Adaptive mitigation of time-varying quantum noise

Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference-based adaptive algorithm that can learn and mitigate quantum noise in response to changing channel conditions. Our study emphasizes the need for dynamic inference of critical channel parameters to improve program accuracy. We use the Dirichlet distribution to model the stochasticity of the Pauli channel. This allows us to perform Bayesian inference, which can improve the performance of probabilistic error cancellation (PEC) under time-varying noise. Our work demonstrates the importance of characterizing and mitigating temporal variations in quantum noise, which is crucial for developing more accurate and reliable quantum technologies. Our results show that Bayesian PEC can outperform non-adaptive approaches by a factor of 4.5x when measured using Hellinger distance from the ideal distribution.Comment: To appear in IEEE QCE 202

Tailoring surface codes: Improvements in quantum error correction with biased noise

For quantum computers to reach their full potential will require error correction. We study the surface code, one of the most promising quantum error correcting codes, in the context of predominantly dephasing (Z-biased) noise, as found in many quantum architectures. We find that the surface code is highly resilient to Y-biased noise, and tailor it to Z-biased noise, whilst retaining its practical features. We demonstrate ultrahigh thresholds for the tailored surface code: ~39% with a realistic bias of = 100, and ~50% with pure Z noise, far exceeding known thresholds for the standard surface code: ~11% with pure Z noise, and ~19% with depolarizing noise. Furthermore, we provide strong evidence that the threshold of the tailored surface code tracks the hashing bound for all biases. We reveal the hidden structure of the tailored surface code with pure Z noise that is responsible for these ultrahigh thresholds. As a consequence, we prove that its threshold with pure Z noise is 50%, and we show that its distance to Z errors, and the number of failure modes, can be tuned by modifying its boundary. For codes with appropriately modified boundaries, the distance to Z errors is O(n) compared to O(n1/2) for square codes, where n is the number of physical qubits. We demonstrate that these characteristics yield a significant improvement in logical error rate with pure Z and Z-biased noise. Finally, we introduce an efficient approach to decoding that exploits code symmetries with respect to a given noise model, and extends readily to the fault-tolerant context, where measurements are unreliable. We use this approach to define a decoder for the tailored surface code with Z-biased noise. Although the decoder is suboptimal, we observe exceptionally high fault-tolerant thresholds of ~5% with bias = 100 and exceeding 6% with pure Z noise. Our results open up many avenues of research and, recent developments in bias-preserving gates, highlight their direct relevance to experiment

Design and implementation of resilient attitude estimation algorithms for aerospace applications

Satellite attitude estimation is a critical component of satellite attitude determination and control systems, relying on highly accurate sensors such as IMUs, star trackers, and sun sensors. However, the complex space environment can cause sensor performance degradation or even failure. To address this issue, FDIR systems are necessary. This thesis presents a novel approach to satellite attitude estimation that utilizes an InertialNavigation System (INS) to achieve high accuracy with the low computational load. The algorithm is based on a two-layer Kalman filter, which incorporates the quaternion estimator(QUEST) algorithm, FQA, Linear interpolation (LERP)algorithms, and KF. Moreover, the thesis proposes an FDIR system for the INS that can detect and isolate faults and recover the system safely. This system includes two-layer fault detection with isolation and two-layered recovery, which utilizes an Adaptive Unscented Kalman Filter (AUKF), QUEST algorithm, residual generators, Radial Basis Function (RBF) neural networks, and an adaptive complementary filter (ACF). These two fault detection layers aim to isolate and identify faults while decreasing the rate of false alarms. An FPGA-based FDIR system is also designed and implemented to reduce latency while maintaining normal resource consumption in this thesis. Finally, a Fault Tolerance Federated Kalman Filter (FTFKF) is proposed to fuse the output from INS and the CNS to achieve high precision and robust attitude estimation.The findings of this study provide a solid foundation for the development of FDIR systems for various applications such as robotics, autonomous vehicles, and unmanned aerial vehicles, particularly for satellite attitude estimation. The proposed INS-based approach with the FDIR system has demonstrated high accuracy, fault tolerance, and low computational load, making it a promising solution for satellite attitude estimation in harsh space environment

