arXiv subjects

Daniel Koch

Publications and source records attributed to Daniel Koch.

At least 19 recordsLinked to original sources

arXiv2026

Generalized saddle-node ghosts and their composite structures in dynamical systems

The study of dynamical systems has long focused on the characterization of their asymptotic dynamics such as fixed points, limit cycles and other types of attractors and how these invariant sets change their properties as systems parameters change. More recently, however, the importance of transient dynamics, especially of long transients and sequential transitions between them, has been increasingly recognized in various fields including ecology, neuroscience and cell biology. Among several possible origins of long transients, ghost attractors have received particular attention due to interesting dynamical properties in non-autonomous settings, new theoretical developments, and an increasing number of systems that empirically show dynamics consistent with ghost attractors. Despite this growing interest in transient dynamics generally and ghost attractors in particular, there are significantly fewer theoretical concepts and software tools available to researchers to classify and characterize their underlying mechanisms compared to asymptotic dynamics. To address this gap, we generalize saddle-nodes to account for higher-dimensional center manifolds and provide a definition for their ghost attractors. We then introduce algorithms to specifically identify and characterize ghost attractors and their composite structures such as ghost channels and ghost cycles and show how these concepts and algorithms can be used to gain new insights into the transient dynamics of a wide range of system models focusing on living systems, allowing, e.g., to describe bifurcations of ghosts. The algorithms are implemented in Python and available as PyGhostID, a user-friendly open-source software package.

nlin.AO↗

arXiv2026

Analysis and Experimental Demonstration of Amplitude Amplification for Combinatorial Optimization

Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional representation of Grover's (orthogonal collective states) to oracles which encode cost functions such as QUBO, and show that linear cost functions are a special case whereby an exact formula exists for determining optimal oracle parameter settings. Using simulations of problem sizes up to 40 qubits we demonstrate QAA's algorithmic performance across all possible solutions, with an emphasis on the closeness in Grover-like performance for solutions near the global optimum. We conclude with experimental demonstrations of generalized QAA on both IBMQ (superconducting) and IonQ (trapped ion) qubits, showing that the observed probabilities of each basis state match our equations as a function of varying the free parameters in the oracle and diffusion operators.

quant-ph↗

arXiv2024

Quantum Boltzmann machine learning of ground-state energies

Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase estimation and hybrid quantum-classical optimizers involving parameterized quantum circuits, the latter falling under the umbrella of the variational quantum eigensolver. Here, we analyze the performance of quantum Boltzmann machines for this task, which is a less explored ansatz based on parameterized thermal states and which is not known to suffer from the barren-plateau problem. We delineate a hybrid quantum-classical algorithm for this task and rigorously prove that it converges to an $\varepsilon$-approximate stationary point of the energy function optimized over parameter space, while using a number of parameterized-thermal-state samples that is polynomial in $\varepsilon^{-1}$, the number of parameters, and the norm of the Hamiltonian being optimized. Our algorithm estimates the gradient of the energy function efficiently by means of a quantum circuit construction that combines classical random sampling, Hamiltonian simulation, and the Hadamard test. Additionally, supporting our main claims are calculations of the gradient and Hessian of the energy function, as well as an upper bound on the matrix elements of the latter that is used in the convergence analysis.

quant-ph↗

arXiv2024

A VUV light source for enhanced production of metastable krypton and xenon beams

We demonstrate excitation of metastable krypton and xenon beams using a vacuum ultraviolet lamp and directly compare the performance of this method to metastable excitation based on a radiofrequency-driven plasma discharge. In our apparatus, lamp-based metastable excitation outperforms the plasma discharge across a wide range of beam flux values relevant for Atom Trap Trace Analysis (ATTA). Moreover, we do not observe significant degradation in lamp performance after over 160 hours of operation. We find that lamp-based excitation is particularly advantageous at the smallest and largest beam fluxes tested, demonstrating the utility of this approach both for improving krypton ATTA and for enabling the detection of radioactive xenon isotopes using ATTA. Finally, we demonstrate an additional enhancement to lamp-based metastable excitation efficiency and stability by applying an external magnetic field.

physics.atom-ph↗

arXiv2024

Biological computations: limitations of attractor-based formalisms and the need for transients

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often noisy information with memory using complex molecular or neuronal networks, they generate a variety of responses beyond simple stimulus-response association, including avoidance behavior, life-long-learning or social interactions. In a broad sense, these processes can be understood as a type of biological computation. Taking as a basis generic features of biological computations, such as real-time responsiveness or robustness and flexibility of the computation, we highlight the limitations of the current attractor-based framework for understanding computations in biological systems. We argue that frameworks based on transient dynamics away from attractors are better suited for the description of computations performed by neuronal and signaling networks. In particular, we discuss how quasi-stable transient dynamics from ghost states that emerge at criticality have a promising potential for developing an integrated framework of computations, that can help us understand how living system actively process information and learn from their continuously changing environment.

