相关论文: Modelling Arbitrary Computations in the Symbolic M…

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…

We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…

In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…

In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative…

We propose a method of optimizing monotone Boolean circuits by re-writing them in a simpler, equivalent form. We use in total six heuristics: Hill Climbing, Simulated Annealing, and variations of them, which operate on the representation of…

Constrained problems are frequently encountered in classical and quantum optimization. Particle conservation, in particular, is commonly imposed when studying energy spectra of chemical and solid state systems. Though particle…

Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns…

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…

For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$.Variational quantum algorithms (VQAs) for the discreted Poisson equation have been studied before. We give a VQA…

A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…

Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…

Noisy intermediate-scale quantum computers (NISQ computers) are now readily available, motivating many researchers to experiment with Variational Quantum Algorithms (VQAs). Among them, the Quantum Approximate Optimization Algorithm (QAOA)…

Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that…

Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices.…

In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as…

The paper considers pseudo-differential boundary value control systems. The underlying operators form an algebra D with the help of which we are able to formulate typical boundary value control problems. The symbolic calculus gives tools to…

Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…

We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…

Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…

We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…