Related papers: Oracle Operators for Non-Boolean Functions
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
Nonadiabatic holonomic quantum computation has been attracting continuous attention since it was proposed. Until now, various schemes of nonadiabatic holonomic quantum computation have been developed and many of them have been…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility…
The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…
This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
While it is well known that finding approximate optima of non-convex functions is computationally intractable, we show that the problem is, in fact, uncomputable in the oracle model. Specifically, we prove that no algorithm with access only…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schr\"odinger equation. Our goal is to find a realization of the annihilation operator for this oscillator by a differential operator. This…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
The challenges of black box optimization arise due to imprecise responses and limited output information. This article describes new results on optimizing multivariable functions using an Order Oracle, which provides access only to the…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
We present an oracle factorisation algorithm which finds a nontrivial factor of almost all positive integers $n$ based on the knowledge of the number of points on certain elliptic curves in residue rings modulo $n$.
In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range…
In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar, for which standard MATLAB matrix operation syntax (e.g.…