Predictive Structure Behind Rare Outcomes in Random Quantum Circuits
Abstract
Local random quantum circuits selected for unusually large output peaks reveal intermediate-state structure that predicts new peak formation and guides circuit construction. In one-dimensional Haar-random brickwall circuits, the selected trajectories combine stronger pairwise correlations and probability redistribution with lower bipartite entanglement and output entropy. We test the predictive value of this structure by keeping each circuit's initial segment fixed and independently regenerating the remaining gates. Across the tested size-depth grid at n=8-14, peak-selected states have higher new-peak probability than normal/nonpeak controls, with an overall probability ratio of 3.23 at the primary depths. Within a separate unconditioned ensemble, a fixed structural score computed from the initial segment predicts new-peak probability and gives a 1.86-fold yield gain in a replay with equal numbers of remaining-circuit evaluations. Randomizing relative phases while preserving computational-basis probabilities strongly attenuates the selected-state advantage, demonstrating a functional contribution from relative-phase organization. Structural and phase-intervention tests extend to n=16. Structure-guided gate selection improves high-peak yield under common local refinement, while guidance using multiple intermediate observables improves new-peak probability over peak-only guidance in all 16 tested size-depth settings. Together, these results show how intermediate-state structure can predict and promote new peak formation under finite-depth local dynamics.
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BibTeX
@misc{kim2026predictive,
title = {{Predictive Structure Behind Rare Outcomes in Random Quantum Circuits}},
author = {Myeongsu Kim and Travis Humble and Sabre Kais},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.17482},
eprint = {2609.17482},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17482},
}
RIS
TY - UNPB
TI - Predictive Structure Behind Rare Outcomes in Random Quantum Circuits
AU - Myeongsu Kim
AU - Travis Humble
AU - Sabre Kais
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.17482
UR - https://arxiv.org/abs/2609.17482
AB - Local random quantum circuits selected for unusually large output peaks reveal intermediate-state structure that predicts new peak formation and guides circuit construction. In one-dimensional Haar-random brickwall circuits, the selected trajectories combine stronger pairwise correlations and probability redistribution with lower bipartite entanglement and output entropy. We test the predictive value of this structure by keeping each circuit's initial segment fixed and independently regenerating the remaining gates. Across the tested size-depth grid at n=8-14, peak-selected states have higher new-peak probability than normal/nonpeak controls, with an overall probability ratio of 3.23 at the primary depths. Within a separate unconditioned ensemble, a fixed structural score computed from the initial segment predicts new-peak probability and gives a 1.86-fold yield gain in a replay with equal numbers of remaining-circuit evaluations. Randomizing relative phases while preserving computational-basis probabilities strongly attenuates the selected-state advantage, demonstrating a functional contribution from relative-phase organization. Structural and phase-intervention tests extend to n=16. Structure-guided gate selection improves high-peak yield under common local refinement, while guidance using multiple intermediate observables improves new-peak probability over peak-only guidance in all 16 tested size-depth settings. Together, these results show how intermediate-state structure can predict and promote new peak formation under finite-depth local dynamics.
ER -