Generating Functions and Automatic Differentiation for Photon-Number-Resolved Simulations with Multimode Gaussian States

• URL: http://arxiv.org/abs/2209.05330v1
• Date: Mon, 12 Sep 2022 15:39:46 GMT
• Title: Generating Functions and Automatic Differentiation for Photon-Number-Resolved Simulations with Multimode Gaussian States
• Authors: Erik Fitzke, Florian Niederschuh, and Thomas Walther
• Abstract summary: A simple and versatile method to simulate the photon statistics of multimode Gaussian states is presented. The generating functions for the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics are derived. Numerical results are obtained by using the machine learning framework PyTorch for automatic differentiation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A simple and versatile method to simulate the photon statistics of multimode Gaussian states based on automatic differentiation of generating functions is presented. The generating functions for the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics are derived. Related expressions for multimode photon-added and photon-subtracted Gaussian states are presented. Numerical results are obtained by using the machine learning framework PyTorch for automatic differentiation. It is demonstrated that this approach is well suited for practical simulations of the photon statistics of quantum optical experiments in realistic scenarios with low photon numbers, in which various sources of imperfections have to be taken into account. As an example, the detection probabilities of a recent multipartite time-bin coding quantum key distribution setup are determined and compared with the corresponding experimental values.

Related papers

• Realistic photon-number resolution in Gaussian Boson Sampling [0.0]
  Gaussian Boson Sampling (GBS) is the model of non-universal quantum computation. We have derived the photocounting probability distribution in the GBS schemes. We have considered a GBS validation technique involving detectors with realistic photon-number resolution.
  arXiv  Detail & Related papers  (2024-03-05T18:20:59Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• Towards Accurate Post-training Quantization for Diffusion Models [73.19871905102545]
  We propose an accurate data-free post-training quantization framework of diffusion models (ADP-DM) for efficient image generation. Our method outperforms the state-of-the-art post-training quantization of diffusion model by a sizable margin with similar computational cost.
  arXiv  Detail & Related papers  (2023-05-30T04:00:35Z)
• Quantum computing of analytical functions by linear optics methods [0.0]
  We propose a model for computing of a certain set of analytical functions based on estimating the output distribution of multiphoton outcomes in an optical scheme. The potential of optical quantum computing based on non-classical states a certain parity can be expanded.
  arXiv  Detail & Related papers  (2023-03-22T19:56:51Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Gaussian boson sampling with partial distinguishability [0.0]
  We investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.
  arXiv  Detail & Related papers  (2021-05-20T08:17:51Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• Single photon randomness originating from the symmetry of dipole emission and the unpredictability of spontaneous emission [55.41644538483948]
  Quantum random number generation is a key ingredient for quantum cryptography and fundamental quantum optics. We experimentally demonstrate quantum random number generation based on the spontaneous emission process. The scheme can be extended to random number generation by coherent single photons with potential applications in solid-state based quantum communication at room temperature.
  arXiv  Detail & Related papers  (2021-02-18T14:07:20Z)
• Boson sampling with random numbers of photons [0.0]
  We show a novel boson sampling scheme where the probability of success increases instead of decreasing. This is achieved by sampling at the same time in the number of occupied input ports and the number of input photons per port.
  arXiv  Detail & Related papers  (2020-06-05T17:53:07Z)
• Fast approximations in the homogeneous Ising model for use in scene analysis [61.0951285821105]
  We provide accurate approximations that make it possible to numerically calculate quantities needed in inference. We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field. The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
  arXiv  Detail & Related papers  (2017-12-06T14:24:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.