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. 2024 May 31;121(23):e2317772121. doi: 10.1073/pnas.2317772121

Fig. 4.

Fig. 4.

(Left) Toffoli complexity to synthesize the system propagator of the Alpha + Hydrogen system for time t=10,20,30,40 (in atomic units) for a range of fidelities. Using the lowest sample complexity considered Ns50 to 100 and 10 total times to estimate the slope the Toffoli complexity is 200 times the Toffoli costs shown. (Right) Toffoli scaling with respect to particle number at fixed rs and a fixed number of planewaves (increasing grid resolution). Time evolution cost is expected to scale as somewhere in between O(η4/3) and O(η8/3) using quantum signal processing. In blue the time evolution cost for t=1 is shown demonstrating the expected scaling along with constant factors. Constant factors associated with QPE are shown in red for 1/t=ϵ=103 which is should proportionally increase the cost. The displayed constant factor resources are in line with what is demonstrated in ref. 76 for constant rs1.

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