We investigate the dynamics of multi-mode optical systems driven by two-photon processes and subject to non-local losses, incorporating quantum noise at the Gaussian level. Our findings show that the statistics from a single Gaussian quantum trajectory exhibit emergent thermal equilibrium governed by an Ising Hamiltonian encoded in the dissipative coupling between modes. The driving strength sets the system’s effective temperature relative to the oscillation threshold. Given the ultra-short time scales typical of all-optical devices, our study demonstrates that such multi-mode optical systems can operate as ultra-fast Boltzmann samplers, paving the way toward the realization of efficient hardware for combinatorial optimization, with promising applications in machine learning and beyond.
Category: Quantum Physics
Non-Abelian Quantum Walk and Entanglement
https://arxiv.org/abs/2412.02429
Non-Abelian evolution is a landmark in modern theoretical physics. However, whether non-commutative dynamics significantly impact the control of entanglement and transport in quantum systems is an open question. Here, we propose to utilize non-Abelian Thouless pumping in one-dimensional discrete-time quantum walks in lattices with degenerate Bloch bands. We show how the interplay of non-commutativity and topology enables geometrically protected quantum coins and shift operators. Different classes of tunable protected quantum walks arise by composing different non-Abelian pumping cycles. Surprisingly, the walks break parity symmetry and generate a dynamic process described by a Weyl-like equation. The amount of entanglement can be varied by acting on the initial conditions. The asymptotic statistical distribution and features are determined by closed-form analytical expressions and confirmed numerically.
Mathstodon https://mathstodon.xyz/@nonlinearxwaves/113610374997139049
Quantum Hyperspins: A New Schroedinger’s Cat ?
https://arxiv.org/abs/2411.05728
We report on the emergence of a highly non-classical collective behavior in quantum parametric oscillators, which we name quantum hyperspin, induced by a tailored nonlinear interaction. This is the second quantized version of classical multidimensional spherical spins, as XY spins in two dimensions and Heisenberg spins in three dimensions. In the phase space, the quantum hyperspins are represented as spherical shells whose radius scales with the number of particles in a way such that it cannot be factorized even in the limit of large particle number. We show that the nonlinearly coupled quantum oscillators form a high-dimensional entangled state that is surprisingly robust with respect to the coupling with the environment. Such a behavior results from a properly engineered reservoir. Networks of entangled quantum hyperspins are a new approach to quantum simulations for applications in computing, Ising machines, and high-energy physics models. From first principles through ab initio numerical simulations, we analyze the properties of quantum hyperspins, including the interplay of entanglement and coupling frustration.
Localization in quantum field theory (a review)
We review the localization issue in quantum field theory and detail the nonrelativistic limit. Three distinct localization schemes are examined: the Newton–Wigner, the algebraic quantum field theory, and the modal scheme. Among these, the algebraic quantum field theory provides a fundamental concept of localization rooted in its axiomatic formulation. In contrast, the Newton–Wigner scheme draws inspiration from the Born interpretation, applying mainly to the nonrelativistic regime. The modal scheme, relying on the representation of single particles as positive frequency modes of the Klein–Gordon equation, is found to be incompatible with the algebraic quantum field theory localization.
This review delves into the distinctive features of each scheme, offering a comparative analysis. A specific focus is placed on independence between state preparations and observable measurements in spacelike-separated regions. Notably, localization in algebraic quantum field theory violates this independence due to the Reeh–Schlieder theorem. Drawing parallels with the quantum teleportation protocol, it is argued that causality remains unviolated. Additionally, we consider the nonrelativistic limit of quantum field theory, revealing the emergence of the Born scheme as the fundamental concept of localization. Consequently,
the nonlocality associated with the Reeh–Schlieder theorem is shown to be suppressed under nonrelativistic conditions.
https://doi.org/10.1016/j.revip.2024.100095
(see also Localization in Quantum Field Theory for Inertial and Accelerated Observers)
Non-Gaussianity in the quantum parametric oscillator
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.063519
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 (electrooptical) 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 ab initio 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 a first-principles method based on exact diagonalization. Non-Gaussianity is quantified by means of three different metrics: the Hilbert-Schmidt distance, quantum relative entropy, and photon distribution. Our findings reveal a nontrivial interplay between parametric drive and applied field: (i) the increasing pump monotonically enhances non-Gaussianity and (ii) the increasing field first sharpens non-Gaussianity, and then restores the Gaussian character of the state when above a threshold value. We also report a first-principles computation in the Fock space of the distance from the mixture of coherent states, a strongly nonclassical behavior that can play a significant role in the quantum parallel search for optimization.
See also arXiv