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IEEE Transactions on Applied Superconductivity

Experimental characterization of the two current states in a Nb persistent-current qubit

K. Segall, Donald S. Crankshaw, D. Nakada, B. Singh, J. Lee, Terry P. Orlando, Karl K. Berggren, Nina Marković, Sergio O. Valenzuela, M. Tinkham

Published Jun 1, 2003• 4 citations
Publisher

Abstract

We present experiments to characterize a Nb persistent-current qubit as a two-state system. The magnetization signal from the qubit is read-out by a DC-SQUID with near single-shot efficiency. Experiments varying SQUID ramp-rate and temperature suggest thermal activation occurs between the two circulating current states. Such data can be used to fit the parameters of the system, in order to characterize its performance as a potential quantum bit.

DOI
10.1109/tasc.2003.814126

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•Aug 6, 2008•2 citations
We present experiments to characterize a Nb persistent-current qubit as a two-state system. The magnetization signal from the qubit is read-out by a DC-SQUID with near single-shot efficiency. Experiments varying SQUID ramp-rate and temperature suggest thermal activation occurs between the two circulating current states. Such data can be used to fit the parameters of the system, in order to characterize its performance as a potential quantum bit.
Measurements of thermal activation are made in a superconducting, niobium persistent-current qubit structure, which has two stable classical states of equal and opposite circulating current. The magnetization signal is read out by ramping the bias current of a dc superconducting quantum interference device. This ramping causes time-ordered measurements of the two states, where measurement of one state occurs before the other. This time ordering results in effective measurement time, which can be used to probe the thermal activation rate between the two states. Fitting the magnetization signal as a function of temperature and ramp time allows one to estimate a quality factor of $3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ for our devices, a value favorable for the observation of long quantum coherence times at lower temperatures.
Single-shot readout experiments were performed on the two lowest-energy states of a superconducting qubit with three Josephson junctions embedded in a superconducting loop. We measured the qubit state via switching current Isw of a current-biased dc-SQUID, a quantum detector surrounding the qubit loop. The qubit signals were measured in a small Isw regime of the SQUID, typically less than 100 nA, where the Isw distribution is particularly narrow. The obtained single-shot data indicate that the qubit state is readout, through the flux generated by the qubit persistent-current, as energy eigenstates rather than current eigenstates.
Two states of a flux qubit with three Josephson junctions were shown in a single measurement with a dc-SQUID. The qubit is an aluminum superconductor loop surrounded by a dc-SQUID for readout. It has two states, which have persistent currents flowing in opposite directions. The readout data for three samples with different junction sizes suggest that the probability distribution for the double-well potential depends on the ratio of E J / E C , where E J is the Josephson energy and E C is the charging energy. The probability distribution was estimated by calculating the wavefunctions and energy levels for the measured samples. We measured the retrapping current of a dc-SQUID without the qubit as a function of the magnetic field. It was found that the relative phase relation for the magnetic field dependence of the retrapping current jumped from 0 to π at E J ≈ E C . This jump can be explained phenomenologically by taking into account the two kinds of dissipation arising from ac currents flowing through the lead and along the SQUID loop. The fact that the jump occurred at E J ≈ E C strongly suggests that the quantum nature of the electromagnetic environment needs to be taken into account in order to understand the origin of the dissipation.
We have investigated the fidelity and speed of single-shot current-pulse measurements of the three lowest energy states of the dc SQUID phase qubit. We apply a short (2ns) current pulse to one junction of a Nb/AlOx/Nb SQUID that is in the zero voltage state at 25 mK and measure if the system switches to the finite voltage state. By plotting the switching rate versus pulse size we can determine average occupancy of the levels down to 0.01%, quantify small levels of leakage, and find the optimum pulse condition for single-shot measurements. Our best error rate is 3% with a measurement fidelity of 94%. By monitoring the escape rate during the pulse, the pulse current in the junction can be found to better than 10 nA on a 0.1 ns time scale. Theoretical analysis of the system reveals switching curves that are in good agreement with the data, as well as predictions that the ultimate single-shot error rate for this technique can reach 0.4% and the fidelity 99.2%.
We have used 2 ns pulses of current to read out the states of a Nb/AlOx/Nb dc SQUID phase qubit at 25 mK. Plotting the number of escape events that occur versus the size of the current pulse reveals a series of steps corresponding to the occupancy of different energy levels. After calibrating the measurement pulses, we fit these steps to determine the population in each level. Rabi oscillations were viewed using this technique. The single-shot measurement fidelity was theoretically analysed and the optimal single pulse in our device was determined.
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.