This thesis consists of two parts: the main part is a theoretical investigation of the ultrastrong coupling regime for atom-light coupling in superconducting circuits, and the second part is concerned with the development of a new high coherence flux qubit design. \n \nThe spin-boson model describes the interaction between a quantum two-level system and a continuum of bosonic modes. When the interaction strength becomes comparable to the system frequency, the system enters the ultrastrong coupling (USC) regime, where the rotating wave approximation breaks and the system dynamics need to be described nonperturbatively. Recently, the ultrastrong coupling has been achieved on a device consisting of a superconducting flux qubit coupled to an electromagnetic continuum, with the coupling strength being verified in experiments by the standard transmission method. The first project in this thesis aims to measure the dynamics of the spin-boson model in a direct and controllable way when the coupling strength is in the USC regime. We propose three experiments to measure the coherence of the two-level system including the relaxation and dephasing, and the the renormalized tunneling frequencies in the ultrastrong coupling regime. The controllable measurements are realized with a fast-switchable ultrastrong coupling system consisting of a two-loop flux qubit galvanically coupled to an open transmission line, flux bias and driving lines, and readout circuits. The design and model of the full device are presented. We demonstrate that the three proposed experiments can be well implemented based on the simulations of qubit properties and coupling strengths. \n \nThe second part of the thesis presents work on the design of a new type of capacitively shunted flux qubit. This work is motivated by improving qubit coherence time and anharmonicity, which is essential for speeding up qubit gates and enhancing the capability of quantum computing. It was demonstrated that adding shunting pads to flux qubits can drastically improve the coherence time and the reliability of qubit fabrication, but the CSFQ was shown with moderate anharmonicities. In this project, we present the a new design of CSFQ and its circuit model, which contains three Josephson junctions and three shunting pads. In experiments, the qubit spectroscopy matches well with the circuit model, which takes into account all the capacitances between the qubit and other circuits. The qubit is found to have both large anharmonicity A = ω₁₂ - ω₀₁ = 2π ⨯ 3.69 GHz, and high coherence with T₁ = 40 ± 5 µs. We also present experiments on the multilevel quantum control and multilevel relaxation measurement. We perform qutrit state tomography to reconstruct the full density matrix with the tomography fidelity reaching 99.2%. We are able to extract the time-dependent state populations for the relaxation process of a qutrit, and extract the exact transition rates between the three levels.
This thesis consists of two parts: the main part is a theoretical investigation of the ultrastrong coupling regime for atom-light coupling in superconducting circuits, and the second part is concerned with the development of a new high coherence flux qubit design. \n \nThe spin-boson model describes the interaction between a quantum two-level system and a continuum of bosonic modes. When the interaction strength becomes comparable to the system frequency, the system enters the ultrastrong coupling (USC) regime, where the rotating wave approximation breaks and the system dynamics need to be described nonperturbatively. Recently, the ultrastrong coupling has been achieved on a device consisting of a superconducting flux qubit coupled to an electromagnetic continuum, with the coupling strength being verified in experiments by the standard transmission method. The first project in this thesis aims to measure the dynamics of the spin-boson model in a direct and controllable way when the coupling strength is in the USC regime. We propose three experiments to measure the coherence of the two-level system including the relaxation and dephasing, and the the renormalized tunneling frequencies in the ultrastrong coupling regime. The controllable measurements are realized with a fast-switchable ultrastrong coupling system consisting of a two-loop flux qubit galvanically coupled to an open transmission line, flux bias and driving lines, and readout circuits. The design and model of the full device are presented. We demonstrate that the three proposed experiments can be well implemented based on the simulations of qubit properties and coupling strengths. \n \nThe second part of the thesis presents work on the design of a new type of capacitively shunted flux qubit. This work is motivated by improving qubit coherence time and anharmonicity, which is essential for speeding up qubit gates and enhancing the capability of quantum computing. It was demonstrated that adding shunting pads to flux qubits can drastically improve the coherence time and the reliability of qubit fabrication, but the CSFQ was shown with moderate anharmonicities. In this project, we present the a new design of CSFQ and its circuit model, which contains three Josephson junctions and three shunting pads. In experiments, the qubit spectroscopy matches well with the circuit model, which takes into account all the capacitances between the qubit and other circuits. The qubit is found to have both large anharmonicity A = ω₁₂ - ω₀₁ = 2π ⨯ 3.69 GHz, and high coherence with T₁ = 40 ± 5 µs. We also present experiments on the multilevel quantum control and multilevel relaxation measurement. We perform qutrit state tomography to reconstruct the full density matrix with the tomography fidelity reaching 99.2%. We are able to extract the time-dependent state populations for the relaxation process of a qutrit, and extract the exact transition rates between the three levels.
