We study the problem of localization in Quantum Field Theory (QFT) from the point of view of inertial and accelerated experimenters. We consider the Newton-Wigner, the Algebraic Quantum Field Theory (AQFT), and the modal localization schemes, which are, respectively, based on the orthogonality condition for states localized in disjoint regions of space, on the algebraic approach to QFT and on the representation of single particles as positive frequency solution of the field equation. We show that only the AQFT scheme obeys causality and physical invariance under differentomorphisms. Then, we consider the nonrelativistic limit of quantum fields in the Rindler frame. We demonstrate the convergence between the AQFT and the modal scheme, and we show the emergence of the Born notion of localization of states and observables. Also, we study the scenario in which an experimenter prepares states over a background vacuum by means of nonrelativistic local operators, and another experimenter carries out nonrelativistic local measurements in a different region. We find that the independence between preparation of states and measurements is not guaranteed when both experimenters are accelerated and the background state is different from Rindler vacuum, or when one of the two experimenters is inertial.
Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called “dimensional annealing” to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.
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Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical realization of hybrid (electro-optical) or all-optical Ising machines, but also the demonstration of quantum-inspired algorithms boosting their performances. To date, the use of the quantum nature of parametrically generated light as a further resource for computation represents a major open issue. A key quantum feature is the non-Gaussian character of the system state across the oscillation threshold. In this paper, we perform an extensive analysis of the emergence of non-Gaussianity in the single quantum OPO with an applied external field. We model the OPO by a Lindblad master equation, which is numerically solved by an ab initio method based on exact diagonalization. Non-Gaussianity is quantified by means of three different metrics: Hilbert-Schmidt distance, quantum relative entropy, and photon distribution. Our findings reveal a nontrivial interplay between parametric drive and applied field: (i) Increasing pump monotonously enhances non-Gaussianity, and (ii) Increasing field first sharpens non-Gaussianity, and then restores the Gaussian character of the state when above a threshold value.
The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy of network optimization that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension.
Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability of success in finite-size scaling. We show that by exploiting high dimensional embedding of the Ising Hamiltonian and subsequent dimensional annealing, the drop is counteracted by an exponential improvement in the performance. Our analysis relies on extensive statistics of the convergence dynamics by high-performance computing. We propose a realistic experimental implementation of the new annealing device by off-the-shelf coherent Ising machine technology. The hyperscaling heuristics can also be applied to other quantum or classical Ising machines by engineering nonlinear gain, loss, and non-local couplings.
Hyperscaling in the coherent hyperspin machine