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.
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.
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.043712
Fully Programmable Spatial Photonic Ising Machine by Focal Plane Division
https://arxiv.org/abs/2410.10689
Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spins. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non von Neumann hardware.
Observation of 2D dam break flow and a gaseous phase of solitons in a photon fluid in PRL
We report the observation of a two-dimensional dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to two-dimensional (2D) nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D solitons gas in integrable systems. We measure the statistical features of this gaseous-like phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.
https://arxiv.org/abs/2409.18738
https://mathstodon.xyz/@nonlinearxwaves/113258813170717367
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.183801