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In recent years, hole-spin qubits based on semiconductor quantum dots have advanced at a rapid pace. We first review the main potential advantages of these hole-spin qubits with respect to their electron-spin counterparts and give a general theoretical framework describing them. The basic features of spin–orbit coupling and hyperfine interaction in the valence band are discussed, together with consequences on coherence and spin manipulation. In the second part of the article, we provide a survey of experimental realizations, which spans a relatively broad spectrum of devices based on GaAs, Si and Si/Ge heterostructures. We conclude with a brief outlook.

Understanding the hyperfine and spin-orbit interactions is important for e.g. quantum information processing with spin qubits. In this thesis, we investigate these interactions in various semiconductor nanostructures. While the methods developed here have been applied to specific nanostructures, they can be generalized to understand interactions (hyperfine, spin-orbit, and potentially others) in other systems and/or materials.This thesis includes an introductory chapter where we derive the hyperfine and spin-orbit interactions from the Dirac equation and discuss the main theoretical tools used throughout the text, k · p theory and density-functional theory. In the succeeding chapter, we calculate the hyperfine couplings for electrons and holes in GaAs and silicon through first-principles density-functional theory. Our results are consistent with Knight-shift measurements for electrons. For holes, experimental results are still limited and a direct comparison to experiment is not possible. In the third chapter, we relate the dynamics of a hole spin after a spin echo pulse sequence to the hole hyperfine coupling. In particular, we demonstrate how the hole hyperfine couplings can be determined from measurements of hole spin echo envelope modulations. We apply this concept to a boron acceptor in silicon, where the value of the hyperfine coupling remains an open question. We show that direct measurements of boron-acceptor hyperfine couplings can be obtained by modifying the direction of the applied magnetic field in existing experiments. Finally, in the fourth chapter, we extend k · p theory beyond the envelope function approximation. In doing so, we find a novel 'dipolar' heavy-hole spin-orbit coupling in III-V semiconductor asymmetric quantum wells. This spin-orbit coupling is parametrized by the heavy-hole/light-hole electric-dipole matrix element. We calculate this matrix element and show that in GaAs, the dipolar spin-orbit coupling can represent a significant portion of the linear Dresselhaus spin-orbit coupling.

An accurate description of the hyperfine interaction between electron spins and nuclear spins is crucial for understanding spin dynamics in semiconductor nanostructures. In this thesis, we study the hyperfine interactions in III-V semiconductors and Si. We use the Elk code to perform a density-functional-theory calculation of the contact hyperfine parameter for Si and the Ga and As sites in GaAs. Our result differs from the experimental values found with NMR by less than 3%, while the previous theoretical result differs from the same experimental values by more than 10%. To the best of our knowledge, the calculations in this thesis give the first theoretical estimate of the contact hyperfine coupling in GaAs derived from first principles. Additionally, we show how to go beyond usual methods to accurately determine hyperfine tensors in strongly spin-orbit coupled materials. We achieve this by combining density-functional theory and group theory, accounting for the full coupled spin-orbit structure of the associated single-particle states. Finally, we show how to verify the predicted electronic structure experimentally spectroscopically, by determining a set of allowed electric-dipole transitions.

Electron shuttling is emerging as a key enabler of scalable silicon spin-qubit quantum computing, but fidelities are limited by atomistic disorder. We introduce a multiscale simulation framework combining time-dependent finite-element electrostatics and atomistic tight-binding to capture the impact of random alloying and interface roughness on the valley splitting and phase of shuttled electrons. We find that shuttling fidelities are strongly suppressed by interface roughness, with a sharp anomaly near the atomic-layer scale, setting quantitative guidelines to realize scalable shuttling.

We propose DIPS Difficulty-based Incentives for Problem Solving), a simple modification of the Bitcoin proof-of-work algorithm that rewards blockchain miners for solving optimization problems of scientific interest. The result is a blockchain which redirects some of the computational resources invested in hash-based mining towards scientific computation, effectively reducing the amount of energy `wasted' on mining. DIPS builds the solving incentive directly in the proof-of-work by providing a reduction in block hashing difficulty when optimization improvements are found. A key advantage of this scheme is that decentralization is preserved and no additional protocol layers are required on top of the standard blockchain. We study two incentivization schemes and provide simulation results showing that DIPS is able to reduce the amount of hash-power used in the network while generating solutions to optimization problems.

