Related papers: Quantum Algorithms for Magic Square Diophantine Eq…
Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…
We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as…
A triorthogonal code is a binary quantum Calderbank-Shor-Steane (CSS) code defined by a triorthogonal matrix. Triorthogonal codes are a key ingredient in magic-state distillation, since they allow for transversal $\mathsf{T}$ gates, a…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and…
Using elementary number theory we study Diophantine equations over the rational integers of the following form, $y^2=(x+a)(x+a+k)(x+b)(x+b+k)$, $y^2=c^2x^4+ax^2+b$ and $y^2=(x^2-1)(x^2-\alpha^2)(x^2-(\alpha+1)^2).$ We express their integer…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the…
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
Nonstabilizerness, commonly referred to as magic, is a fundamental resource underpinning quantum advantage. In this paper, we propose a magic-informed quantum architecture search (QAS) technique that enables control over a quantum resource…
We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends…
We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
A brief history and two formulations of the Diophantine problem's requirements are presented. One tier consisting of three two-parameter solutions is studied for its ability to provide examples for the small natural numbers considered.…
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…
We consider the set of Diophantine equations that arise in the context of the barotropic vorticity equation on periodic domains, when nonlinear wave interactions are studied to leading order in the amplitudes. The solutions to this set of…
In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our…
We show that a simple eavesdropper listening in on classical communication between potentially entangled quantum parties will eventually be able to impersonate any of the parties. Furthermore, the attack is efficient if one-way puzzles do…
Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. CSS codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for…