Francesco Petruccione

• Dr rer nat habil
• Professor (Full) at Stellenbosch University

In order to leverage quantum computers for machine learning tasks such as image classification, consideration is required. Noisy Intermediate-Scale Quantum (NISQ) computers have limitations that include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact complex da...

The potential role of spin in biological systems is a primary topic in quantum biology. However, much of this research focuses on electron spin. A recent hypothesis suggests that nuclear spin may be better suited to biological processes, being less sensitive to decoherence. The hypothesis details how phosphorus nuclei might be prepared in a spin en...

We investigate neutrino decoherence within the framework of quantum spacetime, focusing on the $\kappa$-Minkowski model. We show that stochastic fluctuations in quantum spacetime induce an energy-dependent decoherence effect, where the decoherence rate scales as $E^{-4}$. This result aligns with recent IceCube observations, indicating that quantum...

Open quantum Brownian motion (OQBM) represents a new class of quantum Brownian motion where the dynamics of the Brownian particle depend not only on the interactions with a thermal environment but also on the state of the internal degrees of freedom. For an Ohmic bath spectral density with a Lorentz-Drude cutoff frequency at a high-temperature limi...

We present a computation method to automatically design the n-qubit realisations of quantum algorithms. Our approach leverages a domain-specific language (DSL) that enables the construction of quantum circuits via modular building blocks, making it well-suited for evolutionary search. In this DSL quantum circuits are abstracted beyond the usual gat...

We introduce a method that generates ground state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states (TNS) via an evolutionary algorithm. This language provides operations that allow the generated...

Quantum computers can be used to simulate the evolution of quantum systems via the discretization of this evolution into unitary gate sequences. While Trotter-Suzuki (TS) methods stand as the most prevalent approach for quantum simulation, their effectiveness is contingent upon the sparsity of the Hamiltonian system. This is due to the precision an...

The proposed work presents a nested Photonic Crystal Fiber(PCF) with a hexagonal lattice of air holes, capable of supporting Orbital Angular Momentum modes(OAM) and generating a wide-ranging supercontinuum spectrum, further enhancing its utility in various optical applications. The Photonic Crystal Fiber consists of a dense flint SF6 and a very lig...

The origins of life is a question that continues to intrigue scientists across disciplines. One theory - the iron-sulphur theory - suggests that reactions essential to the synthesis of biological materials got their catalytic 'spark' from mineral surfaces such as iron pyrite, commonly known as fool's gold. Additionally, the binding affinity of the...

Quantum machine learning is in a period of rapid development and discovery, however it still lacks the resources and diversity of computational models of its classical complement. With the growing difficulties of classical models requiring extreme hardware and power solutions, and quantum models being limited by noisy intermediate-scale quantum (NI...

The quantum asymptotically universal multi-feature (QAUM) encoding architecture was recently introduced and showed improved expressivity and performance in classifying pulsar stars. The circuit uses generalized trainable layers of parameterized single-qubit rotation gates and single-qubit feature encoding gates. Although the improvement in classifi...

In order to leverage quantum computers for machine learning tasks such as image classification, careful consideration is required: NISQ-era quantum computers have limitations, which include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact that complex datasets c...

For the first time in history, humankind might conceivably begin to imagine itself as a multi-planetary species. This goal will entail technical innovation in a number of contexts, including that of healthcare. All life on Earth shares an evolution that is coupled to specific environmental conditions, including gravitational and magnetic fields. Wh...

Well-known quantum machine learning techniques, specifically quantum kernel-assisted support vector machines (QSVMs) and quantum convolutional neural networks (QCNNs), are applied to the binary classification of pulsars. In this comparative study, it is illustrated with simulations that both quantum methods successfully achieve effective classifica...

When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algor...

Quantum machine learning is in a period of rapid development and discovery, however it still lacks the resources and diversity of computational models of its classical complement. With the growing difficulties of classical models requiring extreme hardware and power solutions, and quantum models being limited by noisy intermediate-scale quantum (NI...

We apply the hierarchical equations of motion technique to analyzing nonequilibrium heat transport in a spin-boson type model, whereby heat transfer through a central spin is mediated by an intermediate pair of coupled harmonic oscillators. The coupling between each pair of oscillators is shown to introduce a localized gap into the effective spectr...

Kernel methods are an import class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a...

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimization problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost functi...

In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and...

Quantum algorithms for simulating quantum systems provide a clear and provable advantage over classical algorithms in fault-tolerant settings. There is also interest in quantum algorithms and their implementation in Noisy Intermediate Scale Quantum (NISQ) settings. In these settings, various noise sources and errors must be accounted for when execu...

