Strinati, Marcello

Date:   Tuesday, May 11, 2021
Time:   10:00
Place:   scheduled Zoom meeting
Host:    Oded Zilberberg

Coupled parametric oscillators: Coherent Ising machines and beyond

Marcello Strinati
Bar-Ilan University, Israel

The parametric oscillator (PO) is a fundamental type of oscillator, with applications in several fields of modern physics ranging from classical
mechanics to quantum optics. A single degenerate PO is a prototype example of period-doubling instability. When an external pump drives the oscillator to parametric resonance, the PO oscillates with frequency locked to half the frequency of the drive, and admits only two values of the phase of the oscillation: Either in-phase (phase = 0) or out of phase (phase = \pi) with respect to some phase reference imposed by the pump. Due to such a binary nature of the oscillation's phase, a PO can be used to simulate a classical Ising spin, whose states "up" and "down" are represented by the two admitted values "0" or "\pi" of the oscillation's phase.

This simple property has been recently exploited to realize networks of coupled parametric oscillators to simulate the dynamics of coupled Ising spins. This network, called coherent Ising machine (CIM), is envisioned being a new, promising heuristic solver of the classical Ising model: Under certain assumptions, mode competition should steer the network to a steady state that, in terms of the phases of the POs, is the ground state of the corresponding Ising model that the coupling matrix of the system encodes.

While a number of numerical and experimental works have tested the validity of PO networks and Ising solvers for specific Ising models, we have recently shown that the dynamics of coupled POs can be in general much richer than the dynamics of coupled Ising spins [1-3], even in those regimes of parameters that are relevant to CIMs. These results lead us to discern those regimes of parameters where the PO network is intrinsically not an Ising solver, from those regimes where it may work as a probabilistic CIM [4]. In this talk, we will discuss the coherent dynamics of coupled POs beyond the Ising picture, and discuss to what extent coupled POs can be used as heuristic Ising solvers.

[1] L. Bello, MCS, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 123, 083901 (2019)
[2] MCS, L. Bello, A. Pe'er, and E. G. Dalla Torre, Phys. Rev. A 100, 023835 (2019)
[3] MCS, I. Aharonovich, S. Ben-Ami, E. G. Dalla Torre, L. Bello, and A. Pe'er, New. J. Phys. 22, 085005 (2020)
[4] MCS, L. Bello, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 126, 143901 (2021)