In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.
In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.
This thesis examines Josephson tunnel junctions as candidate qubits for quantum computation. A large area current-biased junction, known as a phase qubit, uses the two lowest energy levels in a tilted washboard potential as the qubit states |0> and |1>. I performed experiments with 10 x 10 um^2 Nb/AlOx/Nb qubit junctions, with critical currents of roughly 30 uA. The state of a device was initialized by cooling below 50 mK in a dilution refrigerator. In order for quantum mechanical superpositions to be long-lived, it is necessary to isolate the junction from noisy bias leads that originate at room temperature. I studied two types of isolation: an LC filter, and a broadband scheme that used an auxiliary junction, resulting in a dc SQUID. One of the main goals of this work was to determine how well a simple Hamiltonian, derived assuming just a few lumped elements, describes the observed behavior of a macroscopic Josephson device, including coherent dynamics such as Rabi oscillations. I did this by comparing results to the expected behavior of ideal two-level systems and with more detailed master equation and density matrix simulations. I performed state manipulation by applying dc bias currents and resonant microwave currents, and through temperature control. The tunneling escape rate of the junction from the states |0> and |1> (zero voltage) to the running state (finite voltage) depends on the occupation probability of the energy levels and served as state readout. Experiments to measure the relaxation time T1 between |1> and |0> were performed by examining the dependence of the escape rate with temperature, yielding a maximum T1 = 15 ns. Measuring the decay to the ground state after applying a microwave pulse revealed at least two time constants, one of about 10 ns and another as long as 50 ns. The spectroscopic coherence time T2* was estimated to be roughly 5 ns by measuring resonance widths and the decay envelope of coherent Rabi oscillations was found to have a time constant T' = 10 ns over a wide range of conditions.
This thesis examines the behavior of dc SQUID phase qubits in terms of their proposed use in a quantum computer. In a phase qubit, the two lowest energy states (n=0 and n=1) of a current-biased Josephson junction form the qubit states, with the gauge invariant phase difference across the junction being relatively well defined. In a dc SQUID phase qubit, the Josephson junction is isolated from the environment using an inductive isolation network and Josephson junction, which are connected across the phase qubit junction to form a dc SQUID. Five dc SQUID phase qubits were examined at temperatures down to 25 mK. Three of the devices had qubit junctions that were Nb/AlOx/Nb junctions with critical currents of roughly 30 microamps. The other two had Al/AlOx/Al junctions with critical currents of roughly 1.3 microamps. The device that had the best performance was an Al/AlOx/Al device with a relaxation time of 30 ns and a coherence time of 24 ns. The devices were characterized using microwave spectroscopy, Rabi oscillations, relaxation and Ramsey fringe measurements. I was also able to see coupling between two Nb/AlOx/Nb dc SQUID phase qubits and perform Rabi oscillations with them. The Nb/AlOx/Nb devices had a relaxation time and coherence time that were half that of the Al/AlOx/Al device. One of the goals of this work was to understand the nature of parasitic quantum systems (TLSs) that interact with the qubit. Coupling between a TLS and a qubit causes an avoided level crossing in the transition spectrum of the qubit. In the Al/AlOx/Al devices unintentional avoided level crossings were visible with sizes up to 240 MHz, although most visible splittings were of order ~20 MHz. The measured spectra were compared to a model of the avoided level crossing based on the TLSs coupling to the junction, through either the critical current or the voltage across the junction.
I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.
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.
Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time T Rabi = 78 ns and energy relaxation time T 1 = 315 ns. We found that the value of T Rabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.
This work concerns the study of Josephson junction circuits in the context of their usability for quantum computing. The zero-voltage state of a current-biased Josephson junction has a set of metastable quantum energy levels. If a junction is well isolated from its environment, it will be possible to use the two lowest states as a qubit in a quantum computer. I first examine the meaning of isolation theoretically. Using a master equation, I analyzed the effect of dissipation on escape rates and suggested a simple method, population depletion technique, to measure the relaxation time. Using a stochastic Bloch equation to analyze microwave resonance shapes, I found a relation between current noise induced decoherence and the noise spectrum. I then analyze and test a few qubit isolation schemes, including resistive isolation, inductor-capacitor (LC) isolation, and inductor-junction (LJ) isolation. I found the resistive isolation scheme has a severe heating problem. Macroscopic quantum tunneling and energy level quantization were observed in the LC isolated junction qubits at 25 mK. Relaxation times of 4-12 ns and spectroscopic coherence times of 1-3 ns were obtained for these LC isolated qubits. I measured a relaxation time of 50 ns and a spectroscopic coherence time of 5-8 ns for the LJ isolated junction qubit. Both times are much longer than those of the LC isolated qubits. Rabi oscillations were also observed on this sample with a decay time of around 10 ns. Using microwave spectroscopy techniques, I probed quantum phenomena in a coupled macroscopic three-qubit system that is comprised of two Nb/AlOx/Nb Josephson junctions and an LC resonator. The measured spectrum at 25 mK in the frequency range 4-15 GHz agrees well with quantum mechanical calculations, consistent with the existence of entangled states between the three degrees of freedom. These entangled states and a first-order strong coupling between two junction qubits open the possibility of using a resonator as a data bus for information storage and manipulation in a multi-qubit system. The measurements also demonstrate spectroscopy is a powerful tool and can be used to study a composite system with many qubits.