q-bio.OT↗

arXiv2024

Ghost cycles exhibit increased entrainment and richer dynamics in response to external forcing compared to slow-fast systems

Many natural, living and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that guides the movement of the system trajectories. Recently, we have provided an alternative description in which the slow dynamics result from a non-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical ghosts that form a closed orbit (termed ghost cycles). Here we investigate the response properties of both type of systems to external forcing. Using the classical Van-der-Pol oscillator and two modified versions of this model that correspond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost cycles are characterized by significant increase especially in the 1:1 entrainment regions as demonstrated by the corresponding Arnold tongues and exhibit richer dynamics (bursting, chaos) in contrast to the classical slow-fast system. Phase plane analysis reveals that these features result from the continuous remodeling of the attractor landscape of the ghost cycles models characteristic for non-autonomous systems, whereas the attractor landscape of the corresponding slow-fast system remains qualitatively unaltered. We propose that systems containing ghost cycles display increased flexibility and responsiveness to continuous environmental changes.

nlin.AO↗

arXiv2023

Ghost channels and ghost cycles guiding long transients in dynamical systems

Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels/cycles being central concepts behind the emergence of quasi-stable long transients. Reliable and robust transient dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework that does not rely on the precise knowledge or existence of (un)stable fixed points, but rather on slow directed flows organized by ghost sets in ghost channels and ghost cycles. Moreover, we show that appearance of these novel objects is an emergent property of a broad class of models, typically used for description of natural systems.

physics.bio-ph↗

arXiv2023

Variational Amplitude Amplification for Solving QUBO Problems

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as `cost oracle' operations $U_{\textrm{C}}$, which when combined with the standard Grover diffusion operator $U_{\textrm{s}}$ lead to high probabilities of measurement for states corresponding to the optimal and near optimal solutions. In order to achieve these probabilities, a single scalar parameter $p_{\textrm{s}}$ is required, which we show can be found through a variational quantum-classical hybrid approach.

quant-ph↗

arXiv2023

Physics Simulation Via Quantum Graph Neural Network

We develop and implement two realizations of quantum graph neural networks (QGNN), applied to the task of particle interaction simulation. The first QGNN is a speculative quantum-classical hybrid learning model that relies on the ability to directly utilize superposition states as classical information to propagate information between particles. The second is an implementable quantum-classical hybrid learning model that propagates particle information directly through the parameters of $RX$ rotation gates. A classical graph neural network (CGNN) is also trained in the same task. Both the Speculative QGNN and CGNN act as controls against the Implementable QGNN. Comparison between classical and quantum models is based on the loss value and accuracy of each model. Overall, each model had a high learning efficiency, in which the loss value rapidly approached zero during training; however, each model was moderately inaccurate. Comparing performances, our results show that the Implementable QGNN has a potential advantage over the CGNN. Additionally, we show that a slight alteration in hyperparameters in the CGNN notably improves accuracy, suggesting that further fine tuning could mitigate the issue of moderate inaccuracy in each model.

quant-ph↗

arXiv2022

Information loss and run time from practical application of quantum data compression

We examine information loss, resource costs, and run time from practical application of quantum data compression. Compressing quantum data to fewer qubits enables efficient use of resources, as well as applications for quantum communication and denoising. In this context, we provide a description of the quantum and classical components of the hybrid quantum autoencoder algorithm, implemented using IBM's Qiskit language. Utilizing our own data sets, we encode bitmap images as quantum superposition states, which correspond to linearly independent vectors with density matrices of discrete values. We successfully compress this data with near-lossless compression using simulation, and then run our algorithm on an IBMQ quantum chip. We describe conditions and run times for compressing our data on quantum devices.

quant-ph↗

arXiv2021

Gaussian Amplitude Amplification for Quantum Pathfinding

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding minimum or maximum solutions on a weighted directed graph. We focus on a geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by gaussian distributions. We then demonstrate how an oracle which encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases which are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.

quant-ph↗

arXiv2020

Gate-Based Circuit Designs For Quantum Adder Inspired Quantum Random Walks on Superconducting Qubits

Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen many great mathematical advances, with experimental demonstrations now catching up. In this study, we examine the viability of implementing Coin Quantum Random Walks using a Quantum Adder based Shift Operator, with quantum circuit designs specifically for superconducting qubits. We focus on the strengths and weaknesses of these walks, particularly circuit depth, gate count, connectivity requirements, and scalability. We propose and analyze a novel approach to implementing boundary conditions for these walks, demonstrating the technique explicitly in one and two dimensions. And finally, we present several fidelity results from running our circuits on IBM's quantum volume 32 `Toronto' chip, showcasing the extent to which these NISQ devices can currently handle quantum walks.

