Related papers: Magic squares: Latin, Semiclassical and Quantum
Recent years have seen an increasing body of work examining how quantum entanglement can be measured at high energy particle physics experiments, thereby complementing traditional table-top experiments. This raises the question of whether…
There is a well-known mathematical similarity between two-dimensional classical polarization optics and two-level quantum systems, where the Poincare and Bloch spheres are identical mathematical structures. This analogy implies that the…
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as…
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
In this paper we introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares, and investigate their applications in quantum computer science. Our main results are on applications to unitary error…
A new single-particle shell model is derived by solving the Schr\"odinger equation for a semi-spheroidal potential well. Only the negative parity states of the $Z(z)$ component of the wave function are allowed, so that new magic numbers are…
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures…
Error correction will add so much overhead to large quantum computations that we suspect the most efficient algorithms will use a classical co-processor to do as much work as possible. We present a method to offload portions of a quantum…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
Do you want to know what an anti-chiece Latin square is? Or what a non-consecutive toroidal modular Latin square is? We invented a ton of new types of Latin squares, some inspired by existing Sudoku variations. We can't wait to introduce…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Similar to how standard Young tableaux represent paths in the Young lattice, Latin rectangles may be use to enumerate paths in the poset of semi-magic squares with entries zero or one. The symmetries associated to determinant preserve this…
The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations exponentially imply better…
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…