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Physica Scripta

Quiet Readout of Superconducting Flux States

John L. Clarke, John L. Clarke, Timothy L. Robertson, Timothy L. Robertson, B. L. T. Plourde, B. L. T. Plourde, A. Garc a-Martinez, A. Garc a-Martinez, P. A. Reichardt, P. A. Reichardt, Dale J. Van Harlingen, Dale J. Van Harlingen, Dale J. Van Harlingen, Boris Chesca, R. Kleiner, Yuriy Makhlin, G. Sch?n, Alexander Shnirman, Frank K. Wilhelm

Published Jan 1, 2002• 29 citations
Publisher

Abstract

The INSQUID (INductive Superconducting QUantum Interference Device) can measure the flux state of a superconducting qubit rapidly, while allowing the quantum state of the qubit to evolve with low levels of back action. The INSQUID consists of a dc SQUID with unshunted junctions connected in parallel with a superconducting inductor; the qubit is placed inside the SQUID loop. The inductor is coupled to a readout dc SQUID with resistively-shunted junctions. By applying appropriate fluxes to the input SQUID and the inductor, the INSQUID can be turned "off", so that virtually no flux noise is coupled from the readout SQUID to the qubit. Different flux biases turn the INSQUID "on", enabling the readout SQUID to measure the flux state of the qubit. The INSQUID can also be used to turn on and off the coupling between two or more qubits.

DOI
10.1238/physica.topical.102a00173

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The INSQUID (INductive Superconducting QUantum Interference Device) can measure the flux state of a superconducting qubit rapidly, while allowing the quantum state of the qubit to evolve with low levels of back action. The INSQUID consists of a dc SQUID with unshunted junctions connected in parallel with a superconducting inductor; the qubit is placed inside the SQUID loop. The inductor is coupled to a readout dc SQUID with resistively-shunted junctions. By applying appropriate fluxes to the input SQUID and the inductor, the INSQUID can be turned "off", so that virtually no flux noise is coupled from the readout SQUID to the qubit. Different flux biases turn the INSQUID "on", enabling the readout SQUID to measure the flux state of the qubit. The INSQUID can also be used to turn on and off the coupling between two or more qubits.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
We have investigated the flux transfer characteristics of a switchable flux transformer comprising a superconducting loop and a DC superconducting quantum interference device (DC-SQUID). This system can be used to couple multiple flux qubits with a controllable coupling strength. Its characteristics were measured using a flux input coil and a DC-SQUID for readout coupled to the transformer loop in a dilution refrigerator. The observed characteristics are consistent with the calculation results. We have demonstrated the reversal of the slope of the characteristics and the complete switching off of the transformer, which are useful features for its application as a controllable coupler for flux qubits.
In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.
Flux states of an RF SQUID are promising candidates for the implementation of quantum bits (qubits) for quantum computing. Accurate measurements of the flux states, especially in the time domain, require a controllable coupling between a qubit and a readout circuit (e.g., a dc SQUID magnetometer). Since the readout circuit can also be a source of decoherence, such a controllable coupling also allows one to control (minimize) the back action of the magnetometer. For this purpose we suggest a balanced, tunable transformer. This has a gradiometer configuration such that each arm is broken by a small loop containing two Josephson junctions. As a result the inductance of each arm can be adjusted by an applied bias flux. In the symmetrical case there is no coupling between the qubit and the magnetometer while a desired coupling can be achieved by changing the asymmetry of the arms. Similar transformers may be be useful for achieving controllable, lossless coupling that is required between qubits. Theoretical analysis of the noise back action of the transformer as well as preliminary experimental results are presented.
The readout process of a superconducting flux-qubit is theoretically analyzed in terms of the quantum dynamics of a qubit-SQUID coupled system during measurement. The quantity directly observed by the measurement is the switching current (Isw) of the dc-SQUID placed around the qubit ring. In order to clarify the relation between the Isw and the qubit state, we calculated the time evolution of the density operator of the qubit-SQUID system while increasing the SQUID bias current until switching events occur and obtained the switching current distributions. This clarifies what information of the qubit is obtained by a dc-SQUID switching current measurement under specific conditions, for example, when the qubit eigenstate is a superposition of two different flux states.