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ISTA Thesis

Andrea Trioni

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

Quantum mechanics reveals a world that defies classical determinism, where uncertainty, superposition, and fluctuations are fundamental aspects. Engineering devices that harness these quantum features requires not only precision, but also a deep understanding of how they interact with their surrounding environment. Superconducting circuits, which exploit macroscopic quantum coherence in low-loss superconducting materials, provide a scalable platform for implementing such systems. Among the critical elements in these circuits, superinductors—high-impedance, dissipation-free inductive components—play a central role by suppressing charge fluctuations. They allow quantum states to be delocalized in phase space, protect qubits from environmental noise, and facilitate access to phenomena such as dual Josephson physics and ultra-strong coupling regimes. This thesis explores two complementary implementations of high-impedance circuits: geometric superinductors, demonstrating that high impedance can be achieved beyond kinetic inductance, and Josephson junction chains, used to investigate both microwave mode properties and DC transport across the superconductor-to-insulator transition. Part I addresses geometric superinductors. Contrary to the common belief that high-impedance superconducting circuits require kinetic inductance, we demonstrate that purely geometric designs can achieve characteristic impedance exceeding the resistance quantum. By exploiting mutual coupling between adjacent turns, coil-based inductors achieve enhanced self-inductance, creating a reliable platform for qubits and resonators. Modeling, simulation, fabrication, and characterization confirm that these elements behave as superinductor. With low loss, high linearity, and minimal stray capacitance, these elements are reproducible, free of uncontrolled tunneling events, and capable of strong magnetic coupling. This establishes geometric superinductors as robust, single-wave-function superconducting devices suitable for hardware protected qubits and hybrid systems. Part II presents classical numerical simulations of a Quantum Phase Slip circuit to study dual Shapiro steps. The circuit consists of an ideal Quantum Phase Slip element embedded in a resistive-inductive environment with a parasitic capacitance. Part III extends the investigation of high characteristic-impedance circuit elements to one-dimensional Josephson junction chains, which act as a quantum simulator for many-body physics and the superconductor–insulator transition. Different devices are realized on both sides of the DC phase transition, showing either a supercurrent branch or Coulomb blockade at zero bias. The effect of the crossover on microwave modes, however, remains insufficiently investigated. Studying these modes provides insight into the interplay between disorder and phase-slip events. Small differences in circuit component sizes determine which side of the transition a device falls on, making these results relevant not only for fundamental understanding but also for the design of quantum devices, emphasizing the crucial role of the electromagnetic environment in stabilizing and controlling fragile quantum states. Together, these results illustrate how carefully engineered high characteristic-impedance elements provide a link between macroscopic circuits and the inherently uncertain quantum world, enabling experiments that probe, control, and ultimately exploit quantum fluctuations for applications in quantum information, metrology, solid state physics and beyond.

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ISTA Thesis

Matilda Peruzzo

This work is concerned with two fascinating circuit quantum electrodynamics components, the Josephson junction and the geometric superinductor, and the interesting experiments that can be done by combining the two. The Josephson junction has revolutionized the field of superconducting circuits as a non-linear dissipation-less circuit element and is used in almost all superconducting qubit implementations since the 90s. On the other hand, the superinductor is a relatively new circuit element introduced as a key component of the fluxonium qubit in 2009. This is an inductor with characteristic impedance larger than the resistance quantum and self-resonance frequency in the GHz regime. The combination of these two elements can occur in two fundamental ways: in parallel and in series. When connected in parallel the two create the fluxonium qubit, a loop with large inductance and a rich energy spectrum reliant on quantum tunneling. On the other hand placing the two elements in series aids with the measurement of the IV curve of a single Josephson junction in a high impedance environment. In this limit theory predicts that the junction will behave as its dual element: the phase-slip junction. While the Josephson junction acts as a non-linear inductor the phase-slip junction has the behavior of a non-linear capacitance and can be used to measure new Josephson junction phenomena, namely Coulomb blockade of Cooper pairs and phase-locked Bloch oscillations. The latter experiment allows for a direct link between frequency and current which is an elusive connection in quantum metrology. This work introduces the geometric superinductor, a superconducting circuit element where the high inductance is due to the geometry rather than the material properties of the superconductor, realized from a highly miniaturized superconducting planar coil. These structures will be described and characterized as resonators and qubit inductors and progress towards the measurement of phase-locked Bloch oscillations will be presented.

