Quantum information has the potential to revolutionize the way we store, process, transfer and acquire information [1,14,15,21,37]. In particular, quantum information offers exciting new approaches to secure communication, computation and sensing. However, in order to realize such technologies, we must first understand the effect that environmental noise has on a quantum system. This dissertation builds upon recent studies that have explored the underlying structure of quantum information and the effects of qubit channels in quantum communication protocols. This work is divided into five main chapters, with Chapter 1 being a brief introduction to quantum information. We then begin Chapter 2 by defining the error function for our qubit communication protocols. From there we explore the properties of our error functions and the topological space that they form. In Chapter 3 we consider the newly patented process Adaptive Quantum Information Processing, patent number US9838141 B2; originally outlined by Martin in [23]. We restate the adaptive scheme and exemplify its application through the Prepare and Send Protocol and Quantum Key Distribution. Applying our results from Chapter 2, we obtain an expression for the adaptability of unital channels in these two protocols and classify the channels that admit the most improvement. We dedicate Chapter 4 to the derivation of gravitational noise, and show that in certain circumstances gravity results in a channel that can be maximally improved in Adaptive QKD [3,14,16]. Lastly, we study the set of error functions through the lens of domain theory. Domain theory is a subset of mathematics that was developed in order to rigorously formalize computations. The first four chapters are all consequences of past discoveries in the mathematical structure of quantum channels. In Chapter 5 we characterize the set of error functions through domain theory, extending the mathematical foundations of quantum information. [12,18,20, 22, 23,25].

Quantum mechanical frustration (QMF) in magnetic materials has become a pivotal ingredient in discovering intriguing properties of materials. The quantum spin liquid (QSL) state is a prime consequence of frustration in which spin fluctuations persist to absolute zero temperature. This orderless state is not characterized by symmetry breaking and guarantees an infinite degeneracy in its ground state. The quest to realize such nontrivial ground states in view of spin correlation, elementary excitation, topology, and geometry requires convincing experimental evidence. QMF is often manifested in unique lattice systems, such as spin-1/2 hyper-honeycomb lattices with strong spin-orbit coupling and geometrically frustrated Kagome lattices. Metal-organic frameworks (MOFs) that comprise metal ions with organic linkers via coordinate bonds have recently been proposed to realize the QSL ground state. Owing to the vast versatility of constituent's, the copper-oxalate MOF, [(C2H5)3NH]2Cu2(C2O4)3, unfolds a new avenue for us to realize unusual magnetic phases. To investigate the exotic ground state, we synthesized single crystals of [(C2H5)3NH]2Cu2(C2O4)3 and measured their thermodynamic properties. Our low-temperature and high-magnetic-field heat-capacity (Cp) measurements corroborate an exotic but rich ground state in [(C2H5)3NH]2Cu2(C2O4)3. A finite linear-in temperature Cp term with no indication of any thermal anomaly was observed at low temperature in zero field, indicating the absence of magnetic order and the presence of gapless spinon excitations despite the Mott insulating phase. Applied magnetic fields suppress the low-temperature Cp and drive the system into a gapped phase. The field-induced gap is described by the sine-Gorden model for quasi-one-dimensional antiferromagnetic Heisenberg chains, originating from anisotropic magnetic exchange interactions due to the Jahn-Teller distortion. Kagome lattices are archetypes of potential QSL, superconducting, Chern insulating states due to flat energy bands, Dirac fermions, and van Hove singularities in its electronic band structure. Sc3Mn3Al7Si5 is a transition metal compound with a hexagonal structure in which magnetic Mn atoms form kagome nets and does not show magnetic order down to 2 K, suggestive of a possible itinerant QSL. In this dissertation, to elucidate its exotic ground state, we synthesized single crystals of Sc3Mn3Al7Si5 and measured magnetoresistance, Cp, soft point contact spectroscopy, and torque magnetometry at low temperatures and high magnetic fields. Our experimental results suggest that the unusual ground state is induced by dispersionless energy bands induced by strong electron correlations. Our findings through distinct states of matter spanning from Mott insulators to itinerant metals will provide new insights to characterize the ground state in novel quantum magnets.

