Related papers: A Novel AQC Factoring Algorithm
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…
Programming for today's quantum computers is making significant strides toward modern workflows compatible with high performance computing (HPC), but fundamental challenges still remain in the integration of these vastly different…
Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum…
While quantum computing holds immense potential for tackling previously intractable problems, its current practicality remains limited. A critical aspect of realizing quantum utility is the ability to efficiently interface with data from…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
By leveraging quantum-mechanical properties like superposition, entanglement, and interference, quantum computing (QC) offers promising solutions for problems that classical computing has not been able to solve efficiently, such as drug…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
The advent of fault-tolerant quantum computers marks a significant milestone, yet the development of practical quantum algorithms remains a critical challenge. Effective quantum algorithms are essential for leveraging the power of quantum…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…