•Jan 1, 2021•0 citations

Applications of superinductors in superconducting quantum circuits

Wenyuan Zhang

Superinductors are inductors whose microwave characteristic impedances are greater than the resistance quantum, $R_{Q}=h/(2e)^{2}approx6.5kOmega$. They can be implemented using Josephson junction chains and high kinetic inductance nanowires. In this dissertation, we explore applications of superinductors in both implementations in superconducting quantum circuits. The dissertation consists of three parts. In the first part, we discuss the fluxon-parity-protected qubit consisting of a Cooper-pair box (CPB) shunted by a superinductor made of a chain of coupled asymmetric Superconducting Quantum Interference Devices (CASQUIDs). The spectroscopic measurement of a prototype of the fluxon-parity-protected qubit was performed. We observed almost complete suppression of the single fluxon tunneling across the CPB due to the destructive Aharonov-Casher interference when the offset charge on the CPB island was set to $e$ mod(2$e$). A fluxon-parity-protected qubit with a higher superinductance can potentially be used to perform fault-tolerant Clifford gates. In the second part, we studied the microwave losses in high-kinetic-inductance granular Aluminum films using superconducting coplanar-waveguide (CPW) resonators made of the films. We observed that the intrinsic losses in these resonators at low temperatures were limited by resonator coupling to the two-level systems (TLS) in the environment. The demonstrated internal quality factors are comparable with those for CPW resonators made of conventional superconductors. The characterized granular Aluminum films can be used to fabricate superinductors for a wide range of applications in quantum metrology and quantum information processing. In the third part, we discuss the one-dimensional Josephson metamaterial made of a similar structure as the superinductor used in the fluxon-parity-protected qubit. The metamaterial demonstrated strong Kerr nonlinearity with the Kerr constant tunable over a wide range from positive to negative values by the magnetic field. The metamaterial is promising for use as an active medium for quantum-limited Josephson traveling-wave parametric amplifiers.

•Jan 1, 2019•1 citation

Josephson circuits for protected quantum bits

Wen-Sen Lu

Over the past two decades the performance of superconducting quantum bits (qubits) has been improved tremendously: the coherence time of individual qubits has been increased by five orders of magnitude, from a few nanoseconds to >100 μs. The much-improved coherence, lithographic scalability, and compatibility with microwave control place superconducting qubits in the leading position in the race amongst several quantum systems being considered for quantum information processing. Despite this very impressive progress, experimental realization of quantum error corrections and demonstration of logical qubits remains a considerable challenge.One of possible solutions to this problem is the development of so-called protected qubits whose errors would be suppressed by special symmetries of the underlying Hamiltonian. The realization of such qubits requires elements not found in the conventional superconducting circuit toolbox, such as Josephson elements with cos(ϕ/2) and cos(2ϕ) dependences of the Josephson energy E_J on the phase difference ϕ, circuits with a very large kinetic inductance, and junctions with unusually low E_J.This thesis focuses on design, fabrication and characterization of circuits based on low-E_J Josephson junctions (JJs) and superinductors (SIs). By analyzing limitations on the junction performance imposed by the thermally activated phase slips, we observed a dramatic reduction of the critical currents in the regime E_J≤T which was accompanied by an increase of the zero-bias resistance R_0. The first part of this work provides practical considerations for the use of such junctions in quantum circuits. With the aim of improving elements with a very high kinetic inductance, in the second part we developed superinductors based on the granular Aluminum (grAl) films, in which Josephson junctions are realized between nanoscale grains. The circuits based on such SIs demonstrate low microwave losses at ultra-low temperatures. Superinductors are an essential element of a novel qubit that we have developed – the so-called bifluxon. The qubit consists of a Cooper-pair box (CPB) with low-E_J Josephson junctions shunted by a superinductor, thus forming a superconducting loop. When the loop is threaded by the magnetic flux Φ=Φ_0⁄2 where Φ_0 is the flux quantum, the qubit offers exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. In the last part of this work, we observed an increase of the energy relaxation time by two orders of magnitude, up to 100μs, by turning on protection in the bifluxon qubit.

•Jan 1, 2021•1 citation

Hoge frequentie resonatoren om supergeleidende ringen te onderzoeken. Van metastabiele toestanden tot kwantumcoherentie

Nulens, Lukas

Superconducting circuits combine zero electrical resistance with macroscopic quantum coherence, making them a versatile platform for both fundamental studies and technological applications. Modern thin-film deposition and lithography allow precise control over geometry, material composition, and dimensional scales, enabling the fabrication of complex superconducting structures with tailored properties. These capabilities give access to phenomena not achievable with conventional electronic components, establishing superconducting circuits as a unique tool for exploring quantum physics and developing devices with unique functionalities. In superconducting rings, macroscopic quantum coherence manifests as discrete circulating currents. Fluxoid quantization restricts these currents to discrete winding states. Transitions between winding states occur via phase-slip events. A phase slip event requires overcoming an energy barrier, which can be crossed either through thermal activation, resulting in thermally activated phase slips (TAPS), or via quantum tunneling, resulting in quantum phase slips (QPS) that have no classical analogue. Both processes depend sensitively on temperature, loop geometry, material properties, and the intrinsic properties of the superconductor. Embedding weak links or nanowires in a superconducting ring provides localized regions where phase slips preferentially occur, enabling controlled TAPS and QPS dynamics. When the QPS rate becomes sufficiently high, coherent tunneling between neighboring winding states generates an energy splitting, forming the basis of qubit states. The discrete winding states can thus be exploited for device applications: serving as robust memory elements when the energy barrier is high and phase slips are rare and well controlled, and as qubits when coherent quantum phase slips allow the system to occupy superpositions of distinct winding states, marking the transition from a classical bit to a quantum bit. Phase-slip dynamics in superconducting rings have traditionally been studied using switching-current measurements, in which the bias current is ramped until the ring or nanowire becomes resistive. While this approach provides statistical information about phase-slip rates, it is inherently dissipative and cannot detect events that do not drive the system in the normal state, leaving many phase slips hidden and preventing their unambiguous classification by origin or rate.This thesis develops a non-invasive, radio-frequency resonator-based platform for studying phase-slip dynamics in superconducting rings. Building on magnetooptical imaging of flux penetration in superconducting resonators, we first established methods to apply a local magnetic field to a loop without perturbing the resonator and couple it to the resonator, linking changes in circulating currents to shifts in the resonance frequency. This enabled continuous, timeresolved detection of individual phase-slip events on microsecond-to-nanosecond timescales. Using this platform, we systematically investigated how loop geometry, weak-link properties, kinetic inductance, and temperature govern phase-slip rates and dynamics. Deterministic control of discrete winding states in high-kinetic-inductance aluminum loops, our chosen material platform, was demonstrated, realizing a superconducting memory based on fluxoid quantization. By progressively reducing loop dimensions and introducing weak links, we observed quantum phase-slip events at millikelvin temperatures, providing the first experimental signatures of coherent tunneling between winding states, a first step toward realizing phase-slip-based qubits. Collectively, these results establish a robust experimental pathway from conventional DC measurements to non-invasive RF probing, provide a framework for controlled studies of superconducting phase-slip dynamics, and open the door to exploring and utilizing coherent phase slips in circuit-QED-compatible architectures with device geometries that are simple and easy to fabricate.

•Dec 12, 2025•0 citations

Surpassing the Resistance Quantum with a Geometric Superinductor

Matilda Peruzzo, Andrea Trioni, Farid Hassani +2 more

In superconducting circuits, $s\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s$ are employed to suppress charge fluctuations and increase zero-point voltage, enabling features for hardware-protected qubits, metrological standards, and strongly coupled hybrid devices. Conventionally these devices are based on kinetic inductance, and can suffer from nonlinearity, additional complexity due to multiterminal structure, and the limited control and reliability of bottom-up fabrication. Making use of miniaturization and substrate engineering, the authors realize a geometrically defined, single-wavefunction superinductor---a high-performance, innovative circuit element that promises to expand the scope of quantum circuitry.

