Abstract:Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines. To better understand their working principle and optimize their performance, we analyze the dynamics during the ground state search of 2D Ising models with up to 1936 mutually coupled DOPOs. For r… Show more
“…3b). It is interesting to note here that these domain evaporation dynamics are likewise observed in DOPO-based CIMs 17,24 .Fig. 3Spin dynamics during a ground state search in a square lattice.…”
Section: Resultssupporting
confidence: 54%
“…Based on this, various types of CIMs have been proposed that implement Ising spin networks with bistable coherent optical states, such as coupled lasers 7,14 and degenerate optical parametric oscillators (DOPOs) 8 . Current state-of-the-art CIMs based on DOPOs have demonstrated their ability as global optimizers for various large-scale problems 11,15–17 . By taking advantage of the large bandwidth of optical systems, they can operate at high speed and have shown speed-ups over conventional algorithms 11,18 .…”
Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.
“…3b). It is interesting to note here that these domain evaporation dynamics are likewise observed in DOPO-based CIMs 17,24 .Fig. 3Spin dynamics during a ground state search in a square lattice.…”
Section: Resultssupporting
confidence: 54%
“…Based on this, various types of CIMs have been proposed that implement Ising spin networks with bistable coherent optical states, such as coupled lasers 7,14 and degenerate optical parametric oscillators (DOPOs) 8 . Current state-of-the-art CIMs based on DOPOs have demonstrated their ability as global optimizers for various large-scale problems 11,15–17 . By taking advantage of the large bandwidth of optical systems, they can operate at high speed and have shown speed-ups over conventional algorithms 11,18 .…”
Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.
“…As a comparison, the fiber-based DOPO system has a T sol = 3.3 ms for solving cubic MAX-CUT problems and T sol = 2.3 ms for dense MAX-CUT with N = 100 23 , suggesting that the spatial-multiplexing approach offers promise for accelerating the computing time of an Ising model. As the number of DOPOs in the network increases, the anneal time that corresponds to the pump turn-on time must be controlled to slow down the DOPO dynamics to prevent freeze-out effects that prevent the system from reaching the ground-state solution 23 , 35 . More specifically for our system of microresonator-based DOPOs, it has been reported elsewhere that the rate at which the DOPOs are tuned into resonance is a decisive parameter that determines the success probability of finding the ground-state solution (see Supplementary Note 8 ) 41 .…”
Section: Resultsmentioning
confidence: 99%
“…These demonstrations have utilized a time-multiplexed DOPO system using a 1-km-long fiber ring cavity to simulate the ground state of the Ising model 20 , 21 . In addition, extensive experimental and theoretical analysis has been done to characterize the potential performance of such systems 23 , 33 – 35 . Furthermore, alternative approaches towards a coherent Ising machine, such as opto-electronic oscillators with self-feedback 24 – 26 and spatial light modulation 27 , 28 , has been demonstrated and an approach using a dispersive optical bistability has been proposed 29 .…”
The need for solving optimization problems is prevalent in various physical applications, including neuroscience, network design, biological systems, socio-economics, and chemical reactions. Many of these are classified as non-deterministic polynomial-time hard and thus become intractable to solve as the system scales to a large number of elements. Recent research advances in photonics have sparked interest in using a network of coupled degenerate optical parametric oscillators (DOPOs) to effectively find the ground state of the Ising Hamiltonian, which can be used to solve other combinatorial optimization problems through polynomial-time mapping. Here, using the nanophotonic silicon-nitride platform, we demonstrate a spatial-multiplexed DOPO system using continuous-wave pumping. We experimentally demonstrate the generation and coupling of two microresonator-based DOPOs on a single chip. Through a reconfigurable phase link, we achieve both in-phase and out-of-phase operation, which can be deterministically achieved at a fast regeneration speed of 400 kHz with a large phase tolerance.
“…Borrowing the common terminology from condensed matter, a single parametric oscillator can be viewed as a classical two-level system (spin-1/2, or Ising spin). Based on this analogy, it has been recently suggested that coupled parametric oscillators can be used to simulate chains or networks of Ising spins [30][31][32][33][34][35][36][37][38][39][40]. The Ising simulation relies on the inherent mode competition and positive feedback within the oscillators to find the most efficient (coupled-mode) oscillation, which can reflect the groundstate configuration of the corresponding Ising model (under certain assumptions): A set of optical parametric oscillators can therefore represent a set of independent spin-1/2 systems, where coupling of the optical field between the oscillators gives rise to a coupled network of spins.…”
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -two coupled parametric oscillators, where the oscillators never reach a steady state, but show persistent, full-scale, coherent beats, whose frequency reflects the coupling properties and strength. We present a detailed theoretical and experimental study and show that this new dynamical regime appears over a wide range of parameters near the oscillation threshold and depends on the nature of the coupling (dissipative or energy preserving). Thus, a system of coupled parametric oscillators transcends the Ising description and manifests unique coherent dynamics, which may have important implications for coherent computation machines.
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