arXiv research

A new approach uses circuit topology to study complex polymer interactions.

Develops a braid-theoretic framework to analyze chirality in molecular knots.

Polynomial invariants classify molecular chains based on their contact arrangements.

Two proofs show that removing a loop from a plane circuit splits the plane.

Recently, in the paper "Weight Agnostic Neural Networks" Gaier & Ha utilized architecture search to find networks where the topology completely encodes the knowledge. However, architecture search in topology space is expensive. We use the existing framework of binarized networks to find performant topologies by constra…

Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …

We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…

We consider efficiency in the implementation of deep neural networks. Hardware accelerators are gaining interest as machine learning becomes one of the drivers of high-performance computing. In these accelerators, the directed graph describing a neural network can be implemented as a directed graph describing a Boolean…

UKM framework optimizes VQCs, showing QCL performance is bounded.

The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffia…

A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrari…

This paper characterizes Kashiwara-Vergne groups using algebraic structures of knotted tubes.

Program connects quantum computing and topological field theories.

Generating eye diagrams by using a circuit simulator can be very computationally intensive, especially in the presence of nonlinearities. It often involves multiple Newton-like iterations at every time step when a SPICE-like circuit simulator handles a nonlinear system in the transient regime. In this paper, we leverag…

Study evaluates capacity and trainability of parametrized quantum circuits.

The paper tests if LLMs' capabilities are executed by small subnetworks (circuits).

This work shows how to efficiently simulate parts of quantum landscapes using classical computers.

Study detects if a circuit bounds a disc using curve intersections.

Evolutionary strategy optimizes quantum circuit design and parameters.

This work uses SVM to identify track component failures in AC Track Circuits.

The statistical complexity of quantum circuits is studied using Rademacher complexity.

Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. O…

Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural net…

The study examines how quantum resources enhance the complexity of quantum circuits.

Study bounds VAR model's circuit complexity, showing it's limited to TC^0 circuits.

In this work, a machine learning approach for identifying the multi-omics metabolic regulatory control circuits inside the pathways is described. Therefore, the identification of bacterial metabolic pathways that are more regulated than others in term of their multi-omics follows from the analysis of these circuits . T…

Study shows limitations and possibilities of learning quantum circuit output distributions.

We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the simil…

Spin networks boost quantum algorithms solving SU(2) symmetric problems.

Enhances quantum circuit synthesis using deep learning and geometric methods.

Single T-gate makes distribution learning hard for deep circuits.

We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as…

Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves …

Quantum circuits are hard to learn on average.

Study improves probabilistic circuits using transformations for better predictions.

Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not triv…

Quantum circuit optimization speeds up financial derivatives pricing.

Bayesian approach optimizes quantum circuits for noisy hardware.

The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. How…

The lattice stick number $s_L(L)$ of a link $L$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $L$ in the cubic lattice. Hong, No and Oh found a general upper bound $s_L(K) \leq 3 c(K) +2$. A rational link can be represented by a lattice presentation with exa…

Quantum variational circuits improve reinforcement learning efficiency.

PNCs balance tractability and expressiveness in probabilistic modeling.

Unified tractability conditions for various compositional inference queries.

Quantum circuits predict volatility dynamics preserving asymmetry.

Fix a finite group $G$. We analyze the computational complexity of the problem of counting homomorphisms $π_1(X) \to G$, where $X$ is a topological space treated as computational input. We are especially interested in requiring $G$ to be a fixed, finite, nonabelian, simple group. We then consider two cases: when the in…

Active sampling improves design space exploration for analog circuits.

Quantum circuits explained using Shapley values for better understanding.

Quantum neural tangent kernels help understand variational quantum circuits in machine learning.