Quantum key distribution (QKD) offers information‐theoretic security by leveraging the principles of quantum mechanics. This means the security is independent of all future advances in algorithm or computational power. However, due to the non‐availability of single‐photon sources, most traditional QKD protocols are vulnerable to various attacks, su...

Quantum process tomography (QPT) is a crucial tool for characterizing and validating quantum devices and quantum algorithms. However, the problem of finite sampling leads to an estimated process matrix which is non-positive semi-definite (non-PSD), which can yield a reconstructed quantum channel that is non-physical. To address this problem, variou...

Mechanisms occurring at the atomic level are now known to drive processes essential for life, as revealed by quantum effects on biochemical reactions. Some macroscopic characteristics of organisms may thus show an atomic imprint, which may be transferred across organisms and affect their evolution. This possibility is considered here for the first...

It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that on...

We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing noninvertible Pauli maps and quantify the fraction of the same. The memory kernel perspective appears to be less transpare...

One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more complex open quantum systems. In this tutorial, we introduce the methods used in the simulation of single qub...

While strong system-bath coupling produces rich and interesting phenomena, applications to quantum thermal engines have been so far pointing mainly at detrimental effects. The delicate trade-off between efficiency loss due to strong coupling and power increase due to faster equilibration, while acknowledged, remains largely unexplored owing to the...

Quantum circuit algorithms often require architectural design choices analogous to those made in constructing neural and tensor networks. These tend to be hierarchical, modular and exhibit repeating patterns. Neural Architecture Search (NAS) attempts to automate neural network design through learning network architecture and achieves state-of-the-a...

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimisation problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost functi...

Finding solutions to systems of linear equations is a common problem in many areas of science and engineering, with much potential for a speed up on quantum devices. While the Harrow–Hassidim–Lloyd (HHL) quantum algorithm yields up to an exponential speed up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, whi...

We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP-indivisibility and one not so. Next, we study the production of (non-)Markovian, invertible maps by the process of mixing noninvertible Pauli maps. The memory kernel perspective appears to be less transparent on the issue of invertibility...

Using the Petz map, we investigate the potential of state recovery when exposed to dephasing and amplitude-damping channels. Specifically, we analyze the geometrical aspects of the Petz map for the qubit case, which is linked to the change in the volume of accessible states. Our findings suggest that the geometrical characterization can serve as a...

While strong system-bath coupling produces rich and interesting phenomena, applications to quantum thermal engines have been so far pointing mainly at detrimental effects. The delicate trade-off between efficiency loss due to strong coupling and power increase due to faster equilibration, while acknowledged, remained largely unexplored owing to the...

This work presents a fabricated silica few-mode microstructured optical fiber (MOF) with a special six GeO2-doped core geometry, an outer diameter of 125 µm (that corresponds to conventional commercially available telecommunication optical fibers), and improved induced twisting up to 500 revolutions per 1 m (under a rotation speed of 1000 revolutio...

In the design of quantum devices, it is crucial to account for the interaction between qubits and their environment to understand and improve the coherence and stability of the quantum states. This is especially prevalent in Noisy Intermediate Scale Quantum (NISQ) devices in which the qubit states quickly decay through processes of relaxation and d...

The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A prerequisite for applying quantum algorithms to a wide range of real-world problems is loading classical data to a quantum state. Several circuit-based methods have been proposed for encoding cla...

This work presents the design and simulation of an all-optical sensor for detection of cancer cells. The proposed device is based on the surface plasmon resonance effect on a spiral shaped photonic crystal fiber structure. The finite element method (FEM) based simulations are carried out for the different cancer cells, such as HELA, Basal, Jurkat,...

One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more complex open quantum systems. In this tutorial, we introduce the methods used in the simulation of single qub...

Multi-class classification problems are fundamental in many varied domains in research and industry. To solve multi-class classification problems, heuristic strategies such as One-vs-One or One-vs-All can be employed. However, these strategies require the number of binary classification models developed to grow with the number of classes. Recent wo...

The quantum asymptotically universal multi-feature (QAUM) encoding architecture was recently introduced and showed improved expressivity and performance in classifying pulsar stars. The circuit uses generalized trainable layers of parameterized single-qubit rotation gates and single-qubit feature encoding gates. Although the improvement in classifi...

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated fo...

This manuscript presents a ring-core Bragg Fiber (RC-BF) for orbital angular momentum (OAM) modes propagation and supercontinuum generation. The proposed RC-BF is composed of alternating layers of soft glasses SF57 and LLF1 to render high nonlinearity to the fiber. Mode analysis using full-vectorial finite element method resulted in obtaining HE/EH...

