Designing High-Fidelity Gates for Dissipative Cat Qubits

Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant and universal quantum computing. However, current gate proposals for such qubits induce substantial noise of the unprotected type, whose poor scaling with the relevant experimental parameters limits their practical use. In this work, we provide a new perspective on dissipative cat qubits by reconsidering the reservoir mode used to engineer the tailored two-photon dissipation, and show how it can be leveraged to mitigate gate-induced errors. Doing so, we introduce four new designs of high-fidelity and bias-preserving cat qubit gates, and compare them to the prevalent gate methods. These four designs should give a broad overview of gate engineering for dissipative systems with different and complementary ideas. In particular, we propose both already achievable low-error gate designs and longer-term implementations.Comment: 22 pages, 12 figures. All comments on the preprint are welcom

Combined Dissipative and Hamiltonian Confinement of Cat Qubits

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments.Comment: 24 pages, 18 figure

Anisotropic norm-oriented mesh adaptation for a Poisson problem

International audienceWe present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L 2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed

A tensorial-based Mesh Adaptation for a Poisson problem

International audienceThis paper discusses anisotropic mesh adaptation, addressingeither a local interpolation error, or the error on a functional,or the norm of the approximation error, the two last optionsusing an adjoint state. This is explained with a Poisson modelproblem. We focus on metric-based mesh adaptation using apriori errors. Continuous metric-based methods were developedfor this purpose. They propose a continuous statement of themesh optimisation problem, which need to be then discretisedand solved numerically. Tensorial metric-based methods producedirectly a discrete optimal metric for interpolation errorequirepartition. The novelty of the present paper is to extendthe tensorial discrete method to addressing (1) L 1 errors and(2) adjoint-based analyses, two functionalities already availablewith continuous metric. A first interest is to be able to comparetensorial and continuous methods when they are applied to thereduction of approximation errors. Second, an interesting featureof the new formulation is a potentially sharper analysis of theapproximation error. Indeed, the resulting optimal metric has adifferent anisotropic component. The novel formulation is thencompared with the continuous formulation for a few test casesinvolving high-gradient layers and gradient discontinuities

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Adaptive Full-Multigrid algorithms based on Riemannian metrics

International audienceWe study the combination of successive refinements with Full Multigrid Method. For each FMG phase, we build the new meshes by adaptive anisotropic refinements, using Riemannian metrics. Then, we present test cases solved by this method

Roughness characteristic length scales of micro-machined surfaces: A multi-scale modelling

The MEMS structure integrity, their dynamic properties as well as their electrostatic characteristics, strongly depend on the achieved surfaces roughness produced by the micromachining process. It is therefore, not surprising that numerous works are devoted to propose relations between roughness and physical or mechanical properties in this field. Yet the issue is full of complexities since roughness parameters depend on the method used for their evaluation. This article introduces a new approach of the roughness characterization, based on the scaling analysis. Experimental results obtained on micro machined surfaces show that the range roughness amplitude depends on the scan length and that roughness amplitude follows three stages. The stage I is due to a smoothing effect of the surface induced by the tip radius of the profilometer, stage II presents a piecewise power-law roughness distribution until a critical length that characterises the fractal behaviour of the surface, and stage III is characterised by extreme values statistics. The fractal parameter, the extreme values estimators and the crossover between stages II and III are shown to be related to the micromachining process. As a result, an original probabilistic model based on the Generalized Lambda Distribution (GLD) is proposed to estimate the multi-scale roughness in the stage III. Finally, thanks to a Bootstrap protocol coupled with a Monte-Carlo simulation, the maximal roughness amplitude probability density function is estimated at a scale higher than the scanning length

Cerebral and Peripheral Changes Occurring in Nitric Oxide (NO) Synthesis in a Rat Model of Sleeping Sickness: Identification of Brain iNOS Expressing Cells

International audienceBACKGROUND: The implication of nitric oxide (NO) in the development of human African trypanosomiasis (HAT) using an animal model, was examined. The manner by which the trypanocidal activity of NO is impaired in the periphery and in the brain of rats infected with Trypanosoma brucei brucei (T. b. brucei) was analyzed through: (i) the changes occurring in NO concentration in both peripheral (blood) and cerebral compartments; (ii) the activity of nNOS and iNOS enzymes; (iii) identification of the brain cell types in which the NO-pathways are particularly active during the time-course of the infection. METHODOLOGY/PRINCIPAL FINDINGS: NO concentration (direct measures by voltammetry) was determined in central (brain) and peripheral (blood) compartments in healthy and infected animals at various days post-infection: D5, D10, D16 and D22. Opposite changes were observed in the two compartments. NO production increased in the brain (hypothalamus) from D10 (+32%) to D16 (+71%), but decreased in the blood from D10 (-22%) to D16 (-46%) and D22 (-60%). In parallel with NO measures, cerebral iNOS activity increased and peaked significantly at D16 (up to +700%). However, nNOS activity did not vary. Immunohistochemical staining confirmed iNOS activation in several brain regions, particularly in the hypothalamus. In peritoneal macrophages, iNOS activity decreased from D10 (-83%) to D16 (-65%) and D22 (-74%) similarly to circulating NO. CONCLUSION/SIGNIFICANCE: The NO changes observed in our rat model were dependent on iNOS activity in both peripheral and central compartments. In the periphery, the NO production decrease may reflect an arginase-mediated synthesis of polyamines necessary to trypanosome growth. In the brain, the increased NO concentration may result from an enhanced activity of iNOS present in neurons and glial cells. It may be regarded as a marker of deleterious inflammatory reactions