arXiv:2007.01644•Physical Review Applied•Oct 29, 2020•59 citations

Quarton qubits with stacked Josephson junctions

Alex Kreuzer

Superconducting quantum circuits rely on compact, low-loss inductive elements, strong anharmonicity, and robust flux biasing to realize coherent and controllable quantum bits. This thesis investigates how vertically stacked Josephson junction arrays can be employed to meet these requirements and enable compact flux qubits operated in the quarton regime. In the first part, stacked Al/AlOx/Al Josephson junctions are established as compact linear inductors. Their three-dimensional geometry reduces parasitic capacitance to ground while allowing multiple junctions to be integrated within a small footprint. A numerical modeling approach is used to quantify stray capacitances, Coulomb screening, and collective modes of extended stacked junction arrays. Cryogenic transport measurements confirm strongly underdamped junction dynamics with uniform junction characteristics, demonstrating their suitability as low-loss inductive elements in superconducting circuits. In the second part, these inductors are integrated into flux qubits operated in the quarton regime. In this regime, the qubit potential becomes nearly quartic around half-flux bias, resulting in positive anharmonicity and first-order insensitivity to flux noise at the operating point. Spectroscopy reveals qubit transition frequencies in the 3–5 GHz range and anharmonicities of 0.5–1.5 GHz, consistent with the expected quartic potential landscape. To distinguish intrinsic from externally induced decoherence, a persistent-current bias scheme is implemented, enabling stable and low-noise flux biasing over time scales of up to one week. A direct comparison between conventionally biased and persistently biased devices rules out external flux noise as the dominant coherence-limiting mechanism. High-resolution spectroscopy identifies avoided level crossings caused by microscopic two-level systems (TLS) in the amorphous tunnel barriers of the stacked junctions. A systematic cumulative analysis of splitting statistics across multiple devices shows that the spectral TLS density scales with the total tunnel-barrier area, while the array length determines the effective qubit–TLS coupling strength. The measured relaxation times follow scaling relations consistent with Fermi’s golden rule for a bath of weakly coupled TLS, demonstrating that TLS in the stacked junction arrays constitute the dominant intrinsic decoherence channel in quarton qubits. These results establish stacked Josephson junction arrays as compact superinductive elements and provide an understanding of coherence limitations in superconducting quantum circuits based on Josephson junction arrays, offering guidance for future device optimization.