We propose different designs of switchable coupling between a superconducting flux qubit and a microwave transmission line. They are based on two or more loops of Josephson junctions which are directly connected to a closed (cavity) or open transmission line. In both cases the circuit induces a coupling that can be modulated in strength, reaching the so-called ultrastrong coupling regime in which the coupling is comparable to the qubit and photon frequencies. Furthermore, we suggest a wide set of applications for the introduced architectures.
Superconducting devices as quantum bits (qubits) are one of the most promising candidates for implementing a practical quantum computer. Over the last decade, quantum coherence times of superconducting qubits have been continuously improved. Operating qubits in noise insensitive points, eliminating the participation of the lossy materials, and better isolation from environment increased the decoherence times from nanoseconds to tens of microseconds. One recent approach on the qubit design is to shunt the Josephson junctions with large capacitors to reduce the sensitivity to noise and to redistribute the stored electromagnetic energy in a well-engineered area. This approach was first applied on charge qubits and later adopted to other types of superconducting qubits. \n \nIn this thesis, we present the design and the characterization of a three-Josephson junction superconducting circuit with three large shunt capacitors. We present experiments on decoherence in the circuit used as a qubit. The qubit relaxation time T₁ is reaching as high as 47 μs and the spin-echo dephasing time T₂ = 9.4 μs. In addition, we present spectroscopy experiments and decoherence characterization in the qutrit subspace formed by the lowest three energy levels. The spectroscopy data is in excellent agreement with the complete circuit model based on the system capacitance matrix. At the flux symmetry point, the circuit has a large anharmonicity, defined as the difference between the 1-2 and 0-1 transition frequencies, approaching 2π × 3.7 GHz, which is enabling fast single qubit operations. We performed randomized benchmarking with the qubit gates with a duration of 1.62 ns and an average gate fidelity of 99.9%. \n \nMoreover, we present experiments with multi-level control in qutrit subspace, formed by the lowest three energy levels. We demonstrate a single step experimental implementation of a generalized Walsh-Hadamard gate. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of adjacent pulses. The gate is characterized using tomography process and the average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.
