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Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum-enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. In this work we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a *programmable quantum sensor* operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45(1), outperforming conventional spin-squeezing with a factor of 1.87(3). Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59(6) compared to traditional methods not employing entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to `self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be employed without prior knowledge of the device or its noise environment., Comment: Main: 10 pages including Methods, 4 figures. Supplementary Material: 6 pages, 2 figures, separate references

A digital quantum simulation of a lattice gauge theory is performed on a quantum computer that consists of a few trapped-ion qubits; the model simulated is the Schwinger mechanism, which describes the creation of electron–positron pairs from vacuum. Quantum simulations promise to provide solutions to problems where classical computational methods fail. An example of a challenging computational problem is the real-time dynamics in gauge theories — field theories paramount to modern particle physics. This paper presents a digital quantum simulation of a lattice gauge theory on a quantum computer consisting of a few qubits comprising trapped calcium controlled by electromagnetic fields. The specific model that the authors simulate is the Schwinger mechanism, which describes the creation of electron–positron pairs from vacuum. As an early example of a particle-physics theory simulated with an atomic physics experiment, this could potentially open the door to simulating more complicated and otherwise computationally intractable models. Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons1,2. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator3,4, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented5,6,7. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model8,9) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism10,11, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron–positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields12 in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture13. We explore the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.