We are developing coupled oscillator arrays for closed-loop perception and control. The same dynamical model is tested first in simulation and room-temperature analog hardware, with a roadmap toward cryogenic and superconducting implementations.
That is active inference, expressed here as a physical control loop. A pumped oscillator provides a controllable nonlinear substrate; the coupling matrix encodes priors, constraints, and action paths. The current work compares the same mathematical model across simulation, room-temperature analog hardware, and a cryogenic fabrication roadmap.
The goal is not zero error. A system at zero error has stopped listening. The goal is useful error: structured, causal, and reafferent. It is the same region a musician lives in when a take has feel, predictions good enough to hold coherence, wrong enough to create momentum.
Prototype model: N equals sixteen coupled parametric oscillators. The coupling matrix can be complex valued: the real part dissipative, the imaginary part reactive. In simulation, learned topologies are stored as candidate coupling matrices for hardware evaluation.
In this benchmark, greedy and structured ablations do not beat passive. Cut the action channel and the improvement collapses, pointing to the closed-loop contribution.
The action variable is the homodyne readout phase, selected by expected information gain. Scrambling the action-to-sensation link degrades convergence, matching the causal signature seen in the classical loop.
Title: A Hybrid Superconducting Architecture for Physically Embodied Active Inference: Classical and Quantum Operating Regimes of a Coupled JPO Array
We propose a hybrid superconducting architecture in which active inference [1] is implemented directly in cryogenic hardware across two operating regimes. The system comprises a Josephson Parametric Oscillator (JPO) resonator array coupled to an Adiabatic Quantum-FluxParametron (AQFP) logic fabric [2], with a SQUID-based flux-counting ADC providing environmental input referenced to Φ₀ and photonic cryogenic interconnects providing galvanic isolation between temperature stages.
In the classical regime, the JPO array operates above the parametric threshold at 4.2 K. Each resonator self-oscillates; quantum vacuum fluctuations seed phase selection at bifurcation [3]. Nonlinear inter-resonator coupling produces Kuramoto-like phase synchronisation whose collective configuration encodes a distributed latent state. A designed Q-factor hierarchy provides intrinsic temporal filtering: high-Q resonators encode slowly varying context; low-Q resonators track rapid transients. Learned coupling strengths, stored as persistent superconducting bias currents updated by the AQFP fabric, constitute the trainable parameters of the generative model. The AQFP fabric provides GHz-clocked deterministic logic for feature extraction, prediction-error accumulation, parameter-update primitives, and action formatting, while the effective closed-loop rate is set by the sensory and readout bandwidths. In the quantum regime, the same array operates below threshold at millikelvin temperatures, where a 5 GHz mode has thermal occupancy ranging from approximately 4 × 10⁻¹¹ at 10 mK to 8 × 10⁻³ at 50 mK, with n_th ≈ 6 × 10⁻⁶ at 20 mK.. Bath- mediated two-mode squeezing between resonator pairs encodes prior precision and prediction-error geometry in the quadrature correlations of the quantum state. Engineered Lindblad dissipators define taskdependent steady-state priors, while driven dissipative evolution provides a physical analogue of gradient flow on variational free energy. Homodyne readout aligned to the squeezed quadrature provides prediction-error signals at sensitivities below the standard quantum limit. The parametric threshold provides a control parameter, enabling dynamic selection between classical phase-locking and quantum-correlated inference per task. We identify a structural correspondence between the bias tone in analogue magnetic tape, the AC excitation clock in AQFP logic, and the encoding of priors in active inference: in each case, a sustained oscillation prepares a physical substrate for information-bearing interaction without itself specifying the output. The demonstration platform, an autonomous musical instrument coupled via photonic interconnects to a room-temperature analogue signal chain, provides a real-time test of dynamic criticality maintenance near the Kuramoto synchronisation transition. The architecture generalises to coupled dynamical systems requiring continuous state estimation and low-latency adaptive control, including cryogenic signal processing at the quantum limit. References [1] K. Friston, "The free-energy principle: a unified brain theory?" Nature Reviews Neuroscience, vol. 11, pp. 127-138, 2010. [2] N. Takeuchi et al., "Adiabatic quantum-flux-parametron: a tutorial review," IEICE Trans. Electron., vol. E105C, pp. 251-263, 2022. [3] Z. Wang et al., "Josephson parametric oscillators for quantum information," Applied Physics Letters, vol. 117, 2020If you are a musician, a lab, an investor, or a builder who reads this and recognises something useful, write to us.