Because of the unique electronic properties, intriguing novel phenomena, and potentiality in quantum device applications, the quantum materials with non-trivial band structures have enticed a bulk of research works over the last two decades. The experimental discovery of the three-dimensional topological insulators (TIs) - bulk insulators with surface conduction via spin-polarized electrons - kicked off the flurry of research interests towards such materials, which resulted in the experimental discovery of new topological phases of matter beyond TIs. The topological semimetallic phase in Dirac, Weyl, and nodal-line semimetals is an example, where the classification depends on the dimensionality, degeneracy, and symmetry protection of the bulk band touching. The field of topology has extended to the materials that possess non-trivial topological states at/along lower-dimensional regions of the crystals as well. A class of such materials is the higher-order topological insulator in which both bulk and surface are insulating, but symmetry-protected conducting channels can appear along the hinges or corners of the crystal. Recently, significant focus has been given to the study of the interplay among various physical parameters such as topology, geometry, magnetism, and electronic correlation. Kagome systems have emerged as fertile ground to study the interaction among such parameters in a material class. Charge density wave (CDW) order in quantum materials remains an important topic of study given its co-existence or competence with superconductivity and magnetic ordering. In this dissertation, we study the electronic structure of quantum material systems beyond TIs, particularly the lanthanide element-based and correlated systems, by utilizing state-of-art angle-resolved photoemission spectroscopy with collaborative support from first-principles calculations and transport and magnetic measurements. The lanthanide-based materials are interesting because of the possible magnetic ordering and electron correlations that the lanthanide 4f electrons may bring into the table. Our work on the Europium-based antiferromagnetic material EuIn2As2 highlights this material as a promising ground to study the interplay of different kinds of topological orders including higher-order topology with magnetism. Temperature-dependent measurements reveal a band splitting near the Fermi level below the antiferromagnetic transition. Another study on the samarium- and neodymium-based materials SmSbTe and NdSbTe shows the presence of multiple nodal lines that remain gapless even in the presence of spin-orbit coupling. We also studied a van der Waals kagome semiconductor Nb3I8, where we observed flat and weakly dispersing bands in its electronic structure. These bands are observed to be sensitive to light polarization and originate from the breathing kagome plane of niobium atoms. Next, our study in Gadolinium-based van der Waals material GdTe3 shows the presence of a momentum-dependent CDW gap and the presence of antiferromagnetic ordering that could prove important to study the interaction of CDW and magnetic orders in this material. Overall, the works under this dissertation reveal the electronic properties in correlated systems that range from insulator to metals/semimetals and from topological insulator to topological semimetals, kagome semiconductor, and CDW material.

