We begin this dissertation by studying noise correlations in superconducting heterostructures of various geometries. In recent years there has been a resurgence of interest in the nonlocal transport properties of superconducting heterostructures due to the possibility of their serving as a source of electronic entanglement in solid state quantum information processors. Devices designed for this purpose are called Cooper pair splitting devices. The utility of these devices as entanglement sources is known to have connections to the positivity of noise cross correlations in spatially separated leads. In Chapter 1 we outline the theoretical prerequisites for this work, outlining the scattering theory framework based on the Bogoliubov-de Gennes equations we adopt. Within this framework we apply a methodology first introduced by Demers and by Blonder, Tinkham and Klapwijk (BTK) in the early 1980s to find the scattering matrix for our superconducting structures. The current, local and nonlocal shot noise can all be expressed in terms of the underlying scattering processes. This framework allows us to investigate the behavior of the current and noise correlations in the structure as we change the geometry and other key system parameters such as the system size, superconducting phase difference and temperature. We also introduce the Andreev approximation, a commonly used approximation which simplifies the scattering theory for superconducting heterostructures. In Chapter 2, we study the local and nonlocal shot noise in a quasi-1D normal-superconducting-normal (NSN) geometry using material parameters relevant to high-T [subscript c] superconductivity. The scattering and shot noise distributions are studied in the short, intermediate and long system size limits, allowing us to examine the qualitative differences in these three parameter regimes. This allows us to, for example, identify the signatures of over-the-gap geometric resonances in the shot noise distributions that appear in the long system size limit. We also break the nonlocal shot noise distributions down further and study the individual contributions to the nonlocal shot due to particle-particle, hole-hole and particle-hole scattering processes. In Chapter 3, we extend our investigation of superconducting heterostructures to the more complicated NSNSN geometry. A novel feature introduced in the geometry is the presence of subgap quasibound states, which show up as resonances in the scattering matrix. We show that these quasibound states dramatically impact the nonlocal shot noise distributions in the system. At energies near the quasibound states the dominant transmission channel through the system is a process called particle-hole transmission, which results in sharp positive peaks in the nonlocal shot noise distribution of the system. The behavior of the nonlocal noise correlations as we change the size of the superconducting and normal regions is investigated and it is found that there is a "sweet spot'' with respect to the size of the superconducting regions that maximizes the positivity of the nonlocal noise distributions as well as a periodic-like behavior in the positivity of the noise distributions with respect to the normal region size. The results of the full scattering theory for the NSNSN geometry are compared to the results obtained using the Andreev approximation, where we find that the Andreev approximation breaks down at energies close to the quasibound state energies. In the second half of this dissertation we focus on work related to the development of a prototype special-purpose quantum circuit simulation device based on commercial off-the-shelf high-speed analog signal processing hardware. In Chapter 4 we introduce the embedding scheme used to represent quantum states and quantum gates in the frequency domain of a classical analog voltage signal. Experimental results are presented from an early two-qubit prototype device for the fidelity of the state generation and gate application circuits. In Chapter 5, a more in-depth investigation into the modeling of classical errors within our signal processing based simulation method is performed in terms of the effects this noise has on the results of the quantum computation being simulatied. It is shown, for example, that additive white gaussian noise (AWGN) in our system has the same effect as applying a depolarizing channel to the qubits in the simulation. We then perform a simulation of a simple quantum error correction (QEC) protocol using the device and show that, even in the presence of classical noise in the simulation hardware, an overall enhancement in the performance of gate operations as a result of applying QEC is observed.
