Heisingberg

Publications

Photon liquefaction in time

We provide a mechanism to imprint local temporal correlations in photon streams which have the same character as spatial correlations in liquids. Usual single-photon emitters correspond, in this picture, to a (temporal) gas while uncorrelated light is the ideal gas. We argue that good single-photon sources are those that exhibit such temporal liquid features, i.e., with a plateau for their short-time correlations (as opposed to a linear dependence) and oscillations at later times, which is a direct manifestation of photon time-ordering. We obtain general, closed-form analytical expressions for the second-order coherence function of a broad family of “liquid light” which can be arbitrarily correlated, though never completely crystallized.

Spatial correlations of vortex quantum states

We study spatial correlations of vortices in different quantum states or with Bose or Fermi statistics. This is relevant for both optical vortices and condensed-matter ones such as microcavity polaritons, or any platform that can prepare and image fields in space at the few-particle level. While we focus on this particular case for illustration of the formalism, we already reveal unexpected features of spatial condensation whereby bosons exhibit a bimodal distribution of their distances which places them farther apart than fermions in over 40% of the cases, or on the opposite conceal spatial correlations to behave like coherent states. Such experiments upgrade in the laboratory successful techniques in uncontrolled extreme environments (stars and nuclei).

Benchmarking the optimization optical machines with the planted solutions

We introduce universal, easy-to-reproduce generative models for the QUBO instances to differentiate the performance of the hardware/solvers effectively. Our benchmark process extends the well-known Hebb’s rule of associative memory with the asymmetric pattern weights. We provide a comprehensive overview of calculations conducted across various scales and using different classes of dynamical equations. Our aim is to analyze their results, including factors such as the probability of encountering the ground state, planted state, spurious state, or states falling outside the predetermined energy range. Moreover, the generated problems show additional properties, such as the easy-hard-easy complexity transition and complicated cluster structures of planted solutions. Our method establishes a prospective platform to potentially address other questions related to the fundamental principles behind device physics and algorithms for novel computing machines.

Classical vs Quantum annealing and manifold reduction in soft-spin minimizers of Ising Hamiltonians

We investigate the minimization of the Ising Hamiltonians, comparing the dynamics of semi- classical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a M¨obius graph evolves with increased annealing parameters. Our findings indicate that these semi-classical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the ‘manifold reduction’ method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian’s energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from a blend of classical and quantum annealing techniques.

Macroscopic noise amplification by asymmetric dyads in non-Hermitian optical systems for generative diffusion models

A new generation of sensors, hardware random number generators, and quantum and classical signal detectors are exploiting strong responses to external perturbations or system noise. Here, we study noise amplification by asymmetric dyads in freely expanding non-Hermitian optical systems. We show that modifications of the pumping strengths can counteract bias from natural imperfections of the system’s hardware, while couplings between dyads lead to systems with non-uniform statistical distributions. Our results suggest that asymmetric non-Hermitian dyads are promising candidates for efficient sensors and ultra-fast random number generators. We propose that the integrated light emission from such asymmetric dyads can be efficiently used for an analog all-optical degenerative diffusion models of machine learning to overcome the digital limitations of such models in processing speed and energy consumption.

Published in Physical Review Letters

Beyond Digital: harnessing analog hardware for machine learning

A remarkable surge in utilizing large deep-learning models yields state-of-the-art results in a variety of tasks. Recent model sizes often exceed billions of parameters, underscoring the importance of fast and energy-efficient processing. The significant costs associated with training and inference primarily stem from the constrained memory bandwidth of current hardware and the computationally intensive nature of these models. Historically, the design of machine learning models has predominantly been guided by the operational parameters of classical digital devices. In contrast, analog computations have the potential to offer vastly improved power efficiency for both inference and training tasks. This work details
several machine-learning methodologies that could leverage existing analog hardware infrastructures. To foster the development of analog hardware-aware machine learning techniques, we explore both optical and electronic hardware configurations suitable for executing the fundamental mathematical operations inherent to these models. Integrating analog hardware with innovative machine learning approaches may pave the way for cost-effective AI systems at scale.

Vector Ising Spin Annealer for Minimizing Ising Hamiltonians

We introduce the Vector Ising Spin Annealer (VISA), a framework in gain-based computing that harnesses light-matter interactions to solve complex optimization problems encoded in spin Hamiltonians. Traditional driven-dissipative systems often select excited states due to limitations in spin movement. VISA transcends these constraints by enabling spins to operate in a three-dimensional space, offering a robust solution to minimize Ising Hamiltonians effectively. Our comparative analysis reveals VISA’ s superior performance over conventional single-dimension spin optimizers, demonstrating its ability to bridge substantial energy barriers in complex landscapes. Through detailed studies on cyclic and random graphs, we show VISA’s proficiency in dynamically evolving the energy landscape with time-dependent gain and penalty annealing, illustrating its potential to redefine optimization in physical systems.