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Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have…
We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data…
A new generalization of shifted thin plate splines $$\varphi(x)=(c^{2d}+||x||^{2d})\log\left(c^{2d}+||x||^{2d}\right),\qquad x\in\mathbb{R}^n, d\in \mathbb{N}, c>0$$ is presented to increase the accuracy of quasi-interpolation further. With…
Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…
We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to…
We describe a general approach for constructing a broad class of operators approximating high-dimensional curves based on geometric Hermite data. The geometric Hermite data consists of point samples and their associated tangent vectors of…
The quantum circuit model is an abstraction that hides the underlying physical implementation of gates and measurements on a quantum computer. For precise control of real quantum hardware, the ability to execute pulse and readout-level…
BOUT++ is a 3D nonlinear finite-difference plasma simulation code, capable of solving quite general systems of PDEs, but targeted particularly on studies of the edge region of tokamak plasmas. BOUT++ is publicly available, and has been…
Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even…
We present the C++ library CppSs (C++ super-scalar), which provides efficient task-parallelism without the need for special compilers or other software. Any C++ compiler that supports C++11 is sufficient. CppSs features different…
We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage…
Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have…
A new algebraic cubature formula of degree $2n+1$ for the product Chebyshev measure in the $d$-cube with $\approx n^d/2^{d-1}$ nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree $n$ in three…
We present QuIFS (Quasi-Interpolation driven Feedback Synthesis): an offline feedback synthesis algorithm for explicit nonlinear robust minmax model predictive control (MPC) problems with guaranteed quality of approximation. The underlying…