This paper presents a systematic numerical investigation of a surface plasmon resonance (SPR) sensor based on photonic crystal fiber (PCF). The proposed design is modeled and simulated using the full vectorial finite-element (FV-FEM) technique and sensing characteristics such as confinement loss behaviors, phase matching and sensitivity are investi...

The Quantum Convolutional Neural Network (QCNN) is a quantum circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). The success of CNNs is largely due to its ability to learn high level features from raw data rather than requiring manual feature design. Neural Architecture Search (NAS) continues this trend by learning n...

One of the approaches used to solve for the dynamics of open quantum systems is the hierarchical equations of motion (HEOM). Although it is numerically exact, this method requires immense computational resources to solve. The objective here is to demonstrate whether models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networ...

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral th...

A wellknown approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ishi...

We study the convex combinations of the (d+1)-generalized Pauli dynamical maps in a Hilbert space of dimension d. For certain choices of the decoherence function, the maps are noninvertible, and they remain under convex combinations as well. For the case of dynamical maps characterized by the decoherence function (1−e−ct)/n with the decoherence par...

Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications...

This work presents designed and fabricated silica few-mode optical fiber (FMF) with induced twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical “telecommunication” cladding diameter 125 µm, improved height of quasi-step refractive index profile and numerical aperture 0.22. Proposed FMF supports 4 guided modes over “C”-band. We di...

This work presents results of property researches of fabricated samples of silica few-mode optical fiber (FMF) with induced chirality under twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical “telecommunication” cladding diameter 125 µm and improved height of quasi-step refractive index profile. Proposed FMF supports 4 guided mod...

We study the conditions under which a semigroup is obtained upon convex combinations of channels. In particular, we study the set of Pauli and generalized Pauli channels. We find that mixing only semigroups can never produce a semigroup. Counterintuitively, we find that for a convex combination to yield a semigroup, most of the input channels have...

Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications...

There is an intrinsic link between operations that can be performed on a quantum computer and kernel methods. This has inspired the development of quantum-kernel-based classifiers that exploit the ability of quantum computers to efficiently perform operations in large Hilbert spaces. This work performs a proof of principle demonstration of a quantu...

We study the uniform mixing of the $(d+1)$ generalized Pauli channels in a Hilbert space of dimension $d$, where each channel is characterized by the decoherence function $(1-e^{-ct})/n$, with the decoherence parameter $n$ and decay factor $c$. The channels are invertible if and only if $n > \frac{d}{d-1}$. We show that if the input Pauli channels...

A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ish...

Discrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte-Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often requir...

South Africa has a long history in quantum research with an explosion of activity in the recent decade. Bolstered by this momentum, in March 2021, the South African Quantum Technologies Initiative (SA QuTI) was formally launched by the South African Department of Science and Innovation with the first seed funding released in September 2021. SA QuTI...

We study the conditions under which a semigroup is obtained upon convex combinations of channels. In particular, we study the set of Pauli and generalized Pauli channels. Counter-intuitively, we find that the input channels that are all invertible cannot produce a semigroup. Specifically, mixing only semigroups cannot produce a semigroup.

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral th...

We explain how parametrised quantum circuits—quantum algorithms that are popular in near-term quantum computing—can be used as machine learning models, and review techniques to analyse and train such quantum models in a deep-learning fashion, including measures of expressivity and trainability, as well as parameter-shift rules.

This chapter introduces the foundations of quantum computing, first giving an intuitive idea of how its abstract linear algebra formalism relates to conventional probability theory, and then presenting the apparatus of states, observables and unitary evolutions in more detail. We introduce the building blocks of quantum circuits and walk through so...

In this chapter, we explore two approaches that link quantum machine learning to the Ising model. First, we will look at probabilistic models that emerge when we take a Boltzmann machine and add quantum dynamics to the underlying physical system. We then discuss proposals for quantum machine learning with quantum annealers, which are devices that s...

In this last chapter, we summarise some of the results and efforts to understand the potential power of quantum machine learning algorithms. We will first have a closer look at different criteria for a quantum advantage, and then consider data mining on coherent or “quantum data”. We finally summarise some future perspectives for quantum machine le...

Here, we focus on more traditional approaches to quantum machine learning which try to speed up classical routines by making use of fault-tolerant quantum computers. We discuss quantum machine learning algorithms based on linear algebra subroutines such as matrix inversion, and those based on amplitude amplification or Grover search. We will then h...

This chapter presents one of the most important parts of quantum machine learning algorithms, namely strategies with which a single data point, or sometimes an entire dataset, can be encoded into quantum states. We present quantum routines for this task, discuss their runtimes and review their interpretation as feature maps known in classical machi...

