相关论文: Uniformity is weaker than semi-uniformity for some…

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…

Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational…

Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…

In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…

We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…

As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to…

The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…

Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy…

Large language models (LLMs) are being increasingly adopted in the software engineering domain, yet the robustness of their grasp on core software design concepts remains unclear. We conduct an empirical study to systematically evaluate…

We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural…

Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…

Training a Neural Network (NN) with lots of parameters or intricate architectures creates undesired phenomena that complicate the optimization process. To address this issue we propose a first modular approach to NN design, wherein the NN…

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…

We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…

A recently introduced measure of Boolean functions complexity--disjunc\-tive complexity (DC)--is compared with other complexity measures: the space complexity of streaming algorithms and the complexity of nondeterministic branching programs…

Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

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…

Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial…

We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus…