Fig. 2: Quantum models.
From: Implementing quantum dimensionality reduction for non-Markovian stochastic simulation
Quantum models store one of a set of memory states \(\{|{\sigma }_{j}\rangle \}\) that correspond to an encoding of information from past observations (green). At each time step, a blank ancillary system set to \(\left|0\right\rangle\) (red) is introduced and undergoes a joint interaction U that creates a weighted superposition of possible events imprinted onto the ancilla, coupled with the corresponding updated memory state. The ancilla is then measured to produce the output statistics, leaving the memory ready for the next time step. Depicted are three timesteps, producing a string of outputs x0x1x2.
