arXiv subjects

Maxime Tremblay

Publications and source records attributed to Maxime Tremblay.

9 recordsLinked to original sources

arXiv2024

Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes

A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model noise, while being able to simulate the dynamics of many modes. However, so far, large-scale simulation tools for concatenated GKP codes have been limited to idealized noise models and GKP code implementations. Here, we introduce the Bosonic Pauli+ model (BP+), which can be simulated efficiently for a large number of modes, while capturing the rich dynamics in the bosonic multi-mode Hilbert space. We demonstrate the method by simulating a hybrid surface code, where the data qubits are finite-energy GKP qubits stabilized using the small-Big-small (sBs) protocol, and the syndrome qubits are standard two-level systems. Using BP+, we present logical error rates of such an implementation. Confidence in the accuracy of the method is gained by comparing its predictions with full time evolution simulations for several relevant quantum circuits. While developed specifically for GKP qubits stabilized using the sBs protocol, the mathematical structure of BP+ is generic and may be applicable also to the simulation of concatenations using other bosonic codes.

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arXiv2023

Autonomous quantum error correction of Gottesman-Kitaev-Preskill states

The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum error correction of GKP states based on reservoir engineering of a superconducting device. Error correction is made autonomous through an unconditional reset of an auxiliary transmon qubit. The lifetime of the logical qubit is shown to be increased from quantum error correction, therefore reaching the point at which more errors are corrected than generated.

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arXiv2022

Finite-rate sparse quantum codes aplenty

We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing, finite rate, sparsity, and maximum-degree constraints simultaneously in a CSP that we can then solve numerically. Using a state-of-the-art CSP solver, we obtain convincing evidence for the existence of a satisfiability threshold. Furthermore, the extent of the satisfiable phase increases with the number of qubits. In that phase, finding sparse codes becomes an easy problem. Moreover, we observe that the sparse codes found in the satisfiable phase practically achieve the channel capacity for erasure noise. Our results show that intermediate-size finite-rate sparse quantum codes are easy to find, while also demonstrating a flexible methodology for generating good codes with custom properties. We therefore establish a complete and customizable pipeline for random quantum code discovery.

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arXiv2020

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

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arXiv2020

Rain rendering for evaluating and improving robustness to bad weather

Rain fills the atmosphere with water particles, which breaks the common assumption that light travels unaltered from the scene to the camera. While it is well-known that rain affects computer vision algorithms, quantifying its impact is difficult. In this context, we present a rain rendering pipeline that enables the systematic evaluation of common computer vision algorithms to controlled amounts of rain. We present three different ways to add synthetic rain to existing images datasets: completely physic-based; completely data-driven; and a combination of both. The physic-based rain augmentation combines a physical particle simulator and accurate rain photometric modeling. We validate our rendering methods with a user study, demonstrating our rain is judged as much as 73% more realistic than the state-of-theart. Using our generated rain-augmented KITTI, Cityscapes, and nuScenes datasets, we conduct a thorough evaluation of object detection, semantic segmentation, and depth estimation algorithms and show that their performance decreases in degraded weather, on the order of 15% for object detection, 60% for semantic segmentation, and 6-fold increase in depth estimation error. Finetuning on our augmented synthetic data results in improvements of 21% on object detection, 37% on semantic segmentation, and 8% on depth estimation.

cs.CV↗

arXiv2019

M\'ethodes de calcul avec r\'eseaux de tenseurs en physique (Basic tensor network computations in physics)

Cet article se veut un survol des r\'eseaux de tenseurs et s'adresse aux d\'ebutants en la mati\`ere. Nous y mettons l'accent sur les outils n\'ecessaires \`a l'impl\'ementation concr\`ete d'algorithmes. Quatre op\'erations de base (remodelage, permutation d'indices, contraction et d\'ecomposition) qui sont couramment utilis\'ees dans les algorithmes de r\'eseaux de tenseurs y sont d\'ecrites. Y seront aussi couverts la notation diagrammatique, les \'etats en produit de matrices (MPS), les op\'erateurs en produit de matrices (MPO), \'etat projet\'e de paires intriqu\'ees (PEPS), l'approche par renormalisation d'enchev\^etrement multi-\'echelle (MERA), la d\'ecimation par bloc d'\'evolution temporelle (TEBD) et le groupe de renormalisation de tenseurs (TRG). This article is intended as an overview of tensor networks for beginners looking to perform computations. We focus on the tools necessary for the concrete implementation of algorithms. Four basic operations (reshaping, permutation, contraction, and decomposition) that are commonly used in tensor network algorithms are covered. The article also briefly reviews diagrammatic notation, matrix product states (MPS), matrix product operators (MPO), projected entangled pair states (PEPS), multi-scale entanglement renormalization ansatz (MERA), time evolution block decimation (TEBD), and tensor renormalization group (TRG).

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arXiv2018

Depth versus Breadth in Convolutional Polar Codes

Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the block-structured polarization step of polar codes by a convolutional structure. This article presents a numerical exploration of this so-called convolutional polar codes family to find efficient generalizations of polar codes, both in terms of decoding speed and decoding error probability. The main conclusion drawn from our study is that increasing the convolution depth is more efficient than increasing the polarization kernel's breadth as previously explored.

cs.IT↗

arXiv2018

Convolutional Polar Codes on Channels with Memory using Tensor Networks

Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the same construction also polarizes channels with memory, and a generalization of successive cancellation decoder was proposed with a complexity that scales like the third power of the channel's memory size. In another line of work, the polar code construction was extended by replacing the block polarization kernel by a convoluted kernel. Here, we present an efficient decoding algorithm for finite-state memory channels that can be applied to polar codes and convolutional polar codes. This generalization is most effectively described using the tensor network formalism, and the manuscript presents a self-contained description of the required basic concepts. We use numerical simulations to study the performance of these algorithms for practically relevant code sizes and find that the convolutional structure outperforms the standard polar codes on a variety of channels with memory.

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arXiv2017

Learning to segment on tiny datasets: a new shape model

Current object segmentation algorithms are based on the hypothesis that one has access to a very large amount of data. In this paper, we aim to segment objects using only tiny datasets. To this extent, we propose a new automatic part-based object segmentation algorithm for non-deformable and semi-deformable objects in natural backgrounds. We have developed a novel shape descriptor which models the local boundaries of an object's part. This shape descriptor is used in a bag-of-words approach for object detection. Once the detection process is performed, we use the background and foreground likelihood given by our trained shape model, and the information from the image content, to define a dense CRF model. We use a mean field approximation to solve it and thus segment the object of interest. Performance evaluated on different datasets shows that our approach can sometimes achieve results near state-of-the-art techniques based on big data while requiring only a tiny training set.

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