•Jan 1, 2026•0 citations
Quantum mechanics reveals a world that defies classical determinism, where uncertainty, superposition, and fluctuations are fundamental aspects. Engineering devices that harness these quantum features requires not only precision, but also a deep understanding of how they interact with their surrounding environment. Superconducting circuits, which exploit macroscopic quantum coherence in low-loss superconducting materials, provide a scalable platform for implementing such systems. Among the critical elements in these circuits, superinductors—high-impedance, dissipation-free inductive components—play a central role by suppressing charge fluctuations. They allow quantum states to be delocalized in phase space, protect qubits from environmental noise, and facilitate access to phenomena such as dual Josephson physics and ultra-strong coupling regimes. This thesis explores two complementary implementations of high-impedance circuits: geometric superinductors, demonstrating that high impedance can be achieved beyond kinetic inductance, and Josephson junction chains, used to investigate both microwave mode properties and DC transport across the superconductor-to-insulator transition. Part I addresses geometric superinductors. Contrary to the common belief that high-impedance superconducting circuits require kinetic inductance, we demonstrate that purely geometric designs can achieve characteristic impedance exceeding the resistance quantum. By exploiting mutual coupling between adjacent turns, coil-based inductors achieve enhanced self-inductance, creating a reliable platform for qubits and resonators. Modeling, simulation, fabrication, and characterization confirm that these elements behave as superinductor. With low loss, high linearity, and minimal stray capacitance, these elements are reproducible, free of uncontrolled tunneling events, and capable of strong magnetic coupling. This establishes geometric superinductors as robust, single-wave-function superconducting devices suitable for hardware protected qubits and hybrid systems. Part II presents classical numerical simulations of a Quantum Phase Slip circuit to study dual Shapiro steps. The circuit consists of an ideal Quantum Phase Slip element embedded in a resistive-inductive environment with a parasitic capacitance. Part III extends the investigation of high characteristic-impedance circuit elements to one-dimensional Josephson junction chains, which act as a quantum simulator for many-body physics and the superconductor–insulator transition. Different devices are realized on both sides of the DC phase transition, showing either a supercurrent branch or Coulomb blockade at zero bias. The effect of the crossover on microwave modes, however, remains insufficiently investigated. Studying these modes provides insight into the interplay between disorder and phase-slip events. Small differences in circuit component sizes determine which side of the transition a device falls on, making these results relevant not only for fundamental understanding but also for the design of quantum devices, emphasizing the crucial role of the electromagnetic environment in stabilizing and controlling fragile quantum states. Together, these results illustrate how carefully engineered high characteristic-impedance elements provide a link between macroscopic circuits and the inherently uncertain quantum world, enabling experiments that probe, control, and ultimately exploit quantum fluctuations for applications in quantum information, metrology, solid state physics and beyond.
This work is concerned with two fascinating circuit quantum electrodynamics components, the Josephson junction and the geometric superinductor, and the interesting experiments that can be done by combining the two. The Josephson junction has revolutionized the field of superconducting circuits as a non-linear dissipation-less circuit element and is used in almost all superconducting qubit implementations since the 90s. On the other hand, the superinductor is a relatively new circuit element introduced as a key component of the fluxonium qubit in 2009. This is an inductor with characteristic impedance larger than the resistance quantum and self-resonance frequency in the GHz regime. The combination of these two elements can occur in two fundamental ways: in parallel and in series. When connected in parallel the two create the fluxonium qubit, a loop with large inductance and a rich energy spectrum reliant on quantum tunneling. On the other hand placing the two elements in series aids with the measurement of the IV curve of a single Josephson junction in a high impedance environment. In this limit theory predicts that the junction will behave as its dual element: the phase-slip junction. While the Josephson junction acts as a non-linear inductor the phase-slip junction has the behavior of a non-linear capacitance and can be used to measure new Josephson junction phenomena, namely Coulomb blockade of Cooper pairs and phase-locked Bloch oscillations. The latter experiment allows for a direct link between frequency and current which is an elusive connection in quantum metrology. This work introduces the geometric superinductor, a superconducting circuit element where the high inductance is due to the geometry rather than the material properties of the superconductor, realized from a highly miniaturized superconducting planar coil. These structures will be described and characterized as resonators and qubit inductors and progress towards the measurement of phase-locked Bloch oscillations will be presented.
