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.
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.
Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen EJ/Ec, transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X/Y and Z control lines for each qubit, and a readout bus (a transmission line or a low-Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum RQ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cosφ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time (T1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and EJ to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high-Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.
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.
We proposed and theoretically investigated the self-shunted superconducting flux qubits (SSFQs) with relatively large Josephson junctions with the diameter over1μm. Because of the large self-capacitance of several 10 fF in the junctions, the large shunt capacitor with dimensions of several 100$ \mu \text{m}oftheconventionalcapacitivelyshuntedfluxquantumbits(qubits)canbeeliminated,resultinginsignificantreductionofthefootprint.WesystematicallycalculatedtheSSFQperformances,suchastheanharmonicity,andinvestigatedtheirdependencesonthecircuitparameters.Asaresult,itwasshownthattheSSFQshavethelargeanharmonicityof400–2000MHzforthereasonableparameters,suchasthelargejunctionareaofaround1 \mu \text{m}^{2}andthesmallcriticalcurrentdensityofaround10\text{A/cm}^{2}$. Furthermore, we derived and estimated the relative relaxation time of the SSFQs due to the charge and flux noises. As a result, we found that the high anharmonicity over 800 MHz could be achieved without degrading the relaxation time from that of the high-coherence flux qubits. The SSFQs offer the new choice of the highly scalable qubits, which achieve both the small footprint and high anharmonicity.
The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad frequency tunability, strong anharmonicity, high reproducibility, and relaxation times in excess of 40μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise, and 1/f flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit-resonator interaction.
The field of quantum computing is growing at a rapid rate with the promise of dramatic improvements in the ability to solve critical computational problems. A leading approach for implementing fault-tolerant quantum computers is based on superconducting circuits containing Josephson junctions to form qubits. These qubits have many attractive qualities, but predicting the device performance requires detailed knowledge of the junction properties. Thus, precise characterization is crucial for realizing different qubit designs. The coherence of superconducting qubits is limited by several sources in the circuit en- vironment. Building a quantum computer requires effort to reduce gate errors caused by decoherence. This is typically achieved with quantum error correction. An alternative ap- proach involves designing qubits that are intrinsically protected from noise sources. One such design is the charge-parity qubit, which combines Josephson junctions in a novel regime. The capacitance of the junctions is a critical parameter for this qubit design that directly affects the engineered protection against decoherence. Beyond the conventional geometric capaci- tance, there is an excess contribution from virtual quasiparticle tunneling; we refer to this component as the electronic capacitance. This thesis focuses on the characterization of the capacitance of Josephson junctions, with the goal of isolating and measuring the electronic capacitance contribution, particularly for use in the charge-parity qubit. The thesis first reviews the initial implementation of the charge-parity qubit and the challenges that were encountered. Next, the theoretical origin is described and a framework for measuring the junction capacitance using superconducting resonant circuits is described. This technique is then applied to arrays of junctions fabricated with different parameters and the scaling of the electronic capacitance is presented. Finally, based on this knowledge of the junction capacitance, second-generation charge-parity qubits are implemented and the experimental results are presented.
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.