# A Cryo-CMOS Oscillator With an Automatic Common-Mode Resonance Calibration for Quantum Computing Applications

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## Abstract

This article presents a 4-to-5 GHz LC oscillator operating at 4.2 K for quantum computing applications. The phase noise (PN) specification of the oscillator is derived based on the control fidelity for a single-qubit operation. To reveal the substantial gap between the theoretical predictions and measurement results at cryogenic temperatures, a new PN expression for an oscillator is derived by considering the shot-noise effect. To reach the optimum performance of an LC oscillator, a common-mode (CM) resonance technique is implemented. Additionally, this work presents a digital calibration loop to adjust the CM frequency automatically at 4.2 K, reducing the oscillator&#x2019;s PN and thus improving the control fidelity. The calibration technique reduces the flicker corner of the oscillator over a wide temperature range (10 <inline-formula> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> and 8 <inline-formula> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> reduction at 300 K and 4.2 K, respectively). At 4.2 K, our 0.15-mm<inline-formula> <tex-math notation="LaTeX">$^2$</tex-math> </inline-formula> oscillator consumes a 5-mW power and achieves a PN of <inline-formula> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula>153.8 dBc/Hz at a 10 MHz offset, corresponding to a 200-dB FOM. The calibration circuits consume only a 0.4-mW power and 0.01-mm<inline-formula> <tex-math notation="LaTeX">$^2$</tex-math> </inline-formula> area.

Original language English 1-13 13 IEEE Transactions on Circuits and Systems I: Regular Papers https://doi.org/10.1109/TCSI.2022.3199997 E-pub ahead of print - 2022

## Keywords

• Calibration
• Capacitors
• common-mode resonance calibration
• cryogenic
• Cryogenics
• flicker noise
• frequency noise
• Logic gates
• oscillator
• Oscillators
• phase noise
• PLL
• Quantum capacitance
• Quantum computing
• Qubit
• qubit
• shot noise

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