33 research outputs found
The XP Stabilizer Formalism
Quantum computers are expected to have advantages over classical computers in solving a range
of high impact problems, but they are highly susceptible to errors due to environmental noise.
The Pauli Stabiliser formalism generalises classical error-correction methods and makes use of
quantum error correction codes to protect quantum information. In this thesis, we introduce
the XP stabiliser formalism, which is a generalisation of the Pauli stabiliser formalism with a
number of useful applications.
Quantum algorithms are typically written in terms of quantum circuits which involve a
series of unitary gates followed by measurements which form the output of the computation.
To implement quantum algorithms reliably, we need to perform unitary gates fault-tolerantly so that errors do not propagate in an uncontrolled way.
Transversal logical operators are one way of applying unitary gates fault-tolerantly on Pauli
stabiliser codes. Identifying transversal logical operators for a given Pauli stabiliser code is
challenging, and existing methods have exponential complexity in one or more of the parameters
of the code. Making use of the XP formalism, we present efficient algorithms which identify
all transversal logical operators that are diagonal in the computational basis for any Pauli
stabiliser code. We also show how to construct codes with a transversal implementation of any
desired diagonal logical operator.
The Pauli stabiliser formalism can also be used to efficiently represent certain quantum
states, but many states of interest lie outside the formalism. In the XP formalism, a wider
range of states can be represented than in the Pauli stabiliser formalism, including hypergraph
states which have interesting non-local properties. The braiding of non-Abelian anyons is a
proposed pathway to universal fault-tolerant quantum computation. Certain XP stabiliser
codes are known to harbour non-Abelian anyons, and can be studied within the new formalism
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Transversal Diagonal Logical Operators for Stabiliser Codes
Storing quantum information in a quantum error correction code can protect it
from errors, but the ability to transform the stored quantum information in a
fault tolerant way is equally important. Logical Pauli group operators can be
implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category
of codes, by applying a series of physical Pauli X and Z gates. Logical
operators of this form are fault-tolerant because each qubit is acted upon by
at most one gate, limiting the spread of errors, and are referred to as
transversal logical operators. Identifying transversal logical operators
outside the Pauli group is less well understood. Pauli operators are the first
level of the Clifford hierarchy which is deeply connected to fault-tolerance
and universality. In this work, we study transversal logical operators composed
of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate
algorithms for identifying all transversal diagonal logical operators on a CSS
code that are more general or have lower computational complexity than previous
methods. We also show a method for constructing CSS codes that have a desired
diagonal logical Clifford hierarchy operator implemented using single qubit
phase gates. Our methods rely on representing operators composed of diagonal
Clifford hierarchy gates as diagonal XP operators and this technique may have
broader applications.Comment: 24 pages + 11 page appendix, 4 figures, comments welcom
Satellite Communications
This study is motivated by the need to give the reader a broad view of the developments, key concepts, and technologies related to information society evolution, with a focus on the wireless communications and geoinformation technologies and their role in the environment. Giving perspective, it aims at assisting people active in the industry, the public sector, and Earth science fields as well, by providing a base for their continued work and thinking
Recent Application in Biometrics
