4 research outputs found
Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post‐Quantum Cryptography
In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future
Large-Scale Simulation of Shor's Quantum Factoring Algorithm
Shor's factoring algorithm is one of the most anticipated applications of
quantum computing. However, the limited capabilities of today's quantum
computers only permit a study of Shor's algorithm for very small numbers. Here
we show how large GPU-based supercomputers can be used to assess the
performance of Shor's algorithm for numbers that are out of reach for current
and near-term quantum hardware. First, we study Shor's original factoring
algorithm. While theoretical bounds suggest success probabilities of only 3-4
%, we find average success probabilities above 50 %, due to a high frequency of
"lucky" cases, defined as successful factorizations despite unmet sufficient
conditions. Second, we investigate a powerful post-processing procedure, by
which the success probability can be brought arbitrarily close to one, with
only a single run of Shor's quantum algorithm. Finally, we study the
effectiveness of this post-processing procedure in the presence of typical
errors in quantum processing hardware. We find that the quantum factoring
algorithm exhibits a particular form of universality and resilience against the
different types of errors. The largest semiprime that we have factored by
executing Shor's algorithm on a GPU-based supercomputer, without exploiting
prior knowledge of the solution, is 549755813701 = 712321 * 771781. We put
forward the challenge of factoring, without oversimplification, a non-trivial
semiprime larger than this number on any quantum computing device.Comment: differs from the published version in formatting and style; open
source code available at https://jugit.fz-juelich.de/qip/shorgp
Topological Code Architectures for Quantum Computation
This dissertation is concerned with quantum computation using many-body quantum systems encoded in topological codes. The interest in these topological systems has increased in recent years as devices in the lab begin to reach the fidelities required for performing arbitrarily long quantum algorithms. The most well-studied system, Kitaev\u27s toric code, provides both a physical substrate for performing universal fault-tolerant quantum computations and a useful pedagogical tool for explaining the way other topological codes work. In this dissertation, I first review the necessary formalism for quantum information and quantum stabilizer codes, and then I introduce two families of topological codes: Kitaev\u27s toric code and Bombin\u27s color codes. I then present three chapters of original work. First, I explore the distinctness of encoding schemes in the color codes. Second, I introduce a model of quantum computation based on the toric code that uses adiabatic interpolations between static Hamiltonians with gaps constant in the system size. Lastly, I describe novel state distillation protocols that are naturally suited for topological architectures and show that they provide resource savings in terms of the number of required ancilla states when compared to more traditional approaches to quantum gate approximation
Understanding Quantum Technologies 2022
Understanding Quantum Technologies 2022 is a creative-commons ebook that
provides a unique 360 degrees overview of quantum technologies from science and
technology to geopolitical and societal issues. It covers quantum physics
history, quantum physics 101, gate-based quantum computing, quantum computing
engineering (including quantum error corrections and quantum computing
energetics), quantum computing hardware (all qubit types, including quantum
annealing and quantum simulation paradigms, history, science, research,
implementation and vendors), quantum enabling technologies (cryogenics, control
electronics, photonics, components fabs, raw materials), quantum computing
algorithms, software development tools and use cases, unconventional computing
(potential alternatives to quantum and classical computing), quantum
telecommunications and cryptography, quantum sensing, quantum technologies
around the world, quantum technologies societal impact and even quantum fake
sciences. The main audience are computer science engineers, developers and IT
specialists as well as quantum scientists and students who want to acquire a
global view of how quantum technologies work, and particularly quantum
computing. This version is an extensive update to the 2021 edition published in
October 2021.Comment: 1132 pages, 920 figures, Letter forma