This chapter is an adapted version of the preprint article “Quantum machine learning models are kernel methods” by Maria Schuld [1].

We explain the foundations of supervised and unsupervised machine learning, including the central ingredients of data, models and cost functions, as well as the basic concepts of training, regularisation and generalisation. A number of important models—such as linear models, neural networks, probabilistic graphical models and kernel methods—are int...

The rapid identification and isolation of infected individuals remains a key strategy for controlling the spread of SARS-CoV-2. Frequent testing of populations to detect infection early in asymptomatic or presymptomatic individuals can be a powerful tool for intercepting transmission, especially when the viral prevalence is low. However, RT-PCR tes...

Noisy Intermediate Scale Quantum (NISQ) devices have been proposed as a versatile tool for simulating open quantum systems. Recently, the use of NISQ devices as simulators for non-Markovian open quantum systems has helped verify the current descriptions of non-Markovianity in quantum physics. In this work, convex mixtures of channels are simulated...

Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an exponential speed-up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, wh...

The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world problems is the cost of loading classical data to a quantum state. Several quantum circuit-based methods have b...

The rst cases of a new coronavirus (SARS-CoV-2) were identi ed toward the end of 2019 in Wuhan, China. Over the following months, this virus spread to everywhere in the world. By now no country has been spared the devastation from the loss of lives from the disease (Covid-19) and the economic and social impacts of responses to mitigate the impact o...

We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is g...

Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost funct...

Variational hybrid quantum classical algorithms are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that...

This work presents fabricated silica microstructured optical fiber with special equiangular spiral six-ray geometry, an outer diameter of 125 µm (that corresponds to conventional commercially available telecommunication optical fibers of ratified ITU-T recommendations), and induced chirality with twisting of 200 revolutions per minute (or e.g., und...

The rapid identification and isolation of infected individuals remains a key strategy for controlling the spread of SARS-CoV-2. Frequent testing of populations to detect infection early in asymptomatic or presymptomatic individuals can be a powerful tool for intercepting transmission, especially when the viral prevalence is low. However, RT-PCR tes...

To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for bin...

Continued uncontrolled transmission of the severe acute respiratory syndrome-related coronavirus 2 (SARS-CoV-2) in many parts of the world is creating the conditions for significant virus evolution1,2. Here, we describe a new SARS-CoV-2 lineage (501Y.V2) characterised by eight lineage-defining mutations in the spike protein, including three at impo...

Some of the oldest and most important applications of thermodynamics are operations of refrigeration as well as production of useful energy. Part of the efforts to understand and develop thermodynamics in the quantum regime have been focusing on harnessing quantum effects to such operations. In this review, we present the recent developments regard...

Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O ( N ) to load an N -dimensi...

The first severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in South Africa was identified on 5 March 2020, and by 26 March the country was in full lockdown (Oxford stringency index of 90)¹. Despite the early response, by November 2020, over 785,000 people in South Africa were infected, which accounted for approximately 50% of...

Do quantum effects play a role in consciousness? Or are the two areas being linked simply because they are both difficult to understand? Betony Adams and Francesco Petruccione explore this developing, and contentious, field of quantum biophysics

This book offers an introduction into quantum machine learning research, covering approaches that range from "near-term" to fault-tolerant quantum machine learning algorithms, and from theoretical to practical techniques that help us understand how quantum computers can learn from data. Among the topics discussed are parameterized quantum circuits,...

Continued uncontrolled transmission of the severe acute respiratory syndrome-related coronavirus 2 (SARS-CoV-2) in many parts of the world is creating the conditions for significant virus evolution. Here, we describe a new SARS-CoV-2 lineage (501Y.V2) characterised by eight lineage-defining mutations in the spike protein, including three at importa...

The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arb...

We study the memory property of the channels obtained by convex combinations of Markovian channels that are not necessarily quantum dynamical semigroups (QDSs). In particular, we characterize the geometry of the region of (non-)Markovian channels obtained by the convex combination of the three Pauli channels, as a function of deviation from the sem...

Objectives To investigate introduction and understand the early transmission dynamics of the SARS-CoV-2 in South-Africa, we formed the Network for Genomic Surveillance in South Africa (NGS-SA). Design Here, we present the first results of this effort, which is a molecular epidemiological study of the first twenty-one SARS-CoV-2 whole genomes sampl...

The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. Here we show that for degenerate (or near-degenerate) quantum systems th...

We develop an exact framework for describing the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, whic...

The development of a quantum network relies on the advances of hybrid systems which include ground-to-ground communication. However, the atmospheric turbulence of the environment poses a severe challenge to the optical quantum link. In this paper, we outline a theoretical and experimental investigation of the influence of atmospheric turbulence on...