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IEEE Transactions on Applied Superconductivity

Current Resolution of a Single-Flux-Quantum Readout Circuit Based on Current-to-Time Conversion Toward a Flux Qubit System

Shoichi Nakamura, H. Numabe, Ali Bozbey, Akira Fujimaki

Published Jun 1, 2009• 14 citations

Abstract

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 4.8$\mu{\rm A}$for unshunted junctions and 2.2$\mu{\rm A}$for 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.

DOI: 10.1109/tasc.2009.2018064

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•Jan 1, 2006•16 citations

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 4.8

\mu{\rm A}

for unshunted junctions and 2.2

\mu{\rm A}

for 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.

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.

A single-flux-quantum (SFQ) pulse coincidence detector based on resistively shunted nonhysteretic Josephson junctions was designed and simulated. The coincidence detector generates an SFQ pulse when the delay between the arrival of SFQ pulses at its two inputs is less than the coincidence threshold. Simulations indicate that the minimum coincidence threshold time can be as short as 400+or-200 fs, assuming Josephson junction characteristic voltages of 1 mV, overdamped dynamics, and 4.2 K operating temperatures. Circuit architectures exploiting this gate are suggested. Estimates of the effects of thermal noise on resolution are presented, indicating the potential for various time-domain measurements with subpicosecond resolution.< >

We have applied the Langevin-Heisenberg-Lax formalism for dissipative quantum systems to a balanced Josephson junction comparator operating as a fast, single-shot detector of state of a flux (rf-SQUID) qubit. Earlier experiments and theoretical analysis have shown that such a detector may reach quantum- limited resolution when it measures signal from a high-impedance (current) source. In this work, we have calculated the flux resolution of a detector for a signal source with finite inductive impedance (e.g., a flux qubit) for both an instant switching of the comparator, and for its switching with a realistic SFQ driver. The results show that the flux resolution may be quite high: for typical experimental parameters, the signal-to-noise ratio may be on the order of 10, at 10-ps-scale measurement time. Moreover, the natural energy measure of the resolution, Eout, may be made (within a narrow range of parameters) smaller than planck/2. This situation is similar to the case of continuous flux measurements using SQUIDs. In both cases, a more adequate sensitivity measure requires an account of the fluctuation back-action of the detector on the signal source. In this work we have shown that in the case of single-shot measurements, the back-action effects as characterized by the "information/dephasing" measure, may be brought down to their fundamental limit by at least two methods: coupling quenching and feedback compensation.

We have been developing a time-to-digital converter (TDC) using single-flux-quantum (SFQ) circuits in order to realize an imaging system based on a superconducting strip single-photon detector (SSPD). In this system, the absorption position of a single photon in a meander-shaped SSPD is determined by measuring the delay time of the detected signal propagating through an SSPD delay line. Increasing the time resolution of the TDC is the primary concern for improving the spatial resolution of the system. Here we focused on the double-oscillator SFQ TDC, where the difference of oscillation periods between two SFQ ring oscillators determines the time resolution. In the previous study, a time resolution of about 4 ps was demonstrated by using the Nb standard Josephson integrated circuit (IC) process with a critical current density of 2.5 kA/cm2. In this study, we improved the time resolution by adopting the Nb advanced Josephson IC process with a critical current density of 10 kA/cm2and by optimizing the circuit parameters of the coincidence detector. The histogram and the linearity of the delay measurements show that the time resolution is improved to up to 2 ps.

Direct measurements of propagation delay of single-flux-quantum (SFQ) circuits were performed using SFQ double-oscillator time-to-digital converters. The propagation delay of several SFQ logic gates in our cell library named CONNECT were measured in picosecond resolution. Small discrepancy in the propagation delay of picosecond level was observed between measurement and circuit simulation results. The discrepancy is well explained assuming the parasitic inductance around shunt resistors of Josephson junctions.