In the recent years, a number of recognition and authentication systems based on biometric measurements have been proposed. Algorithms and sensors have been developed to acquire and process many different biometric traits. Moreover, the biometric technology is being used in novel ways, with potential commercial and practical implications to our daily activities. The key objective of the book is to provide a collection of comprehensive references on some recent theoretical development as well as novel applications in biometrics. The topics covered in this book reflect well both aspects of development. They include biometric sample quality, privacy preserving and cancellable biometrics, contactless biometrics, novel and unconventional biometrics, and the technical challenges in implementing the technology in portable devices. The book consists of 15 chapters. It is divided into four sections, namely, biometric applications on mobile platforms, cancelable biometrics, biometric encryption, and other applications. The book was reviewed by editors Dr. Jucheng Yang and Dr. Norman Poh. We deeply appreciate the efforts of our guest editors: Dr. Girija Chetty, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park and Dr. Sook Yoon, as well as a number of anonymous reviewers
Pattern Recognition
A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition
Resiliency Mechanisms for In-Memory Column Stores
The key objective of database systems is to reliably manage data, while high query throughput and low query latency are core requirements. To date, database research activities mostly concentrated on the second part. However, due to the constant shrinking of transistor feature sizes, integrated circuits become more and more unreliable and transient hardware errors in the form of multi-bit flips become more and more prominent. In a more recent study (2013), in a large high-performance cluster with around 8500 nodes, a failure rate of 40 FIT per DRAM device was measured. For their system, this means that every 10 hours there occurs a single- or multi-bit flip, which is unacceptably high for enterprise and HPC scenarios. Causes can be cosmic rays, heat, or electrical crosstalk, with the latter being exploited actively through the RowHammer attack. It was shown that memory cells are more prone to bit flips than logic gates and several surveys found multi-bit flip events in main memory modules of today's data centers. Due to the shift towards in-memory data management systems, where all business related data and query intermediate results are kept solely in fast main memory, such systems are in great danger to deliver corrupt results to their users. Hardware techniques can not be scaled to compensate the exponentially increasing error rates. In other domains, there is an increasing interest in software-based solutions to this problem, but these proposed methods come along with huge runtime and/or storage overheads. These are unacceptable for in-memory data management systems.
In this thesis, we investigate how to integrate bit flip detection mechanisms into in-memory data management systems. To achieve this goal, we first build an understanding of bit flip detection techniques and select two error codes, AN codes and XOR checksums, suitable to the requirements of in-memory data management systems. The most important requirement is effectiveness of the codes to detect bit flips. We meet this goal through AN codes, which exhibit better and adaptable error detection capabilities than those found in today's hardware. The second most important goal is efficiency in terms of coding latency. We meet this by introducing a fundamental performance improvements to AN codes, and by vectorizing both chosen codes' operations. We integrate bit flip detection mechanisms into the lowest storage layer and the query processing layer in such a way that the remaining data management system and the user can stay oblivious of any error detection. This includes both base columns and pointer-heavy index structures such as the ubiquitous B-Tree. Additionally, our approach allows adaptable, on-the-fly bit flip detection during query processing, with only very little impact on query latency. AN coding allows to recode intermediate results with virtually no performance penalty. We support our claims by providing exhaustive runtime and throughput measurements throughout the whole thesis and with an end-to-end evaluation using the Star Schema Benchmark. To the best of our knowledge, we are the first to present such holistic and fast bit flip detection in a large software infrastructure such as in-memory data management systems. Finally, most of the source code fragments used to obtain the results in this thesis are open source and freely available.:1 INTRODUCTION