In recent years, hole-spin qubits based on semiconductor quantum dots have advanced at a rapid pace. We first review the main potential advantages of these hole-spin qubits with respect to their electron-spin counterparts, and give a general theoretical framework describing them. The basic features of spin-orbit coupling and hyperfine interaction in the valence band are discussed, together with consequences on coherence and spin manipulation. In the second part of the article we provide a survey of experimental realizations, which spans a relatively broad spectrum of devices based on GaAs, Si, or Si/Ge heterostructures. We conclude with a brief outlook.

Accurate band offsets are essential for predictive continuum modeling of nanostructures such as quantum wells and quantum dots formed in strained Si/Si1-xGex and Ge/Si1-xGex heterostructures. Experimental offset data for these systems remain sparse away from endpoint compositions, making composition-dependent design difficult. We use atomistic first-principles density functional theory to compute valence- and conduction-band offsets across the full range 0 <= x <= 1. Random alloying is treated with special quasirandom structures, interface lineup terms are extracted from macroscopically averaged local Kohn-Sham potentials in thick periodic superlattices, valence-band spin-orbit coupling is included through species-resolved Mulliken weights, and conduction-band edges are refined using the screened hybrid Heyd-Scuseria-Ernzerhof functional. The resulting offsets show pronounced composition nonlinearity beyond the linear models explored in previous works, agree with experimental benchmarks, and reproduce the high-Ge slope change in the relaxed-alloy band gap. Analytic fitting expressions are provided for direct use in simulations, facilitating practical design of modern quantum technology devices.

Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory (DFT) and \\(k\\) theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-shift measurements performed on GaAs quantum wells and are roughly consistent with prior estimates extrapolated from measurements on InSb. We find that a combination of DFT and \\(k\\) theory is necessary to accurately determine the contact hyperfine interaction for electrons at a conduction-band minimum in silicon that is consistent with bulk Knight-shift measurements. For hole spins in GaAs, the overall magnitude of the hyperfine couplings we find from DFT is consistent with previous theory based on free-atom properties, and with heavy-hole Overhauser shifts measured in GaAs (and InGaAs) quantum dots. In addition, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins is stronger and almost purely Ising-like, while the (weaker) coupling to the Ga nuclear spins has significant non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strength of the hyperfine interaction in the valence band is comparable to that in the conduction band and that the hyperfine tensors are highly anisotropic (Ising-like) in the heavy-hole subspace. These results suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence (\\(T_2^\\)) times recently measured for heavy holes in silicon quantum dots.

RNA 3D motifs are recurrent substructures, modelled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and remains a key challenge in the field of RNA structural biology and network analysis. State of the art methods solve special cases of the motif problem by constraining the structural variability in occurrences of a motif, and narrowing the substructure search space. Here, we relax these constraints by posing the motif finding problem as a graph representation learning and clustering task. This framing takes advantage of the continuous nature of graph representations to model the flexibility and variability of RNA motifs in an efficient manner. We propose a set of node similarity functions, clustering methods, and motif construction algorithms to recover flexible RNA motifs. Our tool, VeRNAl can be easily customized by users to desired levels of motif flexibility, abundance and size. We show that VeRNAl is able to retrieve and expand known classes of motifs, as well as to propose novel motifs.

In the envelope-function approximation, interband transitions produced by electric fields are neglected. However, electric fields may lead to a spatially local (\\(k\\)-independent) coupling of band (internal, pseudospin) degrees of freedom. Such a coupling exists between heavy-hole and light-hole (pseudo-)spin states for holes in III-V semiconductors, such as GaAs, or in group IV semiconductors (germanium, silicon, ...) with broken inversion symmetry. Here, we calculate the electric-dipole (pseudospin-electric) coupling for holes in GaAs from first principles. We find a transition dipole of \\(0.5\\) debye, a significant fraction of that for the hydrogen-atom \\(1s2p\\) transition. In addition, we derive the Dresselhaus spin-orbit coupling that is generated by this transition dipole for heavy holes in a triangular quantum well. A quantitative microscopic description of this pseudospin-electric coupling may be important for understanding the origin of spin splitting in quantum wells, spin coherence/relaxation (\\(T_2^*/T_1\\)) times, spin-electric coupling for cavity-QED, electric-dipole spin resonance, and spin non-conserving tunneling in double quantum dot systems.