Table 1.

Estimated computational cost of simulation

Experiment	d	One amplitude	1 million noisy samples
		(FLOPs)	FLOPs	XEB fidelity	Time
SYC-53 (ref. 4)	20	5 × 1018	2 × 1018	2 × 10−3	6 s
ZCZ-56 (ref. 5)	20	1 × 1020	7 × 1020	6 × 10−4	20 min
ZCZ-60 (ref. 6)	24	6 × 1021	3 × 1023	3 × 10−4	40 days
SYC-70	24	4 × 1024	5 × 1026	2 × 10−3	50 years
SYC-67	32	1 × 1024	1 × 1038	1 × 10−3	1 × 1013 years
			1 × 1029		1 × 104 yearsa
			1 × 1026		12 yearsb

^aWe include the cost estimated by assuming memory is distributed over all RAM, ignoring realistic bandwidth constraints. ^bWe include the cost estimated by assuming memory is distributed over all secondary storage, ignoring realistic bandwidth constraints.The second column shows the depth d of each experiment. The third column shows the FLOP count (number of real multiplications and additions) needed to compute a single output amplitude assuming no memory constraints. The last three columns refer to the cost of simulating the noisy sampling of 1 million bit strings. We used the specifications of Frontier for our estimates. This computer has a theoretical peak performance of 1.685 × 10¹⁸ single-precision FLOPS. We assumed 20% FLOP efficiency^13–15 and accounted for the low target fidelity of the simulation in the computational cost^13,14,18,33, as explained in Supplementary Information section G. SYC-67 refers to the experimental result shown in Fig. 4. All other rows used tensor contraction algorithms embarrassingly parallelizable over each GPU^14,15,32. SYC-70 refers to the experimental results from Supplementary Information section C.