2026/06/10 by Friedrich Hübner, Sun Woo P. Kim · 1 voice
#cond-mat.stat-mech #quant-ph
`Solvable' circuits, such as dual unitaries and its generalisations, have arisen as paradigmatic examples of tractable chaotic non-equilibrium dynamics, both in classical and quantum systems. However, while increasingly more complicated sufficient conditions have been proposed, a systematic theory classifying and understanding general features of solvable circuits is missing. We develop such a theory by introducing influence-solvable circuits, a class of (1+1)D circuits whose influence matrix, which represents the `bath' generated by its own evolution, is given by a uniform MPS with finite bond-dimension χ. This property allows for efficient computation of subsystem dynamics and essentially contains all known examples of solvable circuits. We derive a set of necessary and sufficient local conditions by using a version of the fundamental theorem of MPS for open boundary conditions. Next we apply our theory to brickwork circuits with χ=1 influence-solvability and perform a systematic classification of classical brickwork circuits with local dimension up to d=3 and quantum brickwork circuits with d=2. Our search reveals new solvable circuits that are not captured by known solvability conditions.