Related papers: Countinuous Quantum Hidden Subgroup Algorithms
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
In recent papers of the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In the…
The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…
Coalition Structure Generation (CSG) is an NP-Hard problem in which agents are partitioned into mutually exclusive groups to maximize their social welfare. In this work, we propose QuACS, a novel hybrid quantum classical algorithm for…
In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of a single realization is never smaller than the quantum state manifold…
Quantum compiling aims to construct a quantum circuit V by quantum gates drawn from a native gate alphabet, which is functionally equivalent to the target unitary U. It is a crucial stage for the running of quantum algorithms on noisy…
Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower…
We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…
Quantum computing has evolved quickly in recent years and is showing significant benefits in a variety of fields, especially in the realm of cybersecurity. The combination of software used to locate the most frequent hashes and $n$-grams…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
We present a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which…
We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
Digital signatures represent a crucial cryptographic asset that must be protected against quantum adversaries. Quantum Digital Signatures (QDS) can offer solutions that are information-theoretically (IT) secure and thus immune to quantum…
By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by…
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys…