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Correlated quantum many-body phenomena in lattice models have been identified as a set of physically interesting problems that cannot be solved classically. Analog quantum simulators, in photonics and microwave superconducting circuits, have emerged as near-term platforms to address these problems. An important ingredient in practical quantum simulation experiments is the tomography of the implemented Hamiltonians—while this can easily be performed if we have individual measurement access to each qubit in the simulator, this could be challenging to implement in many hardware platforms. In this paper, we present a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.

High-quality sources of single photons are of paramount importance for quantum communication, sensing, and metrology. To these ends, resonantly excited two-level systems based on self-assembled quantum dots have recently generated widespread interest. Nevertheless, we have recently shown that for resonantly excited two-level systems, emission of a photon during the presence of the excitation laser pulse and subsequent re-excitation results in a degradation of the obtainable single-photon purity. Here, we demonstrate that generating single photons from self-assembled quantum dots with a scheme based on two-photon excitation of the biexciton strongly suppresses the re-excitation. Specifically, the pulse-length dependence of the multi-photon error rate reveals a quadratic dependence in contrast to the linear dependence of resonantly excited two-level systems, improving the obtainable multi-photon error rate by several orders of magnitude for short pulses. We support our experiments with a new theoretical framework and simulation methodology to understand few-photon sources.

Sources of non‐classical light are of paramount importance for future applications in quantum science and technology such as quantum communication, quantum computation and simulation, quantum sensing, and quantum metrology. This Review is focused on the fundamentals and recent progress in the generation of single photons, entangled photon pairs, and photonic cluster states using semiconductor quantum dots. Specific fundamentals which are discussed are a detailed quantum description of light, properties of semiconductor quantum dots, and light–matter interactions. This includes a framework for the dynamic modeling of non‐classical light generation and two‐photon interference. Recent progress is discussed in the generation of non‐classical light for off‐chip applications as well as implementations for scalable on‐chip integration.