Quantum memory

This thesis is devoted to the study of coherent storage of quantum information as well as its potential applications. Quantum memories are crucial to harnessing the potential of quantum physics for information processing tasks. They are required for almost all quantum computation proposals. However, despite the large arsenal of theoretical techniques and proposals dedicated to their implementation, the realization of long-lived quantum memories remains an elusive task. Encoding information in quantum states associated to many-body topological phases of matter and protecting them by means of a static Hamiltonian is one of the leading proposals to achieve quantum memories. While many genuine and well publicized virtues have been demonstrated for this approach, equally real limitations were widely disregarded. In the first two projects of this thesis, we study limitations of passive Hamiltonian protection of quantum information under two different noise models. Chapter 2 deals with arbitrary passive Hamiltonian protection for a many body system under the effect of local depolarizing noise. It is shown that for both constant and time dependent Hamiltonians, the optimal enhancement over the natural single-particle memory time is logarithmic in the number of particles composing the system. The main argument involves a monotonic increase of entropy against which a Hamiltonian can provide little protection. Chapter 3 considers the recoverability of quantum information when it is encoded in a many-body state and evolved under a Hamiltonian composed of known geometrically local interactions and a weak yet unknown Hamiltonian perturbation. We obtain some generic criteria which must be fulfilled by the encoding of information. For specific proposals of protecting Hamiltonian and encodings such as Kitaev's toric code and a subsystem code proposed by Bacon, we additionally provide example perturbations capable of destroying the memory which imply upper bounds for the provable memory times. Chapter 4 proposes engineered dissipation as a natural solution for continuously extracting the entropy introduced by noise and keeping the accumulation of errors under control. Persuasive evidence is provided supporting that engineered dissipation is capable of preserving quantum degrees of freedom from all previously considered noise models. Furthermore, it is argued that it provides additional flexibility over Hamiltonian thermalization models and constitutes a promising approach to quantum memories. Chapter 5 introduces a particular experimental realization of coherent storage, shifting the focus in many regards with respect to previous chapters. First of all, the system is very concrete, a room-temperature nitrogen-vacancy centre in diamond, which is subject to actual experimental control and noise restrictions which must be adequately modelled. Second, the relevant degrees of freedom reduce to a single electronic spin and a carbon 13 spin used to store a qubit. Finally, the approach taken to battle decoherence consists of inducing motional narrowing and applying dynamical decoupling pulse sequences, and is tailored to address the systems dominant noise sources. Chapter 6 analyses unforgeable tokens as a potential application of these room-temperature qubit memories. Quantum information protocols based on Wiesner's quantum money scheme are proposed and analysed. We provide the first rigorous proof that such unentangled tokens may be resistant to counterfeiting attempts while tolerating a certain amount of noise. In summary, this thesis provides contributions to quantum memories in four different aspects. Two projects were dedicated to understanding and exposing the limitations of existing proposals. This is followed by a constructive proposal of a new counter-intuitive theoretical model for quantum memories. An applied experimental project achieves record coherent storage times in room-temperature solids. Finally, we provide rigorous analysis for a quantum information application of quantum memories. This completes a broad picture of quantum memories which integrates different perspectives, from theoretical critique and constructive proposal, to technological application going through a down-to-earth experimental implementation

Mathematical and Technological Aspects of Quantum Information Processing

Since its genesis, quantum mechanics has proved to be a very accurate model for predicting the behavior of the world below the nanoscale. However, crucial breakthroughs in technology were needed in order to be able to e ectively access and manipulate such small magnitudes. During the last twenty years, the eld of quantum information processing has experienced a growing interest, in its many variants, both theoretically and practically. Despite being still at a very basic stage, expectations are high. The uniqueness of quantum phenomena (superposition of states, creation of entanglement, etc.) have no classical analogue and allow novelties such as another paradigm of computation, more secure com- munications, quantum teleportation, quantum dense coding, etc. which are presented and analyzed here. The aim of this Thesis is to present in a uni ed way the main mathematical methods used in quantum information processing, as well as the state of the art of their corresponding technological implementations. Our contributions are based in making a self-contained presentation; seeking completeness, that is,treating the most relevant elds of research involved, focusing on their relations; and picking the most relevant, insightful references, given the quantity of literature produced in this eld. We also discuss some of the fundamental questions that remain still unanswered, and which are the current lines of research to shed light on them

Quantum Technologies for Information Processing

English: Since its genesis, quantum mechanics has proved to be a very accurate model for predicting the behavior of the world below the nanoscale. However, crucial breakthroughs in technology were needed in order to be able to effectively access and manipulate such small magnitudes. During the last twenty years, the field of quantum information processing has experienced a growing interest, in its many variants, both theoretically and practically. Despite being still at a very basic stage, expectations are high. The uniqueness of quantum phenomena (superposition of states, creation of entanglement, etc.) have no classical analogue and allow novelties such as another paradigm of computation, more secure communications, quantum teleportation, quantum dense coding, etc. which are presented and analyzed here. The aim of this Thesis is to present in a unified way the main mathematical methods used in quantum information processing, as well as the state of the art of their corresponding technological implementations. Our contributions are based in making a self-contained presentation; seeking completeness, that is, treating the most relevant fields of research involved, focusing on their relations; and picking the most relevant, insightful references, given the quantity of literature produced in this field. We also discuss some of the fundamental questions that remain still unanswered, and which are the current lines of research to shed light on them.Castellano: El objetivo de el presente proyecto es la presentación en una manera unificada de los métodos matemáticos principales (computación cuántica, corrección de errores cuántica y teoría de la información cuántica) así como el estado del arte de las aplicaciones tecnológicas correspondientes (comunicaciones cuánticas y protocolos de criptografía cuántica). Un objetivo más específico será la aplicación de códigos degenerados de corrección de errores en protocolos de comunicación clásicos bidireccionales.Català: L'objectiu d'aquest projecte és presentar en una manera unificada els mètodes matemàtics principals en el processament de la informació quàntica (computació quàntica, correcció d'errors quàntica i teoria de la informació quàntica), així com l'estat de l'art de les aplicacions tecnològiques corresponents (comunicacions quàntiques i protocols de criptografia quàntics). Un objectiu més específic és l'estudi de codis degenerats de correcció d'errors a protocols de comunicació clàssics en dues direccions