A class of analog optimisation computer that solves Ising-model problems by letting the physics of an oscillator network relax to its ground state. Same maths as a Stochastic / Ising Machines (the energy function is identical), but the dynamics are deterministic (parametric oscillators settling into a phase configuration) rather than stochastic (sampled bit flips). The substrate-class can be optical, electrical, or RF.
Architecture (canonical)
The dynamics follow the slow-envelope ODE from Wang and Roychowdhury OIM 2019:
dA/dt = −Γ A + p(t) conj(A) + J A − α |A|² A + noise- A: complex envelope of each oscillator
- Γ: damping (drives the system toward zero)
- p(t): parametric pump (drives gain, eventually binarises phases to ±1)
- J: coupling matrix (encodes the Ising problem)
- α: nonlinear saturation
- noise: thermal / quantum noise
The parametric pump binarises the phases (each oscillator settles to ±1), the J matrix encodes the problem, and the array’s stable phase configuration encodes the ground-state spin configuration — the answer.
Substrate classes
Key distinction vs related computer classes
- CIM vs p-computer (Stochastic / Ising Machines): CIM is deterministic, the system has one natural ground state and relaxes there. p-computer is stochastic, the system samples many configurations and you collect statistics. Speed regime differs: CIM in nanoseconds, p-computer in microseconds to milliseconds for the same Ising problem.
- CIM vs quantum annealer: Same problem class (Ising minimisation), different physics. Quantum annealer exploits tunneling through energy barriers; CIM uses dissipation to drive to the lowest stable phase configuration. Quantum annealers need cryogenics; CIM doesn’t.
- CIM vs digital annealer (Toshiba SBM, Fujitsu DA): Digital annealers simulate the Ising dynamics on classical hardware (FPGA / GPU cluster) at millisecond scale. CIM runs the dynamics in physics at nanosecond scale.
- CIM vs Thermodynamic Computing: Thermodynamic computers (Extropic, Normal Computing) use thermal noise as the compute resource — stochastic sampling. CIM uses dissipation to drive to a deterministic minimum.
The calibration problem
The historical analog computing graveyard (Mythic AI, HP Labs memristor, Lightelligence) is largely populated by companies that died on this gap. See FDTD-to-Hardware Calibration Wall.