We discuss quantum variational optimization of Ramsey interferometry with ensembles of N entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation.We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits.These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions.Optimization is defined relative to a cost function, which in the present study is the Bayesian mean squared error of the estimated phase for a given prior distribution; i.e., we optimize for a finite dynamic range of the interferometer.In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability.Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks.The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.While in the present work variationally optimized circuits are found with classical simulations, optimization can also be performed "on" the (physical) quantum sensor, also in regimes not accessible to classical computations and in the presence of imperfections.
Quantum sensing is an important application of emerging quantum technologies. We explore whether a hybrid system of quantum sensors and quantum circuits can surpass the classical limit of sensing. In particular, we use optimization techniques to search for encoder and decoder circuits that scalably improve sensitivity under given application and noise characteristics.Our approach uses a variational algorithm that can learn a quantum sensing circuit based on platform-specific control capacity, noise, and signal distribution. The quantum circuit is composed of an encoder which prepares the optimal sensing state and a decoder which gives an output distribution containing information of the signal. We optimize the full circuit to maximize the Signal-to-Noise Ratio (SNR). Furthermore, this learning algorithm can be run on real hardware scalably by using the "parameter-shift" rule which enables gradient evaluation on noisy quantum circuits, avoiding the exponential cost of quantum system simulation. We demonstrate up to 13.12x SNR improvement over existing fixed protocol (GHZ), and 3.19x Classical Fisher Information (CFI) improvement over the classical limit on 15 qubits using IBM quantum computer. More notably, our algorithm overcomes the decreasing performance of existing entanglement-based protocols with increased system sizes.
Variational quantum algorithms (VQAs) have emerged as a leading paradigm in near-term quantum computing, yet their performance can be hindered by the so-called barren plateau problem, where gradients vanish exponentially with system size or circuit depth. While most existing VQA research employs simple Gaussian or zero-initialization schemes, classical deep learning has long benefited from sophisticated weight initialization strategies such as Xavier, He, and orthogonal initialization to improve gradient flow and expedite convergence. In this work, we systematically investigate whether these classical methods can mitigate barren plateaus in quantum circuits. We first review each initialization's theoretical grounding and outline how to adapt the notions from neural networks to VQAs. We then conduct extensive numerical experiments on various circuit architectures and optimization tasks. Our findings indicate that while the initial heuristics, inspired by classical initialization, yield moderate improvements in certain experiments, their overall benefits remain marginal. By outlining a preliminary exploration plan in this paper, we aim to offer the research community a broader perspective and accessible demonstrations. Furthermore, we propose future research directions that may be further refined by leveraging the insights gained from this work.