Related papers: The Topology of Quantum Algorithms
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
We generalize the Deutsch-Jozsa problem and present a quantum algorithm that can solve the generalized Deutsch-Jozsa problem by a single evaluation of a given function. We discuss the initialization of an auxiliary register and present a…
We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group…
Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Localization is a critical aspect of mobile robotics, enabling robots to navigate their environment efficiently and avoid obstacles. Current probabilistic localization methods, such as the Adaptive-Monte Carlo localization (AMCL) algorithm,…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
The first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask. Here we observe how part of Simon's algorithm can be…
We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…
We demonstrated the detailed construction of the hybrid quantum-classical computer. Based on this architecture, the useful concept of amplitude interception is illustrated. It is then embedded into a combination of Depth-First Search and…
Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…