Table 2 Extrapolated simulation time

System size	χ	Factor	Extrapolated walltime
64 × 64	450	T_base	4.16 days
64 × 64	900	16 ⋅ T_base	66.6 days
256 × 256	450	28 ⋅ T_base	116.5 days
256 × 256	900	448 ⋅ T_base	5.1 years
16 × 16 × 16	450	4 ⋅ T_base	16.6 days
16 × 16 × 16	900	64 ⋅ T_base	266 days
64 × 64 × 64	450	1984 ⋅ T_base	23 years
64 × 64 × 64	900	31744 ⋅ T_base	362 years

We derive the baseline from a single-tensor optimization of a 64 × 64 quantum Ising model in (15) simulated with 7192 s on a single A100 GPU with 64 GB memory. Further, we assume a single-tensor update, one tensor and one GPU per MPI thread, and 50 sweeps for the baseline.
To extrapolate to larger systems, we assume a scaling with \({{{{\mathcal{O}}}}}({\chi }^{4}{N}^{D-1})\) as well as seven (31) tensors per MPI thread for 256 × 256 (64 × 64 × 64) systems. The empirical scaling is approximately a factor of 2.3 for doubling the system size of the two-dimensional system versus a theoretical value of 2; for doubling the bond dimension, the computation time grows by a factor of 13 versus a theoretical scaling of 16. The factors are obtained from smaller simulations with χ = 225 and for 32 × 32 qubits. The predictions of times are based on a scaling where d < χ.

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