We begin this dissertation by studying noise correlations in superconducting heterostructures of various geometries. In recent years there has been a resurgence of interest in the nonlocal transport properties of superconducting heterostructures due to the possibility of their serving as a source of electronic entanglement in solid state quantum information processors. Devices designed for this purpose are called Cooper pair splitting devices. The utility of these devices as entanglement sources is known to have connections to the positivity of noise cross correlations in spatially separated leads. In Chapter 1 we outline the theoretical prerequisites for this work, outlining the scattering theory framework based on the Bogoliubov-de Gennes equations we adopt. Within this framework we apply a methodology first introduced by Demers and by Blonder, Tinkham and Klapwijk (BTK) in the early 1980s to find the scattering matrix for our superconducting structures. The current, local and nonlocal shot noise can all be expressed in terms of the underlying scattering processes. This framework allows us to investigate the behavior of the current and noise correlations in the structure as we change the geometry and other key system parameters such as the system size, superconducting phase difference and temperature. We also introduce the Andreev approximation, a commonly used approximation which simplifies the scattering theory for superconducting heterostructures. In Chapter 2, we study the local and nonlocal shot noise in a quasi-1D normal-superconducting-normal (NSN) geometry using material parameters relevant to high-T [subscript c] superconductivity. The scattering and shot noise distributions are studied in the short, intermediate and long system size limits, allowing us to examine the qualitative differences in these three parameter regimes. This allows us to, for example, identify the signatures of over-the-gap geometric resonances in the shot noise distributions that appear in the long system size limit. We also break the nonlocal shot noise distributions down further and study the individual contributions to the nonlocal shot due to particle-particle, hole-hole and particle-hole scattering processes. In Chapter 3, we extend our investigation of superconducting heterostructures to the more complicated NSNSN geometry. A novel feature introduced in the geometry is the presence of subgap quasibound states, which show up as resonances in the scattering matrix. We show that these quasibound states dramatically impact the nonlocal shot noise distributions in the system. At energies near the quasibound states the dominant transmission channel through the system is a process called particle-hole transmission, which results in sharp positive peaks in the nonlocal shot noise distribution of the system. The behavior of the nonlocal noise correlations as we change the size of the superconducting and normal regions is investigated and it is found that there is a "sweet spot'' with respect to the size of the superconducting regions that maximizes the positivity of the nonlocal noise distributions as well as a periodic-like behavior in the positivity of the noise distributions with respect to the normal region size. The results of the full scattering theory for the NSNSN geometry are compared to the results obtained using the Andreev approximation, where we find that the Andreev approximation breaks down at energies close to the quasibound state energies. In the second half of this dissertation we focus on work related to the development of a prototype special-purpose quantum circuit simulation device based on commercial off-the-shelf high-speed analog signal processing hardware. In Chapter 4 we introduce the embedding scheme used to represent quantum states and quantum gates in the frequency domain of a classical analog voltage signal. Experimental results are presented from an early two-qubit prototype device for the fidelity of the state generation and gate application circuits. In Chapter 5, a more in-depth investigation into the modeling of classical errors within our signal processing based simulation method is performed in terms of the effects this noise has on the results of the quantum computation being simulatied. It is shown, for example, that additive white gaussian noise (AWGN) in our system has the same effect as applying a depolarizing channel to the qubits in the simulation. We then perform a simulation of a simple quantum error correction (QEC) protocol using the device and show that, even in the presence of classical noise in the simulation hardware, an overall enhancement in the performance of gate operations as a result of applying QEC is observed.
Recent experiments on Cooper pair splitters using superconductor-quantum dot hybrids have embarked on creating entanglement in the solid-state, by engineering the sub-gap processes in the superconducting region. Using the thermoelectric Cooper pair splitter setup [Nat. Comm., 12, 21, (2021)] as a prototype, we present a comprehensive analysis of the fundamental components of the observed transport signal, aiming to critically clarify the operating regimes and confirm the nonlocal and nonclassical nature of correlations arising from crossed Andreev processes. By making a nexus with quantum discord, we identify operating points of nonlocal quantum correlations in the CPS device—information that cannot be extracted from the transport signal alone. A notable consequence of our analysis is the finding that contact-induced level broadening of the quantum dot’s discrete energy spectrum, along with its hybridization with the superconducting segment, can lead to shifted resonances in the crossed Andreev process as well as a parity reversal in the thermoelectric current. Our work thereby provides detailed insights into the gate voltage control of the quantum correlations in superconducting-hybrid Cooper pair splitters, revealing new avenues for harnessing quantum correlations in solid-state systems.
Superconducting circuits are a leading platform for quantum computation and quantum simulation. Interactions are typically mediated by pairwise coupling elements between nearest neighbor qubits. The development of tunable couplers has been essential to achieving high fidelity entangling gates alongside high fidelity single qubit gates in quantum processors. In quantum simulators, tunable coupling allows flexibility in emulating different systems and the exploration of different parameter regimes of those models in a single physical device. Distributed element circuitry has enabled long range coupling and leveraging of interference effects and spatial mode variations to enhance device performance. In this thesis I will discuss work towards developing a distributed element tunable coupling circuit: a transmission line cavity terminated by SQUIDs, which serve as flux tunable impedances, at either boundary. With this device we hope to integrate the dynamic programmability of interactions mediated by a tunable coupler with the long-range, multi-qubit coupling enabled by distributed transmission lines in a single system. We experimentally demonstrate the core functionality, including tunability of the coupling rates, programmability of the connectivity graph, and parallel operation via multiplexing. Additionally, we utilize this device to explore photon blockade effects in the Tavis-Cummings Model, highlighting the value of tunability and controllability when simulating novel light-matter interactions in highly connected systems. These results contribute to ongoing research towards designing, calibrating, and operating highly connected superconducting circuit systems. Devices with high connectivity enable more efficient circuit compilation and are useful as quantum routers in quantum networks. In recent years, understanding the role of connectivity in quantum error correction has emerged as an important research focus. There is ongoing work evaluating the tradeoff between performance and connectivity in real devices. The development of coupling architectures that enable denser and/or longer range connectivity will play a critical role in optimizing this tradeoff.
