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With the rise of big data sets, the popularity of kernel methods declined and neural networks took over again. The main problem with kernel methods is that the kernel matrix grows quadratically with the number of data points. Most attempts…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
The qubit SWAP gate has been shown to be an integral component of quantum circuitry design. It permutes the states of two qubits and allows for the storage quantum information, teleportation of atomic or ionic states, and is a fundamental…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…
In this paper we study a combinatorial reconfiguration problem that involves finding an optimal sequence of swaps to move an initial configuration of tokens that are placed on the vertices of a graph to a final desired one. This problem…
We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a…
Trapped-ion (TI) quantum computer is one of the forerunner quantum technologies. However, TI systems can have a limited number of qubits in a single trap. Execution of meaningful quantum algorithms requires a multiple trap system. In such…
Most quantum compiler transformations and qubit allocation techniques to date are either peep-hole focused or rely on sliding windows that depend on a number of external parameters. Thus, global optimization criteria are still lacking. In…
Quantum computing offers unparalleled computational capabilities but faces significant challenges, including limited qubit counts, diverse hardware topologies, and dynamic noise/error rates, which hinder scalability and reliability.…
Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state…
We consider the best approximation problem (BAP) of projecting a point onto the intersection of a number of convex sets. It is known that Dykstra's algorithm is alternating minimization on the dual problem. We extend Dykstra's algorithm so…
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a new construction of inner- and outer-bounding polytopes…
Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…
This paper deals with the Stochastic Capacitated Arc Routing Problem (SCARP), obtained by randomizing quantities on the arcs in the CARP. Optimization problems for the SCARP are characterized by decisions that are made without knowing their…
Current superconducting quantum devices impose strict connectivity constraints on quantum circuit execution, necessitating circuit transformation before executing quantum circuits on physical hardware. Numerous quantum circuit…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates,…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…