This thesis presents circuit quantum electrodynamic (cQED) experiments done with artificial atoms coupled to a high quality factor superconducting microwave resonator. This work discusses the theoretical framework, design, fabrication, implementation and characterization of a multi-qubit system using superconducting persistent current qubits, often referred as flux qubits. \n \nWe developed a new type of cryogenic aid for fast turnaround microwave experiments. The minimum turnaround time to perform microwave experiments in dilution refrigerators is typically a few days, as required by cooling down and warming up the entire refrigerator. The cryogenic microwave payload and wiring needed for each qubit and resonator add a significant heat load to \nthe system which typically only has a few µW s of cooling power at millikelvin temperatures. We present a new experimental approach we developed in which a suitable sample holder is attached to a cold-insertable probe and brought in contact with transmission lines permanently mounted inside the cryostat. The total turnaround time is reduced to 8 hours if the target temperature is 80 mK. This new measurement method increased our ability to successfully identify good devices with fast design-characterization iterations, while allowing months-long measurements at 30 mK. \n \nOur device architecture uses several qubits, each of which is controlled via on-chip fast flux bias lines. Readout of the qubit’s quantum state is performed by homodyne detection of the resonator field at large driving power. We observe long coherence times at the optimal bias point of the flux qubits and present decoherence measurements around this optimal point, where the \nflux qubits couple mostly to magnetic flux noise. Dynamical decoupling techniques employing fast microwave pulses are used to protect the qubit’s coherence and allow calculating the magnetic flux noise power spectral density of the qubit’s environment. Photon-mediated interaction between distant qubits in the resonator allows the implementation of a two-qubit controlled-NOT gate \nusing the selective darkening technique. \n \nThis multi-qubit superconducting design is an interesting platform to study the decoherence properties of flux qubits, the properties of strong interaction of electromagnetic radiation with macroscopic quantum systems. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
This thesis discusses a series of experimental and theoretical studies on fast control and decoherence in superconducting quantum circuits. These two subjects are complementary aspects of the problem of improving the gate fidelities in quantum information processing devices based on superconducting circuits. \n \nIn the first part of this thesis, we present experiments on fast control of a superconducting flux qubit using strong driving. We explore driving with short pulses and a driving strength significantly exceeding the transition frequency. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. We observe the role of pulse shaping in the dynamics, as determined by non-adiabatic transitions between Floquet states. In addition, based on adiabatic perturbation theory in the Floquet picture, we propose a control scheme for fast and high-fidelity single-qubit operations with strong driving. These results pave the way to quantum control with a fidelity beyond the threshold of fault-tolerant quantum computation. \n \nIn the second part of this thesis, we discuss experimental methods and present the characterization of decoherence in superconducting resonators and superconducting qubits. Firstly, we present an analysis method on the measurements of photon loss in superconducting resonators. We use this method to characterize the microwave loss of aluminum oxide, an important material in superconducting circuits. The power and temperature dependence of the measured loss is consistent with loss due to two-level defects in amorphous materials. Secondly, we present experimental results on decoherence and noise spectroscopy of a superconducting flux qubit. Using the qubit as a noise spectrometer, we perform detailed measurements on the power spectral density of the flux noise in superconducting circuits over a wide range of frequencies, from 10^-3 to 10^8 Hz, and over a temperature range from 35 to 130 mK. We also present measurements of frequency and temperature dependence of the qubit energy relaxation.
Superconducting devices have emerged as leading candidates for building practical quantum computers, owing to their scalability, designability, and ease of control. Development of superconducting devices has been accompanied by increases in coherence times from nanoseconds to tens of microseconds, and a multitude of new types of superconducting qubits. In turn, these improvements in coherence, and study of superconducting qubits has produced models for these devices accurate and trustworthy enough to enable design decisions to be determined prior to device fabrication. Recent work by the superconducting quantum devices (SQD) group has produced a variant of the capacitively-shunted flux qubit that features fast control over the lowest three levels, allowing the device to be used as a qutrit. This thesis presents a model and characterization results for this device. \n \nThis thesis also presents experimental results characterizing control fidelity for a qutrit using randomized benchmarking (RB). Quantum process tomography and application of repeated gate sequences are also used to support the randomized benchmarking results. The method of synthesizing the gates in the qutrit Clifford group can decompose any gate into two-state rotations. The fidelity of 99.0 +/- 0.2% obtained by randomized benchmarking establishes the device as a useful qutrit, and outlines interesting directions in using higher levels to improve qubit-based quantum computers, and in using higher levels to pack more states into fewer devices in quantum computers. Analysis of experimental results indicates errors are dominated by ac-Stark and Bloch-Siegert shifts during qutrit control. \n \nThis thesis then presents two new devices meant to study the impact of changing design parameters on the suitability of flux qubits for multilevel control. The first device test individual qubits, with the goal of further improving the coherence time, and improving qutrit control. The second device couples two devices together, so that two-qubit gates can be studied. The available design parameters and their impact on qubit properties are discussed, and design variations are selected for the single and two-qubit devices. The result is a set of devices ready for manufacture and experimental characterization.