Implementation of a periodic quantum clock based on coherent feedback*

Clocks play an integral part in a variety of applications but have recently drawn interest in the context of fundamental questions such as the connection between time and thermodynamics and the limits of timekeeping. From a thermodynamic point of view, a clock is a nonlinear dissipative system that relies on the increase in entropy to keep track of time. It was recently shown that the resolution of a periodic clock is directly proportional to the energy dissipated per cycle. Therefore, a good clock, both classical and quantum, necessitates a high energy dissipation rate.

We realise a new type of periodic quantum clock based on coherent feedback between two coupled resonators. As the feedback is not done via readout, there is no measurement-induced noise, allowing for the characterisation of the system’s inherent quantum noise and its effects on the clock's thermodynamical and metrological properties.

We implement the coherent feedback clock on a superconducting circuit consisting of two coupled high-Q coplanar resonators, where one is rendered nonlinear by a Josephson junction embedded in the centre conductor. This provides the nonlinearity necessary for a periodic clock. We show the existence of limit cycles in the low-power regime, where quantum fluctuations become the dominant noise source, and demonstrate the system's applicability as a new type of quantum clock. Specifically, we show the relation between dissipated energy and clock resolution, and how quantum fluctuations in the feedback cycle affect the clock tick accuracy.

In addition, our clock is a candidate for the implementation of spiking neural networks, a novel deep learning model that mimics the behaviour of biological neurons and shows promising advantages in dynamic learning tasks compared to conventional perceptron models.