About CIM

See also: P. L. McMahon, To Crack the Toughest Optimization Problems, Just Add Lasers (2018)
See also: Y. Yamamoto, Coherent Ising machines — optical neural networks operating at the quantum limit (2017)
See also: A. Lucas, Ising formulation of many NP problems (2014)

The CIM architecture [1] cannot be viewed simply as a neural network or an annealer working on principles of thermalization or the quantum adiabatic theorem. It is inspired by all of these predecessors, however, and is designed to build on their strengths while avoiding some key weaknesses. Its operating principle [1,2] is fundamentally different from that of previous hardware approaches and of all current algorithms for performing optimization on classical computers.

A conceptually straightforward realization of the CIM architecture can be constructed as an optically pumped network of coupled degenerate optical parametric oscillators (DOPOs) [1,3]. The coupling coefficients implemented among the constitutent DOPOs encodes a specific Ising Hamiltonian. The phase portrait of the ntework — a driven dissipative dynamical system — undergoes bifurcations as the pump strength is increased from zero. Theoretically [4], the equilibrium states of an ideal CIM realization just above its lowest-lying bifurcation coincide with ground states of the Ising Hamiltonian encoded by the coupling coefficients among its constituent DOPOs. While we do not yet fully understand the physical dynamics of the “search process” by which the network re-equilibrates when a bifurcation point is crossed, and many questions remain regarding the quantitative impact of implementation errors and exogenous noise, currently laboratory implementations achieve impressive computational performance.

Recent studies [5] have investigated the computational performance of current prototypes [6] and near-term-realizable variants [7] of CIM, relative to conventional computing approaches and emerging quantum platforms. Such results are motivating intensive investigations of CIM theory and implementations by a growing community of researchers, which held its first international conference in March, 2019 with plans for a follow-up meeting in July, 2020 (details coming soon).


  1. Z. Wang, A. Marandi, K. Wen, R. L. Byer and Y. Yamamoto, “Coherent Ising machine based on degenerate optical parametric oscillators,” Phys. Rev. A 88, 063853 (2013).
  2. Y. Haribara, S. Utsunomiya and Y. Yamamoto, “Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network,” Entropy 18, 151 (2016).
  3. A. Marandi, Z. Wang, K. Takata, R. L. Byer and Y. Yamamoto, “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine,” Nature Photonics 8, 937 (2014).
  4. T. Leleu, Y. Yamamoto, S. Utsunomiya and K. Aihara, “Combinatorial optimization using dynamical phase transitions in driven-dissipative systems,” Phys. Rev. E 95, 022118 (2017).
  5. R Hamerly et al., “Experimental investigation of performance differences between coherent Ising machines and a quantum annealer,” Science Advances 5, eaau0823 (2019).
  6. P. L. McMahon et al., “A fully programmable 100-spin coherent Ising machine with all-to-all connections,” Science 354, 614 (2016).
  7. T. Leleu, Y. Yamamoto, P. L. McMahon and K. Aihara, “Destabilization of Local Minima in Analog Spin Systems by Correction of Amplitude Heterogeneity,” Phys. Rev. Lett. 122, 040607 (2019).