Related papers: Magic squares: Latin, Semiclassical and Quantum
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of…
While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…
Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…
We present an asymptotically optimal generalized measurement for the Classical information that is retrieved from a quantum tetrahedron is intrinsically fuzzy. We present an asymptotically optimal generalized measurement for the extraction…
Magic-square constraints define Diophantine systems whose solutions, in several natural families, exhibit rigid periodic structure. We study this structure in an oracle setting, where a marked set of integers is given by black-box access…
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more…
A Latin square of order $n$ is an $n \times n$ matrix of $n$ symbols, such that each symbol occurs exactly once in each row and column. For an odd prime power $q$ let $\mathbb{F}_q$ denote the finite field of order $q$. A quadratic Latin…
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…
Quantum computers promise to solve computational problems significantly faster than classical computers. These 'speed-ups' are achieved by utilizing a resource known as magic. Measuring the amount of magic used by a device allows us to…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
Quantum-enhanced measurements use highly non-classical quantum states in order to enhance the precision of the measurement of classical quantities, like the length of an optical cavity. The major goal is to beat the standard quantum limit…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
A strong confluence result for Q*, a quantum lambda-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but…
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a…
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…