Superinductors are inductors whose microwave characteristic impedances are greater than the resistance quantum, RQ=h/(2e)2approx6.5kOmegaR_{Q}=h/(2e)^{2}approx6.5kOmegaRQ​=h/(2e)2approx6.5kOmega. They can be implemented using Josephson junction chains and high kinetic inductance nanowires. In this dissertation, we explore applications of superinductors in both implementations in superconducting quantum circuits. The dissertation consists of three parts. In the first part, we discuss the fluxon-parity-protected qubit consisting of a Cooper-pair box (CPB) shunted by a superinductor made of a chain of coupled asymmetric Superconducting Quantum Interference Devices (CASQUIDs). The spectroscopic measurement of a prototype of the fluxon-parity-protected qubit was performed. We observed almost complete suppression of the single fluxon tunneling across the CPB due to the destructive Aharonov-Casher interference when the offset charge on the CPB island was set to eee mod(2eee). A fluxon-parity-protected qubit with a higher superinductance can potentially be used to perform fault-tolerant Clifford gates. In the second part, we studied the microwave losses in high-kinetic-inductance granular Aluminum films using superconducting coplanar-waveguide (CPW) resonators made of the films. We observed that the intrinsic losses in these resonators at low temperatures were limited by resonator coupling to the two-level systems (TLS) in the environment. The demonstrated internal quality factors are comparable with those for CPW resonators made of conventional superconductors. The characterized granular Aluminum films can be used to fabricate superinductors for a wide range of applications in quantum metrology and quantum information processing. In the third part, we discuss the one-dimensional Josephson metamaterial made of a similar structure as the superinductor used in the fluxon-parity-protected qubit. The metamaterial demonstrated strong Kerr nonlinearity with the Kerr constant tunable over a wide range from positive to negative values by the magnetic field. The metamaterial is promising for use as an active medium for quantum-limited Josephson traveling-wave parametric amplifiers.
Over the past two decades the performance of superconducting quantum bits (qubits) has been improved tremendously: the coherence time of individual qubits has been increased by five orders of magnitude, from a few nanoseconds to >100 μs. The much-improved coherence, lithographic scalability, and compatibility with microwave control place superconducting qubits in the leading position in the race amongst several quantum systems being considered for quantum information processing. Despite this very impressive progress, experimental realization of quantum error corrections and demonstration of logical qubits remains a considerable challenge.One of possible solutions to this problem is the development of so-called protected qubits whose errors would be suppressed by special symmetries of the underlying Hamiltonian. The realization of such qubits requires elements not found in the conventional superconducting circuit toolbox, such as Josephson elements with cos(ϕ/2) and cos(2ϕ) dependences of the Josephson energy E_J on the phase difference ϕ, circuits with a very large kinetic inductance, and junctions with unusually low E_J.This thesis focuses on design, fabrication and characterization of circuits based on low-E_J Josephson junctions (JJs) and superinductors (SIs). By analyzing limitations on the junction performance imposed by the thermally activated phase slips, we observed a dramatic reduction of the critical currents in the regime E_J≤T which was accompanied by an increase of the zero-bias resistance R_0. The first part of this work provides practical considerations for the use of such junctions in quantum circuits. With the aim of improving elements with a very high kinetic inductance, in the second part we developed superinductors based on the granular Aluminum (grAl) films, in which Josephson junctions are realized between nanoscale grains. The circuits based on such SIs demonstrate low microwave losses at ultra-low temperatures. Superinductors are an essential element of a novel qubit that we have developed – the so-called bifluxon. The qubit consists of a Cooper-pair box (CPB) with low-E_J Josephson junctions shunted by a superinductor, thus forming a superconducting loop. When the loop is threaded by the magnetic flux Φ=Φ_0⁄2 where Φ_0 is the flux quantum, the qubit offers exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. In the last part of this work, we observed an increase of the energy relaxation time by two orders of magnitude, up to 100μs, by turning on protection in the bifluxon qubit.
Superconducting circuits combine zero electrical resistance with macroscopic quantum coherence, making them a versatile platform for both fundamental studies and technological applications. Modern thin-film deposition and lithography allow precise control over geometry, material composition, and dimensional scales, enabling the fabrication of complex superconducting structures with tailored properties. These capabilities give access to phenomena not achievable with conventional electronic components, establishing superconducting circuits as a unique tool for exploring quantum physics and developing devices with unique functionalities. In superconducting rings, macroscopic quantum coherence manifests as discrete circulating currents. Fluxoid quantization restricts these currents to discrete winding states. Transitions between winding states occur via phase-slip events. A phase slip event requires overcoming an energy barrier, which can be crossed either through thermal activation, resulting in thermally activated phase slips (TAPS), or via quantum tunneling, resulting in quantum phase slips (QPS) that have no classical analogue. Both processes depend sensitively on temperature, loop geometry, material properties, and the intrinsic properties of the superconductor. Embedding weak links or nanowires in a superconducting ring provides localized regions where phase slips preferentially occur, enabling controlled TAPS and QPS dynamics. When the QPS rate becomes sufficiently high, coherent tunneling between