34.5 A Calibration-Free 12.8-16.5GHz Cryogenic CMOS VCO with 202dBc/Hz FoM for Classic-Quantum Interface

Recently, physical quantum-bits (Qubits) have achieved a remarkable operational fidelity >99.9% and a coherence time ranging from milliseconds to seconds with classic quantum controller (300K). Quantum error correction has also been successfully demonstrated. This paves the way towards a scalable, error-corrected quantum computer. However, the manipulation and sensing of large-scale Qubit array with high fidelity are still facing many challenges of error management. One error mechanism is the dephasing of the coherent superposition states of Qubits, induced by the phase noise (PN) of microwave driving pulses [1]. For the X/Y axis rotation in the Bloch sphere, a phase error of 0.57° corresponds to a Qubit fidelity of 99.99% (Fig. 34.5.1) [2]. The cryogenic CMOS phase-locked loops (PLLs) in the pulse generator and reflectometry enjoy a $10\sim 100\times$ lower thermal noise, which mitigates the frequency/phase error. However, the cryogenic CMOS voltage-controlled oscillators (VCOs) inside the PLLs suffer from a surprisingly high flicker noise. This is due to the generation-recombination noise with varying relaxation time constant and the shifting trap density with energy. This work presents a calibration-free 12.8-to-16.5GHz cryogenic VCO on 65nm bulk CMOS process. Using an eight-shape head resonator, this VCO achieves 2 ^nd and 3 ^rd harmonic-resonance alignment for flicker noise suppression. Under 4.2K, a highest VCO figure-of-merit (FoM) of 202.3dBc/Hz, a temperature-invariant flicker noise corner frequency of $450\sim 950\text{kHz}$ and a relative bandwidth of 25.1% have been measured.