quant-ph↗

arXiv2020

Fundamentals In Quantum Algorithms: A Tutorial Series Using Qiskit Continued

With the increasing rise of publicly available high level quantum computing languages, the field of Quantum Computing has reached an important milestone of separation of software from hardware. Consequently, the study of Quantum Algorithms is beginning to emerge as university courses and disciplines around the world, spanning physics, math, and computer science departments alike. As a continuation to its predecessor: "Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit", this tutorial series aims to help understand several of the most promising quantum algorithms to date, including Phase Estimation, Shor's, QAOA, VQE, and several others. Accompanying each algorithm's theoretical foundations are coding examples utilizing IBM's Qiskit, demonstrating the strengths and challenges of implementing each algorithm in gate-based quantum computing.

quant-ph↗

arXiv2020

Demonstrating NISQ Era Challenges in Algorithm Design on IBM's 20 Qubit Quantum Computer

As superconducting qubits continue to advance technologically, the realization of quantum algorithms from theoretical abstraction to physical implementation requires knowledge of both quantum circuit construction as well as hardware limitations. In this study we present results from experiments run on IBM's 20-qubit `Poughkeepsie' architecture, with the goal of demonstrating various qubit qualities and challenges that arise in designing quantum algorithms. These include experimentally measuring $T_1$ and $T_2$ coherence times, gate fidelities, sequential CNOT gates, techniques for handling ancilla qubits, and finally CCNOT and QFT$^{\dagger}$ circuits implemented on several different qubit geometries. Our results demonstrate various techniques for improving quantum circuits which must compensate for limited connectivity, either through the use of SWAP gates or additional ancilla qubits.

quant-ph↗

arXiv2019

Simulating Quantum Algorithms Using Fidelity and Coherence Time as Principle Models for Error

As various quantum computing technologies continue to compete for quantum supremacy, several parameters have emerged as benchmarks for the quality of qubits. These include fidelity, coherence times, connectivity, and a few others. In this paper, we aim to study the importance of these parameters and their impact on quantum algorithms. We propose a realistic connectivity geometry and form quantum circuits for the Bernstein-Vazirani, QFT, and Grover Algorithms based on the limitations of the chosen geometry. We then simulate these algorithms using error models to study the impact of gate fidelity and coherence times on success of the algorithms. We report on the findings of our simulations and note the various benchmarking values which produce reliably successful results.

quant-ph↗

arXiv2019

Revisiting $\pi$ Backbonding: The Influence of $d$ Orbitals on Metal-CO Bonds and Ligand Red Shifts

The concept of $\pi$ backbonding is widely used to explain the complex stabilities and CO stretch frequency red shifts of transition metal carbonyls. We theoretically investigate a non-transition metal 18-electron carbonyl complex (Mg(CO)$_8$) and find a pronounced CO red shift without metal-carbon $\pi$ bonds. Moreover, we use truncated basis sets on the "honorary" and true transition metals Ca and Ti in Ca(CO)$_8$ and [Ti(CO)$_8$]$^{2+}$ complexes to probe the influence of $d$ functions on carbonyl complex stability, C-O bond strength, metal-to-ligand charge transfer and bond order compared to hypothetical complexes without metal-$d$ contributions. We find that the occurrence of metal-ligand $\pi$ bonds through metal $d$ functions greatly enhances the complex stabilities on one hand but only slightly affects the CO red shift on the other hand. This does not correspond to the classical rationalization of transition metal-CO bonds as synergistic $\sigma$ donation/$\pi$ backdonation.

physics.chem-ph↗

arXiv2019

Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit

As the field of Quantum Computing continues to grow, so too has the general public's interest in testing some of the publicly available quantum computers. However, many might find learning all of the supplementary information that goes into quantum algorithms to be a daunting task, and become discouraged. This tutorial is a series of lessons, aimed to teach the basics of quantum algorithms to those who may have little to no background in quantum physics and/or minimal knowledge of coding in python. Each lesson covers select physics/coding topics needed for writing quantum algorithms, eventually building up a toolset for tackling more and more challenging quantum algorithms. This tutorial series is designed to provide readers from any background with two services: 1) A concise and thorough understanding of some of the most popular/academically important quantum algorithms. 2) A fluent understanding of how to write code for quantum algorithms, using IBM's publicly available Qiskit.

quant-ph↗

arXiv2019

Introduction to Coding Quantum Algorithms: A Tutorial Series Using Pyquil

quant-ph↗