Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.
Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.
Superconducting qubits are solid state electrical circuits fabricated using techniques borrowed from conventional integrated circuits. They are based on the Josephson tunnel junction, the only non-dissipative, strongly non-linear circuit element available at low temperature. In contrast to microscopic entities such as spins or atoms, they tend to be well coupled to other circuits, which make them appealling from the point of view of readout and gate implementation. Very recently, new designs of superconducting qubits based on multi-junction circuits have solved the problem of isolation from unwanted extrinsic electromagnetic perturbations. We discuss in this review how qubit decoherence is affected by the intrinsic noise of the junction and what can be done to improve it.
Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.
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.
The research work discussed in this thesis deals with the study of superconducting Josephson qubits. Superconducting qubits are solid-state artificial atoms which are based on lithographically defined Josephson tunnel junctions properties. When sufficiently cooled, these superconducting devices exhibit quantized states of charge, flux or junction phase depending on their design parameters. This allows to observe coherent evolutions of their states. The results presented can be divided into two parts. In a first part we investigate operations of superconducting qubits based on the quantum coherence in superconducting quantum interference devices (SQUID). We explain experimental data which has been observed in a SQUID subjected to fast, large-amplitude modifications of its effective potential shape. The motivations for this work come from the fact that in the past few years there have been attempts to interpret the supposed quantum behavior of physical systems, such as Josephson devices, within a classical framework. Moreover, we analyze the possibility of generating GHZ states, namely maximally entangled states, in a quantum system made out of three Josephson qubits. In particular, we investigate the possible limitations of the GHZ state generation due to coupling to bosonic baths. In the second part of the thesis we address a particular cause of decoherence of flux qubits which has been disregarded until now: thermal gradients, which can arise due to accidental non equilibrium quasiparticle distributions. The reason for these detrimental effects is that heat currents flowing through Josephson tunnel junctions in response to a temperature gradient are periodic functions of the phase difference between the electrodes. The phase dependence of the heat current comes from Andreev reflection, namely an interplay between the quasiparticles which carry heat and the superconducting condensate which is sensitive to the superconducting phase difference. Generally speaking, the flux qubit states are characterized by different values of the phase difference through their Josephson junctions. Consequently, the phase-dependent thermal current through a device subject a temperature gradient is related to the phase-dependent qubit states. We study how the thermal currents change according to the state of the qubits hence yielding a measurement of the qubit state. This in turn leads to an impact of temperature gradient on the dynamics of the system. We show that flux qubits in the Delft qubit design can have limitations of the decoherence time to the order of microseconds as a result of this newly discovered source of decoherence. In contrast, the fluxonium qubit is found to be well protected due to its superinductance.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.
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.