A thermodynamically favoured molecular computer

Computers, like life, are usually out of equilibrium^1,2. Undesired error states are thwarted by energetically costly kinetic control processes: proofreading of biological polymers, error correction in computing and redundancy in molecular programming. Unlike life as we know it, theory shows that computation can be embedded in a system relaxing to a thermodynamically favoured equilibrium state^3,4. Machine learning and search algorithms use this idea^5,6, although executed on non-equilibrium architectures at enormous energy cost. Physically implementing thermodynamically favoured computation requires a programmable medium amenable to energy landscape engineering. Here we demonstrate a thermodynamically favoured Scaffolded DNA Computer (SDC) on 10 programs, including MULTIPLICATION-by-3, DIVISION-by-2, 8-bit PARITY-detection and ADDITION of 25-bit numbers-a 100-bit computation. SDC algorithms have simple experimental protocols, can be reused dozens of times and small instances run in under a minute. Mathematical, physical and computer science principles explain why the SDC is thermodynamically favoured, why it does not require error-correction or precise kinetic control, and how it is programmable and scalable. This work creates a new way to think about equilibrium computation in all manner of synthetic systems.