We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.
We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.
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.
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.
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.
Solid state quantum bit circuits (qubits) are candidates for the implementation of quantum processors, which can in principle perform some computational tasks beyond reach of classical sequential processors. Decoherence is there a key issue since electrical circuits are more prone to decoherence than microscopic objects such as atoms. We introduce the different families of solid state qubits, which are either based on single particle states in semiconductor nanostructures, or on global quantum states of superconducting Josephson circuits. We treat more in detail the Cooper pair box Josephson circuit, and the quantronium circuit derived from it. In this device, a decoupling strategy of the circuit from the outside circuitry allows to improve quantum coherence. We expose results obtained on the manipulation of the qubit state in the quantronium. We develop a general framework for understanding decoherence in qubit circuits, and show how coherence time measurements allow to characterize noise sources coup. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We study the dynamics of a quantum superconducting circuit which consists of a Josephson charge qubit, coupled capacitively to a current biased Josephson junction. Under certain conditions, the eigenstates of the qubit and the junction become entangled. We obtain the time evolution of these states in the limit of weak coupling. Rabi oscillations occur, as a result of the spontaneous emission and re-absorption of a single oscillation quantum in the junction. We discuss a possible way to experimentally determine the quantum state of the junction and hence observe the Rabi oscillations.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.