Fig. 3

Experimental setup. a Single photons are generated from a degenerate spontaneous parametric down-conversion (SPDC) source pumped by a 410 nm continuous-wave laser. After filtering the generated photons with (820 ± 1.5) nm bandpass filters, photons in the lower beam (red) and upper beam (orange) are separately prepared in their respective input states, |S₀〉 or |S₁〉, using half-wave plates (HWP). Polarisation qubits, one from each beam, are used as memory states for the simulation of two separate and potentially different processes Π₁ (red) and Π₂ (orange). (For the first experiment described in the text, where only one process is required, the second SPDC output (orange) is sent straight to a heralding detector, rather than through the apparatus.) To implement the three-step simulation, three processor blocks are built—labelled Step 1, Step 2 and Step 3. In each step, path and arrival time modes are also employed to realise the relevant physical operation, as explained further in Methods. The output of one of the simulators (lower beam) is used to perform the polarisation tomography and to measure the arrival times of each photon in order to sample the statistical future. To measure the overlap of the future statistics of two processes, both photons are used, and the other outputs of the third beam splitter (BS) are interfered in a fibre BS (yellow box). An automated translation stage is used to move one of the couplers in order to vary the relative delay between the single-photon wave packets. Avalanche photodiodes (APD) and a single-photon counting module are used to count the photons. SMF stands for single-mode fibre, QWP quarter-wave plate, GT Glan-Taylor prism, PBS polarising beam splitter, and FPC fibre polarisation controller. b The inset shows a close-up of two vertically separated beams passing through two HWPs with holes, each of which only acts on one of the beams