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Journal of Physics Conference Series

Unshunted QOS Comparator for Qubit Readout

Thomas Ohki, Michael Wulf, M. J. Feldman, Mark F. Bocko

Published Jun 1, 2006• 7 citations
Publisher

Abstract

State measurements of flux-based superconducting quantum bits (qubits) require the sensitive discrimination of small differences of magnetic flux, with measurement times short compared to the timescales of coherent quantum mechanical behaviour. The single-flux-quantum (SFQ) superconducting comparator may be the best device for this purpose. An SFQ comparator design using a quasi-one-junction SQUID (QOS) acting as the comparator junction has two advantages over earlier designs—increased sensitivity and the possibility to eliminate shunt resistors. Here we report the first measurements of the sensitivity of an unshunted QOS comparator. The gray zone of this device at 4.2K is 6 mΦo.

DOI
10.1088/1742-6596/43/1/346

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Physical Review B•Jul 11, 2005•23 citations
State measurements of flux-based superconducting quantum bits (qubits) require the sensitive discrimination of small differences of magnetic flux, with measurement times short compared to the timescales of coherent quantum mechanical behaviour. The single-flux-quantum (SFQ) superconducting comparator may be the best device for this purpose. An SFQ comparator design using a quasi-one-junction SQUID (QOS) acting as the comparator junction has two advantages over earlier designs—increased sensitivity and the possibility to eliminate shunt resistors. Here we report the first measurements of the sensitivity of an unshunted QOS comparator. The gray zone of this device at 4.2K is 6 mΦo.
We study a single-shot single-flux-quantum (SFQ) readout circuit based on current-to-time conversion for superconducting flux qubits. Circulating currents representing states of a qubit were converted to propagation delay time of SFQ pulses, and then detected by a time discriminator. The key parameter which determines the availability of single-shot readout is current resolution. We evaluated the current resolution by measuring the gray zone which was defined as the transition width in the output probability of the current-to-time converter with 1000 trials for each value of an input current. For reducing unwanted effects on the qubit, shunt resistors are required to be removed for Josephson junctions in the readout circuit. We designed two readout circuits for comparison, the circuit composed of shunted junctions and that of unshunted junctions. Gray zones were measured to be 4.8μA\mu{\rm A}μAfor unshunted junctions and 2.2μA\mu{\rm A}μAfor the shunted ones at 4.2 K. These gray zones may originate from Johnson noise. Operation at a reduced temperature and employment of a likelihood decision circuit will lead to reduced gray zone, i.e., improved current resolution sufficient for single-shot readout.
We evaluated the relationship between the gray zone width and the operating margin for comparators composed of quasi-one-junction superconducting quantum interference devices (QOSs) with shunt resistors, which are often used as high-speed readout circuits in multiple superconductor detector systems. The gray zone width is a good measure of current sensitivity of a single-bit comparator. We numerically analyzed the gray zone width of a QOS comparator and determined the circuit parameters. The gray zone width obtained from the experiments concurred with the results of the numerical analysis and was 2–3 µA at 4.2 K in a QOS comparator composed of three Nb/AlOx/Nb junctions with critical currents of less than 90 µA. The experimentally obtained operating margin for the bias current provided to the comparator was ±15% at the bias current of around 140 µA. These results show that QOS comparators are promising for readout circuits operating up to tens of GHz and imply that gray zone width is the thermal noise in the resistors at 4.2 K.
Successful utilization of the quasi one-junction SQUID (QOS) as a signal comparator for analog-to-digital conversion (ADC) has been demonstrated by several groups, This idea is extended to show how similar comparators can be integrated into an all rapid single flux quantum (RSFQ) digital architecture. Comparators are interrogated by SFQ sampling pulses and in turn give output according to the RSFQ convention. One- and two-bit ADC's have been simulated, fabricated and tested at low speed. Total performance of these devices is estimated within the framework of a multiple bit parallel flash ADC architecture.>
The balanced comparator is an essential part of RSFQ-based readout for superconducting qubits. In this paper we report measurements of the sensitivity of the balanced comparator fabricated in a specialized 30 A/cm2process with 3.6 muA critical currents and measured at 30-500 mK. At sampling frequency of 3.5 GHz the measured gray zone is DeltaI = 104 nA. Due to electron overheating in the shunt resistors the effective noise temperature is 140 mK. The gray zone has a strong dependence on sampling frequency above 5 GHz due to over-clocking. Related measurements have been reported where cooling fins and reduced critical current density of 10 A/cm2were used, and a quantum limited gray zone of 40 nA was achieved. This makes single shot readout possible for the phase, RF-SQUID and persistent current qubits. The readout speed is 30-50 ps, which is quite favorable for error correction schemes.
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.