Quantum information processing has the potential of implementing faster algorithms for numerous problems, communicating with more secure channels, and performing higher precision sensing compared to classical methods. Recent experimental technology advancement has brought us a promising future of harnessing such quantum advantage. Yet, quantum engineering entails wise control and strategy under the current noisy intermediate-scale quantum era. Developing robust and efficient approaches to manipulating quantum systems based on constrained and limited resources is imperative. This dissertation focuses on two major topics theoretically. In the first part, this work present how to conceive robust quantum control on matter-based qubits with a geometric approach. We have proposed the method of designing noise robust control pulses suitable for practical devices by combining spatial curves, filter functions, and machine learning. In the second part, this work stresses the topic of photonic multipartite entangled graph states. An improved protocol of generating arbitrary graph states is introduced. We show that one can efficiently find the deterministic photon emission circuit with minimal overhead on the number of quantum emitters. / Doctor of Philosophy / As classical information technology has revolutionized our modern world, theoretically, quantum information technology outperforms its classical counterpart and has the potential to achieve further progress. Utilizing the non-classical features unique to quantum physics, one can build quantum computers capable of accelerating data searching, breaking most current cryptographic systems, simulating molecular-level dynamics, and enhancing artificial intelligence. Furthermore, one can use the entangled quantum resource to establish secure communication or increase the capacity of the classical communication channel. Although numerous applications may reshape our daily life, industry, and scientific research, the mastery of quantum information technology is still challenging since quantum systems are more susceptible to noise than classical systems. Unlike classical signal processing, reading out an unknown quantum state will irreversibly change the state, while copying an unknown quantum state is strictly infeasible. Therefore, detecting and correcting errors from quantum data can be tricky. Depending on different platforms, establishing a complicated quantum network can also be constrained by the near-term noisy device. Mainly, what this work attempts to innovate are the previous results on quantum dynamical control pulse design and the protocol of entangling photons. For the former, the goal of this work is to develop control pulses that can decouple coherent noise in the quantum computer when manipulating the quantum information. This work combines the mathematical framework of spatial curve quantum control with filter functions and machine learning to yield new outcomes. The flexibility of this framework enables us to give neat mathematical analysis and obtain satisfying control pulses design for physical implementations through numerical experiments. For the latter, this work studies a promising scheme of deterministically producing an entangling photonic quantum network, where quantum emitters are treated as the media to build up quantum non-locality. Achieving this emission process in the real world is desirable for distributing entangled quantum resources and realizing measurement-based quantum computation. In this case, we analyze the emitter overhead needed to generate an entangling photonic resource state, specifically when sending photons back for interactions is inaccessible. At last, we propose an efficient algorithm for producing the generation protocol along with several practical examples whose overheads on quantum emitters number are strictly optimized.

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Quantum spin models are useful in many areas of physics, such as strongly correlated materials and quantum phase transitions, or, generally, quantum many-body systems. Most of the models of interest are not analytically solvable. Therefore they are often investigated using computational methods. However, spin models with frustrated interactions are not easily simulated numerically with existing methods, and more effective algorithms are needed. In this thesis, I will cover two areas of quantum spin research: 1. studies of several quantum spin models and 2. development of more efficient computational methods. The discussion of the computational methods and new algorithms is integrated with the physical properties of the models and new results obtained. I study the frustrated S=1/2 J1-J2 model Heisenberg model, the J-Q model, the Ising model with a transverse magnetic field, and a two-orbital spin model describing the magnetic properties of iron pnictides. I will discuss several computational algorithms, including a cluster variational method using mean-field boundary conditions, variational quantum Monte Carlo simulation with clusters-based wave functions, as well as a method I call "optilization" -- an algorithm constructed in order to accelerate the process of optimization with a large number of parameters. I apply it to matrix product states. / 2031-01-02

<p>Worldwide there are significant efforts to build networks that can distribute photonic entanglement, first with applications in communication, with a long-term vision of constructing fully connected quantum processing networks (QPN). We have constructed a network of atom-light interfaces, providing a scalable QPN platform by creating connected room-temperature qubit memories using dark-state polaritons (DSPs). Furthermore, we combined ideas from two leading elements of quantum information namely collective enhancement effects of atomic ensembles and Cavity-QED to create a unique network element that can add quantum processing abilities to this network. We built a dual connection node consisting of two moderate finesse Fabry-Perot cavities. The cavities are configured to form a cross-cavity layout and coupled to a cold atomic ensemble. The physical regime of interest is the non-limiting case between (i) low N with high cooperativity and (ii) free-space-high-N ensembles. Lastly, we have explored how to use light-matter interfaces to implement an analog simulator of relativistic quantum particles following Dirac and Jackiw-Rebbi model Hamiltonians. Combining this development with the cross-cavity node provides a pathway towards quantum simulation of more complex phenomena involving interacting many quantum relativistic particles.

