suspendues de nitrure de silicium amorphe. En utilisant un faisceau d'électrons focalisé et un faisceau d'ions focalisé, des diamètres entre 0.7 nm et 315 nm ont été obtenus. La relaxation struturelle de nanopores fabriqués par faisceau focalisé d'électrons a été observée. Dépendamment du diamètre inital du nanopore et de sa longueur, deux phases distinctes ont été identifiées. Un montage expérimental permettant la mesure de l'écoulement de masse d'hélium causé par l'application d'une différence de pression a été réalisé. La mesure de conductance de nanopores ayant un diamètre compris entre 25 nm et 315 nm a été effectuée. Un simple modèle phénoménologique permet de décrire quantitativement l'écoulement de gaz dans un court nanopore cylindrique

La correction d'erreur pour les anyons non abéliens

Bien que le calcul quantique topologique soit tolérant aux fautes de manière intrinsèque à température nulle, cette protection topologique est perdue à toute température plus élevée. L'utilisation de méthodes servant à contrecarrer les effets délétères des excitations thermiques sera donc nécessaire pour construire un ordinateur quantique basé sur ces principes. Dans cette thèse, nous développons des outils de simulation numérique permettant l'analyse de systèmes donnant lieu à des anyons d’Ising. Nous présentons également une méthode de correction d'erreur pouvant être appliquée pour tout modèle anyonique non cyclique, abélien ou non. Cette procédure est fondée sur les travaux de Gács et de Harrington et est basée sur l'utilisation d'automates cellulaires. Une analyse détaillée démontre l'existence d'un taux de création d'excitations critique en deçà duquel l'information peut être protégée. Des simulations numériques permettent d’estimer ce dernier entre $10^{-4}$ et $10^{-3}$

« Ça reste encore mystérieux pour moi » : récits et expériences du genre chez les personnes autistes

This article focuses on the experiences of gender in the narratives of autistic people and their entourage. The social category of gender would make less subjective sense for autistic people because of an alternative relationship to learned social norms. We analyzed interviews conducted with autistic people, their relatives, clinicians and blogs. In the accounts, autistic people describe themselves as impervious to social, and therefore gender, norms. Signs of gender atypia in childhood are often posited in their accounts as precursors to the diagnosis to come: the relationship to gender and society is described by them as an intersection of dissonant experiences. Female autism is described as a phenotype, a kind of autism in itself. Thus, these experiences testify to the impossibility of disentangling (or at least distinguishing completely) the interweaving of the experiences of autism and gender