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The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
Quantum Random Access Memory (QRAM) has the potential to revolutionize the area of quantum computing. QRAM uses quantum computing principles to store and modify quantum or classical data efficiently, greatly accelerating a wide range of…
The development of quantum computing systems has been a staple of academic research since the mid-1990s when the first proposal for physical platforms were proposed using Nuclear Magnetic Resonance and Ion-Trap hardware. These first…
Operating on the principles of quantum mechanics, quantum algorithms hold the promise for solving problems that are beyond the reach of the best-available classical algorithms. An integral part of realizing such speedup is the…
We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms…
Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of…
Quantum machine learning (QML) sits at the intersection of quantum computing and classical machine learning, offering the prospect of new computational paradigms and advantages for processing complex data. This chapter introduces the…
Classical program analysis techniques, such as abstract interpretation and symbolic execution, are essential for ensuring software correctness, optimizing performance, and enabling compiler optimizations. However, these techniques face…
We use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory.…
Quantum computing presents a promising alternative to classical computational methods for modeling strongly correlated materials with partially filled d orbitals. In this study, we perform a comprehensive quantum resource estimation using…
This document describes a family of quantum circuits which load classical data into a quantum state. When loading $N$ classical bits, the result quantum state is of order $\log_2(N)$ qubits. Furthermore the gate depth of the data loading…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
While significant progress has been made on the hardware side of quantum computing, support for high-level quantum programming abstractions remains underdeveloped compared to classical programming languages. In this article, we introduce…
Quantum computer technology harnesses the features of quantum physics for revolutionizing information processing and computing. As such, quantum computers use physical quantum gates that process information unitarily, even though the final…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
In this paper the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial…
Quantum computing has shown great potential to revolutionize traditional computing and can provide an exponential speedup for a wide range of possible applications, attracting various stakeholders. However, understanding fundamental quantum…