A programmable hybrid digital chemical information processor based on the Belousov-Zhabotinsky reaction

As transistor miniaturization approaches physical limits and power dissipation constraints, alternative computing paradigms based on physical and chemical processes are being explored. Quantum computing promises advantages but currently faces scalability and error-correction challenges. Other architectures map computation onto physical phenomena, including Boolean circuits realized in materials, reaction–diffusion systems, and neuromorphic devices. However, many such systems are either problem-specific or difficult to program in a general way. The challenge is to create a programmable platform that can exploit chemical substrates while remaining digitally addressable. Building on concepts from heterotic and physical computation, the authors propose a hybrid electronic–chemical architecture that unites analogue chemical dynamics with digitally controlled finite state logic, using the Belousov–Zhabotinsky (BZ) oscillatory reaction as the analogue substrate and a digital control/readout loop to realize programmable information processing with a tunable probabilistic component.

The paper situates its contribution within unconventional computation: chemical reaction–diffusion computing, DNA computing, optical and photonic systems, neuromorphic devices, and reservoir computing. Prior efforts have mapped computational primitives to physical phenomena, designed Boolean circuits in materials, or used AI to discover architectures. Reaction–diffusion and other chemical systems can compute but are often hard to program generally; DNA computing tends to be problem-specific; reservoir computing may suffer from poorly controlled local rules; quantum and optical systems show promise but face scalability, cost, and complexity challenges. The authors also reference heterotic computing and the framework of physical computation, emphasizing combining substrates to leverage their natural strengths. Their earlier programmable chemical computers and light-sensitive BZ systems provide precedent for controllable chemical information processing that this work extends with a hybrid programmable architecture.

Platform: A digitally programmable array of interconnected BZ reaction cells (1D and 2D grids) is implemented in a 3D-printed reactor array. Each cell has a central stirrer driven by a DC motor with magnets; interfacial stirrers at cell boundaries enable tunable nearest-neighbour coupling via hydrodynamic mass transfer. Motor speeds are controlled by PWM from microcontrollers; all motors are individually addressable. A camera records oscillatory color changes. Chemistry: The BZ reaction mixture (malonic acid, potassium bromate, ferroin catalyst, sulfuric acid) is prepared in stock solutions and mixed via syringe pumps into a mixing chamber (constant stirring at 140 RPM), then delivered to the reactor array. As the reaction proceeds and fuel (malonic acid) is consumed, oscillation amplitudes decrease over time. State definition and clocking: Because BZ oscillations are sensitive to initial conditions and timing, cells exhibit phase drift; weak global coupling through interfacial stirrers establishes a SYNC clock to prevent decoherence and synchronize oscillations. Chemical states are discretized with a CNN trained on labeled images to classify time-dependent color states as red, light blue, or blue. A recognition finite state machine (rFSM) maps CNN sequences to digital chemical states CS ∈ {0,1}: weak wave patterns (e.g., RLB→R) map to CS=0; strong oscillation cycles (R→LB→B→LB→R) map to CS=1. Low-amplitude oscillations (generated by pulsed stirring) represent CS=0; high-amplitude continuous stirring represents CS=1. Hybrid loop: Four coupled state machines operate per loop: C (probabilistic chemical evolution in analogue domain), T (analogue-to-digital transfer via CNN/rFSM), D (deterministic digital FSM that reads CS and outputs actuator states), and P (digital-to-analogue via PWM on cell and interfacial stirrers). The loop iterates synchronously on the chemical clock. Deterministic mode enforces one-to-one mapping between PWM and CS; probabilistic mode leverages nonlinear hysteresis and nearest-neighbour coupling so that multiple PWM settings can yield stochastic CS outcomes. 1D and 2D CCA: Elementary CA rules (e.g., Rule 30, 110, 250) are instantiated deterministically by mapping CA state to cell PWM without interfacial coupling. 1D chemical cellular automata (1D-CCA) introduce interfacial PWM to enable probabilistic behaviour; rules are defined by two components {C_rule, f_rule} updating the cell PWM based on neighbour CS and the two interfacial PWMs based on adjacent cell pairs. A phenomenological probabilistic model captures deviations from one-to-one mappings and simulates emergent patterns. 2D-CCA and Chemits: Extending to 2D with von Neumann neighbourhood, the system defines multi-cell life-like entities (Chemits) shaped by PWM states S0–S3: S0 inactive, S1 introduces weak random oscillations, S2 creates a Chemit core (high CS=1), S3 extends the interacting body. A digital FSM drives PWM based on CS to realize probabilistic propagation, replication, and competition in a 7×7 array with periodic boundaries. Simulations of a probabilistic chemical state machine extend to up to 150×150 arrays to characterize population dynamics. Optimization problems: Two hybrid algorithms solve quadratic unconstrained binary optimization via Ising/QUBO mappings. In the first, chemical CS map to spins (−1, +1); energies are computed in-silico from a Hamiltonian with offsets, self-interactions, and pairwise couplings; the loop iterates flips toward minima. In the second, PWM states map to spins and chemical pair interactions inform probabilistic decisions via a lookup table of expected chemical outcomes. Variables are embedded on the array using auxiliary cells to realize all pairwise couplings. Acceptance is based on energy change aggregation across pairs. Problems demonstrated include number partitioning (4-number example S={1,3,4,8}; 8-number example), Boolean satisfiability, and travelling salesman (details in Supplementary Information). Data handling and training: CNN state recognition uses >13,000 images (1D) and >7,000 images (2D), trained with TensorFlow (Conv2D). Experiments are recorded under controlled lighting in an acrylic housing. Cleaning and solution management are automated via pumps. Simulations (Mathematica) of Chemits run 25 repeats per parameter set to estimate mean dynamics.

