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Applied Physics Letters

Error rate of a superconducting circuit

Quentin Herr, M. J. Feldman

Published Jul 29, 1996• 31 citations
Publisher

Abstract

The bit-error rate of the Josephson junction single-flux-quantum comparator was measured as a function of bias current offset, at clock rates up to 10 GHz. The bit-error rate versus offset is a smooth curve, measured over 16 decades of incidence, which linearly extrapolates to 10−49 for optimal bias. The lowest rate actually measured was 5×10−17, corresponding to 4 errors counted in 130 h.

DOI
10.1063/1.117809

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The bit-error rate of the Josephson junction single-flux-quantum comparator was measured as a function of bias current offset, at clock rates up to 10 GHz. The bit-error rate versus offset is a smooth curve, measured over 16 decades of incidence, which linearly extrapolates to 10−49 for optimal bias. The lowest rate actually measured was 5×10−17, corresponding to 4 errors counted in 130 h.
We measured the bit-error rate (BER) of an RS latch, a clocked SFQ circuit. A digital error-detection circuit was used to detect BER in the range unity to 10/sup -13/; below 10/sup -7/, the circuit was operated with a 12 GHz on-chip clock. BER was measured as a function of control current; both positive and negative control current was applied, leading to two distinct modes of error incidence. The error function curves extrapolate to 10/sup -80/ for optimal control current at a temperature of 5.5 K. Measurements were repeated over the range 3-7 K. Comparison to theoretical error-function estimates of BER indicate that the noise is strictly thermal.
Abstract A circuit-simulation-based method is used to determine the thermally-induced bit error rate of superconducting Single Flux Quantum logic circuits. Simulations are used to evaluate the multidimensional Gaussian integral across noise current sources attached to the active devices. The method is data-assisted and has predictive power. Measurement determines the value of a single parameter, effective noise bandwidth, for each error mechanism. The errors in the distributed networks of comparator-free Reciprocal Quantum Logic nucleate across multiple Josephson junctions, so the effective critical current is about three times that of the individual devices. The effective noise bandwidth is only 6%–23% of the junction plasma frequency at a modest clock rate of 3.4 GHz, which is 1% of the plasma frequency. This analysis shows the ways measured bit error rate comes out so much lower than simplistic estimates based on isolated devices.
Timing jitter is an important constraint for the performance of SFQ circuits. We focus on the timing jitter in a Josephson transmission line (JTL) that induces timing errors at logic gates. A proper data analysis of 2-bit shift registers gave a jitter value of about 0.08 ps for a single Josephson junction in a JTL powered at a designed bias current. The variations in timing parameters of logic cells also give rise to timing errors. We experimentally determined the timing parameters in several logic cells and found that the deviations between actual and nominal values are within 2 ps. The relationship between the gray zone and circuit scale was estimated by extrapolating the transition curves observed in 2-bit shift registers. The estimated circuit scale was 20,000-100,000 JJs and 1,000 JJs at an operating clock frequency of 20 GHz and 40 GHz, respectively.
The application of high temperature superconductor (HTS) Josephson junctions in digital rapid single flux quantum circuits requires a careful study of the influence of thermal noise on the bit error rate (BER). We have determined experimentally, for the first time, the BER of a HTS rapid single flux quantum circuit. A comparator, formed by two Josephson junctions, was integrated in a Josephson transmission line ring oscillator, allowing us to perform high speed testing of the comparator at GHz frequencies. For fabrication, focused-electron-beam-irradiated junctions have been used because of their small parameter spread and excellent alignment possibilities. A BER of less than 10−11 was obtained at 39 K.
Error rates of rapid-single-flux-quantum (RSFQ) shift register memories were investigated using a high-speed error-rate measurement system in order to demonstrate their reliability and stability. We designed and implemented an 8 times 8-bit shift register memory using the CONNECT cell library and the SRL 2.5 kA/cm2Nb process. The total number of Josephson junctions including the test system is 4184, and the circuit area is 2.1 mm times 3.2 mm. We measured the error rates of every storage node by reading out the data 216times at the clock frequency of 16 GHz. The measured error rates were lower than 10-10with DC bias margin better than plusmn5%.