1.1 Contributions of this Thesis
1.2 Outline
2 PROBLEM DESCRIPTION AND RELATED WORK
2.1 Reliable Data Management on Reliable Hardware
2.2 The Shift Towards Unreliable Hardware
2.3 Hardware-Based Mitigation of Bit Flips
2.4 Data Management System Requirements
2.5 Software-Based Techniques For Handling Bit Flips
2.5.1 Operating System-Level Techniques
2.5.2 Compiler-Level Techniques
2.5.3 Application-Level Techniques
2.6 Summary and Conclusions
3 ANALYSIS OF CODING TECHNIQUES
3.1 Selection of Error Codes
3.1.1 Hamming Coding
3.1.2 XOR Checksums
3.1.3 AN Coding
3.1.4 Summary and Conclusions
3.2 Probabilities of Silent Data Corruption
3.2.1 Probabilities of Hamming Codes
3.2.2 Probabilities of XOR Checksums
3.2.3 Probabilities of AN Codes
3.2.4 Concrete Error Models
3.2.5 Summary and Conclusions
3.3 Throughput Considerations
3.3.1 Test Systems Descriptions
3.3.2 Vectorizing Hamming Coding
3.3.3 Vectorizing XOR Checksums
3.3.4 Vectorizing AN Coding
3.3.5 Summary and Conclusions
3.4 Comparison of Error Codes
3.4.1 Effectiveness
3.4.2 Efficiency
3.4.3 Runtime Adaptability
3.5 Performance Optimizations for AN Coding
3.5.1 The Modular Multiplicative Inverse
3.5.2 Faster Softening
3.5.3 Faster Error Detection
3.5.4 Comparison to Original AN Coding
3.5.5 The Multiplicative Inverse Anomaly
3.6 Summary
4 BIT FLIP DETECTING STORAGE
4.1 Column Store Architecture
4.1.1 Logical Data Types
4.1.2 Storage Model
4.1.3 Data Representation
4.1.4 Data Layout
4.1.5 Tree Index Structures
4.1.6 Summary
4.2 Hardened Data Storage
4.2.1 Hardened Physical Data Types
4.2.2 Hardened Lightweight Compression
4.2.3 Hardened Data Layout
4.2.4 UDI Operations
4.2.5 Summary and Conclusions
4.3 Hardened Tree Index Structures
4.3.1 B-Tree Verification Techniques
4.3.2 Justification For Further Techniques
4.3.3 The Error Detecting B-Tree
4.4 Summary
5 BIT FLIP DETECTING QUERY PROCESSING
5.1 Column Store Query Processing
5.2 Bit Flip Detection Opportunities
5.2.1 Early Onetime Detection
5.2.2 Late Onetime Detection
5.2.3 Continuous Detection
5.2.4 Miscellaneous Processing Aspects
5.2.5 Summary and Conclusions
5.3 Hardened Intermediate Results
5.3.1 Materialization of Hardened Intermediates
5.3.2 Hardened Bitmaps
5.4 Summary
6 END-TO-END EVALUATION
6.1 Prototype Implementation
6.1.1 AHEAD Architecture
6.1.2 Diversity of Physical Operators
6.1.3 One Concrete Operator Realization
6.1.4 Summary and Conclusions
6.2 Performance of Individual Operators
6.2.1 Selection on One Predicate
6.2.2 Selection on Two Predicates
6.2.3 Join Operators
6.2.4 Grouping and Aggregation
6.2.5 Delta Operator
6.2.6 Summary and Conclusions
6.3 Star Schema Benchmark Queries
6.3.1 Query Runtimes
6.3.2 Improvements Through Vectorization
6.3.3 Storage Overhead
6.3.4 Summary and Conclusions
6.4 Error Detecting B-Tree
6.4.1 Single Key Lookup
6.4.2 Key Value-Pair Insertion
6.5 Summary
7 SUMMARY AND CONCLUSIONS
7.1 Future Work
A APPENDIX
A.1 List of Golden As
A.2 More on Hamming Coding
A.2.1 Code examples
A.2.2 Vectorization
BIBLIOGRAPHY
LIST OF FIGURES
LIST OF TABLES
LIST OF LISTINGS
LIST OF ACRONYMS
LIST OF SYMBOLS
LIST OF DEFINITION
Improving Group Integrity of Tags in RFID Systems
Checking the integrity of groups containing radio frequency identification (RFID) tagged objects or recovering the tag identifiers of missing objects is important in many activities. Several autonomous checking methods have been proposed for increasing the capability of recovering missing tag identifiers without external systems. This has been achieved by treating a group of tag identifiers (IDs) as packet symbols encoded and decoded in a way similar to that in binary erasure channels (BECs). Redundant data are required to be written into the limited memory space of RFID tags in order to enable the decoding process. In this thesis, the group integrity of passive tags in RFID systems is specifically targeted, with novel mechanisms being proposed to improve upon the current state of the art.
