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Superconductor Science and Technology

An RF SQUID readout for a flux qubit-based microwave single photon counter

V. I. Shnyrkov, Andrii P. Shapovalov, V. Yu. Lyakhno, Andrii Dumik, A. A. Kalenyuk, Pascal Febvre

Published Jan 6, 2023• 7 citations
Publisher

Abstract

Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.

DOI
10.1088/1361-6668/acb10e

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arXiv:1010.0954•Applied Physics Letters•Dec 27, 2010•13 citations
Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.
Superconducting qubits demonstrate good perspectives as scalable blocks for quantum information processing. These systems can be individually readout, addressed, and controlled, making them some of the most attractive thin-film qubits. Quantum measurements should be performed in order to readout the final state of flux qubits. To observe the dynamics of such systems, one requires a fast magnetometer with exceptional sensitivity and low back-action. We address the problem of reducing the back-action of an RF SQUID readout circuit, which may significantly destroy a Josephson flux qubit in the case of the circuits integration. The main sources of such back-action in conventional RF SQUID and DC SQUID circuits are low-ohmic shunting resistors ensuring high damping. The advantage of flux qubits is the presence of an optimal bias point at which, in the first-order approximation, the device is immune to fluctuations in readout and control lines. Nonetheless, even such systems have characteristics limited by a second-order dissipation. The dissipation can be eliminated by using an “ideal parametric readout” based on an RF SQUID acting in non-hysteretic adiabatic mode. In this paper, we propose an RF SQUID in a non-hysteretic regime as a fast, sensitive, and scalable readout system with low back-action for measurements of a single MW photon counter based on a flux qubit.
The nonhysteretic mode of a RF SQUID with a MoRe–Si(W)–MoRe Josephson junction is analyzed in order to detect the states of a single-photon counter based on a superconducting quantum interferometer with a discrete Hamiltonian. The absorption of a photon with 10 GHz frequency brings the counter to the excited level causing tunnelling into the adjacent potential well and a change in the magnetic flux in the interferometer, which can be detected by the SQUID magnetometer. Measurement of a quantum system requires minimization of the back action of the signal read-out channel at the counter, high sensitivity, and speed of the magnetometer. The MoRe–Si(W)–MoRe contacts are optimized for various concentrations of tungsten (W) in silicon (Si) and barrier layer thickness. It is shown that using MoRe–Si(W)–MoRe contacts with a tungsten concentration of approximately 11% for the RF SQUID at excitation frequencies of ∼1 GHz makes it practically an ideal parametric upward frequency shifter with noise determined by the cooled amplifier.
Single-photon detectors are crucial elements of prospective quantum devices and techniques such as quantum communication systems, quantum computers, quantum radars, astrophysical detectors, etc. The detection of individual photons in microwave range is a much larger challenge as compared to that of in optics due to the quanta energy difference of 4 to 5 orders of magnitude which requires a quite different approach. So "artificial atoms" with discrete energy spectrum such as superconducting qubits are used here exploiting resonance transitions between their quantum states. A scheme incorporating a flux qubit with controllable spectrum as a single photon counter for 3-12 GHz range and weak continuous readout circuit based on rf superconducting quantum interferometer (SQUID) with UHF pumping is proposed and analyzed. High SQUID pumping frequency (about 500 MHz) along with using cooled microwatt HEMT preamplifier provides the measurement frequency band of up to 30 MHz while substantially diminishing the back-action effect.
The design and performance of a planar microwave RF-SQUID (superconducting quantum interference device) read out by a cryogenic high-electron-mobility-transistor (HEMT) preamplifier are described. The SQUID sensor consists of a planar half-wavelength microstrip resonator, into which the SQUID loop is integrated. The SQUID is operated at a pump frequency of 1.7 GHz. The cryogenic preamplifier uses a microwave HEMT, located close to the SQUID sensor. Measurements of the flux noise and the fractional step rise parameter were carried out in the temperature range between 4.2 K and 1.5 K. In an open loop, a flux noise of 2*10/sup -6/ Phi /sub 0// square root Hz was measured at 4.2 K, resulting in an energy resolution of about 100 h. The design of a 3-GHz magnetometer is also described, and the preliminary results of the measurements are reported.>
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 present experimental results on a microwave scheme for reading out a Josephson phase qubit. A capacitively shunted superconducting quantum interference device (SQUID) is used as a nonlinear resonator which is inductively coupled to the qubit. The flux state of the qubit is detected by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, the qubit state measurement time is reduced to 25 μs, which is much faster than the conventional readout performed by switching the SQUID to its nonzero dc voltage state. The readout scheme presented here allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.