neighboring winding states generates an energy splitting, forming the basis of qubit states. The discrete winding states can thus be exploited for device applications: serving as robust memory elements when the energy barrier is high and phase slips are rare and well controlled, and as qubits when coherent quantum phase slips allow the system to occupy superpositions of distinct winding states, marking the transition from a classical bit to a quantum bit. Phase-slip dynamics in superconducting rings have traditionally been studied using switching-current measurements, in which the bias current is ramped until the ring or nanowire becomes resistive. While this approach provides statistical information about phase-slip rates, it is inherently dissipative and cannot detect events that do not drive the system in the normal state, leaving many phase slips hidden and preventing their unambiguous classification by origin or rate.This thesis develops a non-invasive, radio-frequency resonator-based platform for studying phase-slip dynamics in superconducting rings. Building on magnetooptical imaging of flux penetration in superconducting resonators, we first established methods to apply a local magnetic field to a loop without perturbing the resonator and couple it to the resonator, linking changes in circulating currents to shifts in the resonance frequency. This enabled continuous, timeresolved detection of individual phase-slip events on microsecond-to-nanosecond timescales. Using this platform, we systematically investigated how loop geometry, weak-link properties, kinetic inductance, and temperature govern phase-slip rates and dynamics. Deterministic control of discrete winding states in high-kinetic-inductance aluminum loops, our chosen material platform, was demonstrated, realizing a superconducting memory based on fluxoid quantization. By progressively reducing loop dimensions and introducing weak links, we observed quantum phase-slip events at millikelvin temperatures, providing the first experimental signatures of coherent tunneling between winding states, a first step toward realizing phase-slip-based qubits. Collectively, these results establish a robust experimental pathway from conventional DC measurements to non-invasive RF probing, provide a framework for controlled studies of superconducting phase-slip dynamics, and open the door to exploring and utilizing coherent phase slips in circuit-QED-compatible architectures with device geometries that are simple and easy to fabricate.
In superconducting circuits, $s\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s$ are employed to suppress charge fluctuations and increase zero-point voltage, enabling features for hardware-protected qubits, metrological standards, and strongly coupled hybrid devices. Conventionally these devices are based on kinetic inductance, and can suffer from nonlinearity, additional complexity due to multiterminal structure, and the limited control and reliability of bottom-up fabrication. Making use of miniaturization and substrate engineering, the authors realize a geometrically defined, single-wavefunction superinductor---a high-performance, innovative circuit element that promises to expand the scope of quantum circuitry.
Superconducting quantum circuits rely on compact, low-loss inductive elements, strong anharmonicity, and robust flux biasing to realize coherent and controllable quantum bits. This thesis investigates how vertically stacked Josephson junction arrays can be employed to meet these requirements and enable compact flux qubits operated in the quarton regime. In the first part, stacked Al/AlOx/Al Josephson junctions are established as compact linear inductors. Their three-dimensional geometry reduces parasitic capacitance to ground while allowing multiple junctions to be integrated within a small footprint. A numerical modeling approach is used to quantify stray capacitances, Coulomb screening, and collective modes of extended stacked junction arrays. Cryogenic transport measurements confirm strongly underdamped junction dynamics with uniform junction characteristics, demonstrating their suitability as low-loss inductive elements in superconducting circuits. In the second part, these inductors are integrated into flux qubits operated in the quarton regime. In this regime, the qubit potential becomes nearly quartic around half-flux bias, resulting in positive anharmonicity and first-order insensitivity to flux noise at the operating point. Spectroscopy reveals qubit transition frequencies in the 3–5 GHz range and anharmonicities of 0.5–1.5 GHz, consistent with the expected quartic potential landscape. To distinguish intrinsic from externally induced decoherence, a persistent-current bias scheme is implemented, enabling stable and low-noise flux biasing over time scales of up to one week. A direct comparison between conventionally biased and persistently biased devices rules out external flux noise as the dominant coherence-limiting mechanism. High-resolution spectroscopy identifies avoided level crossings caused by microscopic two-level systems (TLS) in the amorphous tunnel barriers of the stacked junctions. A systematic cumulative analysis of splitting statistics across multiple devices shows that the spectral TLS density scales with the total tunnel-barrier area, while the array length determines the effective qubit–TLS coupling strength. The measured relaxation times follow scaling relations consistent with Fermi’s golden rule for a bath of weakly coupled TLS, demonstrating that TLS in the stacked junction arrays constitute the dominant intrinsic decoherence channel in quarton qubits. These results establish stacked Josephson junction arrays as compact superinductive elements and provide an understanding of coherence limitations in superconducting quantum circuits based on Josephson junction arrays, offering guidance for future device optimization.