Related papers: CNOT operator and its similar matrices in quantum …
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. In this work, we…
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…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We introduce a framework for implementing logic in CSS quantum error correction codes, building on the surgery methods of Cowtan and Burton [CB24]. Our approach offers a systematic methodology for designing and analysing surgery protocols.…
Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantum computation. We present simulation results for basic quantum…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal…
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more…
This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.