Fig. 3
q-machine simulators of renewal processes. a Analogue simulator for a discrete-time renewal process, where a continuous chain of qubits is used to encode the quantum causal state. The simulator sweeps along the chain and alters the future of the chain conditional on the current qubit, with the mappings \(\left| 0 \right\rangle \left| {1_n} \right\rangle \to \left| 0 \right\rangle \left| {1_n} \right\rangle\) and \(\left| 1 \right\rangle \left| 0 \right\rangle ^{ \otimes \infty } \to \left| 1 \right\rangle \left| {\sigma _0} \right\rangle\). Measurement of the qubit state signifies whether an emission occurs in a given timestep. b Analogue simulator for continuous-time renewal processes, where the quantum causal state is encoded into the position of a particle. The simulator sweeps along this position and generates additional particles encoding future emissions conditional on the presence of the particle. Detection of the particle signals an emission event