<p> It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, &ndash;&gamma;, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction, we extract a finite topological term, &ndash;&gamma; , in the region of bond-strength parameter space corresponding to high geometrical frustration. Thus, we provide strong evidence for the existence of an exotic topologically ordered state and shed light on the nature of this model's strongly frustrated, and long controversial, intermediate phase.</p>

<p> Bose-Einstein condensates (BECs) are a recent addition to the portfolio of quantum materials some of which have profound commercial and military applications e.g., superconductors, superfluids and light emitting diodes. BECs exist in the lowest motional modes of a trap and have the lowest temperatures achieved by mankind. With full control over the shape of the trap the experimentalist may explore an extremely diverse set of Hamiltonians which may be altered mid-experiment. These properties are particularly suited for realizing novel quantum systems.</p><p> This thesis explores interaction-driven domain formation and the subsequent domain coarsening for two immiscible BEC components. Because quantum coherences associated with interactions in BECs can be derived from low energy scattering theory we compare our experimental results to both a careful simulation (performed by Brandon Anderson) and an analytical prediction. This result very carefully explores the question of how a metastable system relaxes at the extreme limit of low temperature.</p><p> We also explore spin-orbit coupling (SOC) of a BEC which links the linear and discrete momentum transferable by two counterpropagating ''Raman'' lasers that resonantly couple the ground electronic states of our BECs. SOC is used similarly in condensed matter systems to describe coupling between charge carrier spin and crystal momentum and is a necessary component of the quantum spin Hall effect and topological insulators.</p><p> SOC links the linear and discrete momentum transferable by two counterpropagating ''Raman'' lasers and a subset of the ground electronic states of our BEC. The phases of an effective 2-spin component spin-orbit coupling (SOC) in a spin-1 BEC are described in Lin et al. (2011). We measure the phase transition between two phases of a spin-1 BEC with SOC which cannot be mimicked by a spin-1/2 system. The order parameter that describes transitions between these two phases is insensitive to magnetic field fluctuations.</p><p> I also describe a realistic implementation of Rashba SOC. This type of SOC is expected to exhibit novel many-body phases [Stanescu et al. 2008, Sedrakyan et al. 2012, Hu et al. 2011].</p>

<p> This thesis describes the mechanisms by which organic surfactants, particularly thiophenols and phenyldithiocarbamates, reduce the confinement potential experienced by the exciton of semiconductor quantum dots (QDs). The reduction of the confinement potential is enabled by the creation of interfacial electronic states near the band edge of the QD upon ligand adsorption. In the case of thiophenols, we find that this ligand adsorbs in two distinct binding modes, (i) a tightly bound mode capable of exciton delocalization, and (ii) a more weakly bound mode that has no discernable effect on exciton confinement. Both the adsorption constant and reduction in confinement potential are tunable by para substitution and are generally anticorrelated. For tightly bound thiophenols and other moderately delocalizing ligands, the degree of delocalization induced in the QD is approximately linearly proportional to the fractional surface area occupied by the ligand for all sizes of QDs. In the case of phenyldithiocarbamates, the reduction in the confinement potential is much greater, and ligand adjacency must be accounted for to model exciton delocalization. We find that at high surface coverages, exciton delocalization by phenyldithiocarbamates and other highly delocalizing ligands is dominated by ligand packing effects. Finally, we construct a database of electronic structure calculations on organic molecules and propose an algorithm that combines experimental and computational screening to find novel delocalizing ligands.</p>

<p> The continuous improvement of modern electronics has been sustained by the scaling of silicon based MOSFETs over the last 4 decades. However, the frequency of the processors has been saturated since 2005 when the power dissipation in CPUs reached its cooling limit (100W/cm2). The thermionic emission in MOSFET limits the SS to 60 mV/dec, which prevents CMOS from further reducing the power consumption. Tunnel-FETs (TFETs) were proposed to solve this problem by removing thermal emission. Although, <i>SS</i> &lt; 60 has been demonstrated experimentally in conventional TFETs, they suffer from low ON current, orders of magnitude lower than MOSFETs. Hence achieving high ON-current and performance requires novel device structures. </p><p> Low dimensional materials have unique features which can be used to solve the challenges of TFETs. In this work, several novel TFETs based on low dimensional materials (new channel material candidates such as Bilayer graphene, Black Phosphorous and interlayer TFETs based by stacking TMD materials) have been proposed to solve the low ON current issue. Their device performance and the scalability have been studied by means of atomistic quantum transport simulations. </p><p>