In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices.
This is a course on noise which covers some of the scattering theory for normal metals, Hanbury Brown and Twiss analogs for noise correlations with electrons, noise correlations in superconducting/normal metal junctions. Entanglement in such NS systems is described with a criterion for violating Bell inegalities. The last section is devoted to the perturbative derivation of noise in a particular one dimensional correlated electron system (Luttinger liquid): edge states in the fractional quantum Hall effect, where the comparison of the quasiparticle tunneling current and noise allow to identidy the fractional charge of quasiparticles.
New strategies to generate and to detect spin-entangled pairs of electrons in mesoscopic solid-state heterostructures are proposed. A bilayer-graphene device is designed in which Cooper pairs from an s-wave superconductor are injected into an electrostatically-defined topological channel. Due to a particular band structure, two electrons of a Cooper pair propagate in opposite directions and are hence spatially separated if atomic-scale defects are sparse. Neither energy filtering nor Coulomb repulsion are required. The device can be interpreted as a normal/superconducting/normal junction, in which emission of nonlocal singlets is equivalent to local Andreev reflection, in contrast to the widespread identification of Cooper pair splitting with crossed Andreev reflection. To detect entanglement, the Josephson current through two parallel single-level quantum dots is investigated at all occupations. Combining exact diagonalization and perturbation theory, signatures of nonlocal Cooper pair transport are identified in the critical current, a macroscopic quantity. The model reproduces recent experimental observations and predicts a nonlocal triplet ground state on the quantum dots due to a tunable superconductor-mediated exchange coupling, which, too, is visible in the critical current exactly if nonlocal Cooper pairs are transported. Entanglement detection is pursued, too, by converting spin-entangled Cooper pairs into polarization-entangled photons, which are subsequently probed by a Bell-type measurement. A closed emission cycle is constructed, such that no correlations between the photons and the electrons remain, which are detrimental for entanglement transfer. Inevitable side channels and imperfections are identified and accounted for by a particular measurement protocol. Furthermore, it is discussed how spin-charge separation can be used to extract signatures of nonlocal spin singlets from the average current through an electronic beam splitter. This complements a known mechanism based on exchange statistics by which only the more difficult-to-access noise is sensitive for entanglement. The device can be realized by two crossed nanowires or by quantum-Hall edge states in Corbino geometry. The thesis also contains a review on entanglement and on recent theoretical and experimental progress in solid-state systems towards entanglement detection and generation, focusing on Cooper pair splitting.
Spintronic technologies require efficient generation and control of spin-polarized currents. Conventional ferromagnet-based methods suffer from sensitivity to external magnetic fields. Andreev reflection spectroscopy is vital for measuring spin polarization and superconducting gaps, yet prevailing theories assume isotropic interface scattering. This neglects ubiquitous anisotropy in heterostructures, causing misinterpretation of material properties. To resolve this, we develop a generalized model incorporating spin-dependent anisotropic scattering. Introducing distinct interface barriers for spin-up and spin-down electrons extends both the Blonder-Tinkham-Klapwijk formalism and the Chen-Tesanovic-Chien extension. This unified framework describes transport from normal metals to half-metals. Solving the Bogoliubov-de Gennes equations with modified boundary conditions yields current formulae with a transmission probability judgment function identifying dominant spin channels. In non-magnetic metals, interfacial anisotropy generates sizable spin-polarized currents via transmission spin filtering, suppressing Andreev reflection and reducing sub-gap conductance. For positively polarized ferromagnets, anisotropy nonlinearly modulates polarization, enhancing Andreev reflection to a threshold before suppression. Negatively polarized materials exhibit inverse spectra, enabling unambiguous polarization sign determination via conductance comparisons. Epitaxial Co film measurements validate the model, resolving subtle anisotropies. This refines Andreev spectrum interpretation and supports interference-resistant spin sources using non-magnetic platforms, benefiting magnetoresistive devices and superconducting quantum technologies.