Due to the sparseness property of low density parity check (LDPC) codes and the mitigation of the progressive edge-growth (PEG) method for short cycles, the research is begun with the use of the PEG method in RFID systems to construct the parity check matrix of LDPC codes in order to increase the recovery capabilities with reduced memory consumption. It is shown that the PEG-based method achieves significant recovery enhancements compared to other methods with the same or less memory overheads. The decoding complexity of the PEG-based LDPC codes is optimised using an improved hybrid iterative/Gaussian decoding algorithm which includes an early stopping criterion. The relative complexities of the improved algorithm are extensively analysed and evaluated, both in terms of decoding time and the number of operations required. It is demonstrated that the improved algorithm considerably reduces the operational complexity and thus the time of the full Gaussian decoding algorithm for small to medium amounts of missing tags.
The joint use of the two decoding components is also adapted in order to avoid the iterative decoding when the missing amount is larger than a threshold. The optimum value of the threshold value is investigated through empirical analysis. It is shown that the adaptive algorithm is very efficient in decreasing the average decoding time of the improved algorithm for large amounts of missing tags where the iterative decoding fails to recover any missing tag. The recovery performances of various short-length irregular PEG-based LDPC codes constructed with different variable degree sequences are analysed and evaluated. It is demonstrated that the irregular codes exhibit significant recovery enhancements compared to the regular ones in the region where the iterative decoding is successful. However, their performances are degraded in the region where the iterative decoding can recover some missing tags.
Finally, a novel protocol called the Redundant Information Collection (RIC) protocol is designed to filter and collect redundant tag information. It is based on a Bloom filter (BF) that efficiently filters the redundant tag information at the tag’s side, thereby considerably decreasing the communication cost and consequently, the collection time. It is shown that the novel protocol outperforms existing possible solutions by saving from 37% to 84% of the collection time, which is nearly four times the lower bound. This characteristic makes the RIC protocol a promising candidate for collecting redundant tag information in the group integrity of tags in RFID systems and other similar ones
Some Notes on Code-Based Cryptography
This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem
Primary Structure and Solution Conditions Determine Conformational Ensemble Properties of Intrinsically Disordered Proteins
Intrinsically disordered proteins (IDPs) are a class of proteins that do not exhibit well-defined three-dimensional structures. The absence of structure is intrinsic to their amino acid sequences, which are characterized by low hydrophobicity and high net charge per residue compared to folded proteins. Contradicting the classic structure-function paradigm, IDPs are capable of interacting with high specificity and affinity, often acquiring order in complex with protein and nucleic acid binding partners. This phenomenon is evident during cellular activities involving IDPs, which include transcriptional and translational regulation, cell cycle control, signal transduction, molecular assembly, and molecular recognition. Although approximately 30% of eukaryotic proteomes are intrinsically disordered, the nature of IDP conformational ensembles remains unclear. In this dissertation, we describe relationships connecting characteristics of IDP conformational ensembles to their primary structures and solution conditions.
Using molecular simulations and fluorescence experiments on a set of base-rich IDPs, we find that net charge per residue segregates conformational ensembles along a globule-to-coil transition. Speculatively generalizing this result, we propose a phase diagram that predicts an IDP\u27s average size and shape based on sequence composition and use it to generate hypotheses for a broad set of intrinsically disordered regions (IDRs). Simulations reveal that acid-rich IDRs, unlike their oppositely charged base-rich counterparts, exhibit disordered globular ensembles despite intra-chain repulsive electrostatic interactions. This apparent asymmetry is sensitive to simulation parameters for representing alkali and halide salt ions, suggesting that solution conditions modulate IDP conformational ensembles. We refine the ion parameters using a calibration procedure that relies exclusively on crystal lattice properties. Simulations with these parameters recover swollen coil behavior for acid-rich IDRs, but also uncover a dependence on sequence patterning for polyampholytic IDPs.
These contributions initiate an endeavor to elucidate general principles that enable prediction of an IDP\u27s conformational ensemble based on primary structure and solution conditions, a goal analogous to structure prediction for folded proteins. Such principles would provide a molecular basis for understanding the roles of IDPs in physiology and pathophysiology, guide development of agents that modulate their behavior, and enable their rational design from chosen specifications