• A hybrid electronic–chemical processor based on BZ oscillators was built with digitally addressable cell and interfacial stirrers, enabling programmable nearest-neighbour coupling and a global SYNC clock to counteract phase drift.
• Discrete chemical states were robustly classified via a CNN and mapped by an rFSM to digital CS ∈ {0,1}, with low-amplitude oscillations representing CS=0 and high-amplitude continuous oscillations representing CS=1.
• Deterministic instantiation of elementary cellular automata (e.g., Rule 30, 110, 250) was demonstrated with one-to-one mapping between PWM and CS. Introducing interfacial coupling yielded probabilistic 1D-CCA with many-to-one mappings and nonlinear intensity–PWM relationships (qualitative data with n=2 runs for peak intensity vs PWM).
• 2D probabilistic CCA created emergent life-like entities (Chemits) composed of von Neumann neighbourhoods, showing propagation, replication, and competition in experiments on a 7×7 array with periodic boundaries. Population peaks and subsequent declines were observed due to localized replication and competition. Simulations up to 150×150 arrays replicated clustering, annihilation, and size-dependent stabilization; smaller arrays showed unstable populations, while larger arrays reached steady-state levels dependent on spatial resources. Each parameter setting used 25 runs to estimate mean populations.
• Hybrid probabilistic optimization: Two hybrid algorithms minimized Ising/QUBO energies. A four-number partitioning instance S={1,3,4,8} converged to the global minimum under both schemes, with spin configurations visualized and energies tracked over steps. Efficient embeddings using auxiliary cells enabled full pairwise couplings on the array.
• Performance quantification on an 8-number partitioning instance S={1,3,4,9,3,5,3,6} across all 2^8=256 initial configurations showed that introducing probabilistic chemical decision-making (deterministic index reduced from 1.0 to 0.99 or 0.95) narrowed the distribution of success probabilities across initial conditions, improving the chance of finding the global minimum irrespective of start state. Purely deterministic algorithms exhibited trapping in local minima for many configurations.
• The architecture demonstrates that distributing computation between digital finite-state logic and probabilistic chemical dynamics increases effective connectivity in configuration space, enabling efficient exploration and error mitigation via global synchronization.

The results show that a hybrid electronic–chemical architecture can make chemistry an active computational component rather than a passive medium. By combining deterministic digital control with analogue, probabilistic chemical dynamics and a global chemical clock, the system achieves programmability, synchronization, and error correction within a chemical substrate. Deterministic CA rules validate precise control, while probabilistic 1D/2D CCAs exploit hysteresis and local interactions to produce emergent dynamics (Chemits) akin to Conway’s Game of Life, but instantiated physically. For optimization tasks formulated as Ising/QUBO problems, the hybrid approach leverages probabilistic transitions to escape local minima more effectively than purely deterministic algorithms, with evidence from exhaustive initial-condition sweeps on an 8-number partitioning instance. The approach sits between fully digital and purely unconventional processors, offering tunable nonlinearity and stochasticity—key ingredients for classes of problems that benefit from exploration in high-dimensional spaces. The demonstrated system is generalizable to other digitally programmable physicochemical processes and can be scaled and refined by increasing the role of analogue processing, minimizing digital readout complexity, and enhancing I/O via scalable hardware.

This work introduces a programmable hybrid digital–chemical information processor using BZ oscillations with digitally controlled stirring and tunable coupling. It establishes robust state recognition and synchronization, demonstrates deterministic and probabilistic chemical cellular automata (including emergent life-like Chemits), and implements hybrid probabilistic algorithms for combinatorial optimization via Ising/QUBO mappings. The main contributions are: (1) a closed-loop hybrid state-machine framework (C, T, D, P) that unites analogue chemical dynamics with digital FSMs; (2) experimentally validated programmability and error correction through a global chemical clock; (3) demonstration of emergent probabilistic behaviours useful for computation; and (4) hybrid optimization that benefits from probabilistic chemical decision-making. Future directions include miniaturization to strengthen molecular-scale probabilistic effects, scaling via optical inputs (SLMs) or electrochemical actuation on high-density CMOS electrode arrays, sensor integration (e.g., CMOS OCP arrays) and weak continuous flow to stabilize oscillations, reducing reliance on CNN-based vision, and designing algorithms that further increase the proportion of analogue chemical computation. The architecture may be extended to deep learning and other domains where nonlinearity and stochasticity are advantageous.

• The BZ oscillations are highly sensitive to initial conditions and timing, leading to phase drift and decoherence without synchronization; a global SYNC coupling is required to maintain phase alignment.
• As the reaction proceeds (fuel depletion), oscillation amplitudes decrease over time, constraining experiment duration and necessitating clocking and readout strategies that accommodate amplitude decay.
• Interactions are limited to nearest neighbours via hydrodynamic coupling; implementing full connectivity requires auxiliary cells and embeddings, increasing resource usage.
• Some characterization data are qualitative with small sample sizes (e.g., intensity vs PWM measured with n=2), and CNN-based classification introduces a digital processing dependency.
• Experimental 2D demonstrations were on relatively small arrays (e.g., 7×7), with larger-scale behaviours inferred from simulations; smaller arrays showed unstable Chemits populations.
• In optimization tests, much of the energy calculation and acceptance logic currently occurs in the digital domain; increasing the proportion of chemical processing remains a goal for future iterations.