The phrase "quantum advantage" is not earned by running a large circuit. A serious claim needs a strong classical competitor, an accuracy target, and honest timing boundaries.
For this project, the classical competitor was not a generic statevector simulator. It was the tracker-linked TensorNetworkQuantumSimulator.jl route, which evolves the ZZZ operator in the Heisenberg picture using belief propagation and bond-dimension truncation.
That is a natural competitor because the quantum task asks for one observable, not the entire 80-qubit wavefunction.
Validating the runner first
Before attempting Q80, the new Julia runner was tested against an existing six-qubit tracker BP-TN artifact at bond dimension 64. It reproduced the stored observable to an absolute difference of 1.1e-16 and the pre-rescale norm to 2.3e-18.
That regression establishes that the gate reversal, CZ decomposition, local tensor normalization, and final overlap follow the prior tracker implementation.
The Q80 convergence ladder
At bond dimension 16, both halves completed:
- Delta:
0.40925590, wall time 209.21 seconds, truncation sum 4.12081 - Delta zero:
0.41780650, wall time 155.93 seconds, truncation sum 3.80119 - Apparent ratio:
0.97953456
That ratio is not trustworthy. The truncation errors are too large.
At bond dimension 32, the delta value moved to 0.76129858 with a truncation sum of 1.32017. The change from bond dimension 16 was 0.35204, or 86 percent. This shift is more than twenty times the hardware standard error.
At bond dimension 64, the delta half did not produce a result within a hard 900-second limit. A complete ratio would still require the delta-zero half and then a higher-bond convergence check.
Is the quantum computer faster?
For this tested local implementation, yes. The complete mitigated 16-circuit Fire Opal action finished in 328 seconds. The classical BD64 delta half alone exceeded 901 seconds. That gives an observed end-to-end lower bound above 2.75x for this machine and workflow.
Compared only with the 43.85-second QPU usage estimate, the observed lower bound is above 20.55x. That number is less fair as an end-to-end comparison because it excludes managed quantum overhead.
Why this is not yet a universal advantage claim
The classical result has not converged to the quantum error scale. We also have not benchmarked every classical algorithm, GPU implementation, distributed tensor contraction, or optimized compute node.
The supported statement is narrower:
The Q80 hardware workflow produced its finite-sample observable within minutes, while the tested tracker BP-TN route did not reach a controlled higher-bond answer within the same time scale.
That is evidence of a local practical runtime advantage, sometimes called a time-to-answer advantage. It is not proof that all classical computers fail on all formulations of the task.
This nuance becomes especially important when we connect OLE to information scrambling and black holes. A beautiful physical analogy should make our standards stronger, not weaker.