Part 5: Results and the classical comparison

Our own measurement alongside classical calculations

The hardware measurement ran on IBM Kingston, Heron R2, using the Open plan. It included 31 N80 points and three N12 controls. For the errors below, we consistently use the same reference: the arithmetic mean of the original TEBD and TDVP curves. That mean is not an exact solution.

The ratio 130.7/76 is approximately 1.72. Our quantum run used fewer QPU seconds than this refined classical run required in CPU execution seconds, but with a larger deviation. This is a concrete comparison of two measured settings, not a demonstrated speedup at matched quality. QPU usage here also includes the small control circuits; it is not the same metric as CPU execution time or total turnaround time.

IBM separately recorded 66.93 seconds of circuit execution. Approximately 46 minutes elapsed between submission and completion; local preparation took 56.17 seconds. Including process startup and preparation, the classical run took 133.95 seconds. The classical computer was an AMD Ryzen 5 3500U, using one CPU thread in our established Qiskit/Quimb environment. This is not a comparison with the fastest available classical hardware.

There is also a much cheaper classical approximation: chi=16 and dt=1/6 computed the same 31 time points in a median of 8.01 seconds across five runs. It satisfied our original, relatively loose error criteria against both source curves, but failed a separate convergence test. The refined chi=64 run has not been shown to be converged either. All nine convergence runs together took 446.2 seconds. That total validation time is not the time needed for a single classical simulation.

A later quantum attempt with a 40-second limit was terminated without producing a complete curve. The successful demonstration in this article is the 76-second run, not that interrupted attempt.