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Neutral atom arrays have become a promising platform for quantum computing, especially the field programmable qubit array (FPQA) endowed with the unique capability of atom movement. This feature allows dynamic alterations in qubit connectivity during runtime, which can reduce the cost of executing long-range gates and improve parallelism. However, this added flexibility introduces new challenges in circuit compilation. Inspired by the placement and routing strategies for FPGAs, we propose to map all data qubits to fixed atoms while utilizing movable atoms to route for 2-qubit gates between data qubits. Coined flying ancillas, these mobile atoms function as ancilla qubits, dynamically generated and recycled during execution. We present Q-Pilot, a scalable compiler for FPQA employing flying ancillas to maximize circuit parallelism. For two important quantum applications, quantum simulation and the Quantum Approximate Optimization Algorithm (QAOA), we devise domain-specific routing strategies. In comparison to alternative technologies such as superconducting devices or fixed atom arrays, Q-Pilot effectively harnesses the flexibility of FPQA, achieving reductions of 1.4x, 27.7x, and 6.3x in circuit depth for 100-qubit random, quantum simulation, and QAOA circuits, respectively. 

We study a model-free federated linear quadratic regulator (LQR) problem where M agents with unknown, distinct yet similar dynamics collaboratively learn an optimal policy to minimize an average quadratic cost while keeping their data private. To exploit the similarity of the agents' dynamics, we propose to use federated learning (FL) to allow the agents to periodically communicate with a central server to train policies by leveraging a larger dataset from all the agents. With this setup, we seek to understand the following questions: (i) Is the learned common policy stabilizing for all agents? (ii) How close is the learned common policy to each agent's own optimal policy? (iii) Can each agent learn its own optimal policy faster by leveraging data from all agents? To answer these questions, we propose a federated and model-free algorithm named FedLQR. Our analysis overcomes numerous technical challenges, such as heterogeneity in the agents' dynamics, multiple local updates, and stability concerns. We show that FedLQR produces a common policy that, at each iteration, is stabilizing for all agents. We provide bounds on the distance between the common policy and each agent's local optimal policy. Furthermore, we prove that when learning each agent's optimal policy, FedLQR achieves a sample complexity reduction proportional to the number of agents M in a low-heterogeneity regime, compared to the single-agent setting. 

Theory predicts that rising CO₂increases global photosynthesis, a process known as CO₂fertilization, and that this is responsible for much of the current terrestrial carbon sink. The estimated magnitude of the historic CO₂fertilization, however, differs by an order of magnitude between long-term proxies, remote sensing-based estimates and terrestrial biosphere models. Here we constrain the likely historic effect of CO₂on global photosynthesis by combining terrestrial biosphere models, ecological optimality theory, remote sensing approaches and an emergent constraint based on global carbon budget estimates. Our analysis suggests that CO₂fertilization increased global annual terrestrial photosynthesis by 13.5 ± 3.5% or 15.9 ± 2.9 PgC (mean ± s.d.) between 1981 and 2020. Our results help resolve conflicting estimates of the historic sensitivity of global terrestrial photosynthesis to CO₂and highlight the large impact anthropogenic emissions have had on ecosystems worldwide.