A numerical preprint reports a split result for a proposed way to track information loss during noisy operator evolution. Under uniform synthetic noise, entropy MPF had a lower reported mean per-site entropy loss than the best noisy sample on both tested lattice layouts. In a heavy-hex case using hardware PTMs, the method showed no reported improvement.
On the rectangular 7 by 7 lattice, the best noisy sample recorded a mean per-site entropy loss of 3.680, while the entropy MPF result was 2.783, corresponding to a reported 24% reduction. On heavy-hex under uniform noise, the figures were 1.058 and 0.538, with a reported 49% reduction.
Following the information frontier
The paper asks whether information lost during noisy operator evolution can be quantified site by site and cycle by cycle against a noiseless reference. Its proposed wavemap combines each site's noisy-versus-noiseless arrival delay with cross-entropy loss, a mismatch score, and a space-time frontier tracking the operator's spread.
MPF was the reconstruction step used in the comparisons. The analysis compared a squared-error objective based on frontier distance with a cross-entropy objective.
What the simulations measured
CppSim generated the numerical data using 16 by 16 real PTMs and Householder QR truncation. The heavy-hex computational configuration contained 68 sites and 76 bonds. The rectangular configuration contained 49 sites and 84 bonds and used synthetic depolarizing noise with p = 0.01.
The frontier varied across the test conditions
One structural measure was nearly unchanged across the tests. Across both topologies, the off-diagonal fraction of the PTMs stayed constant across noise amplification, with a change of less than 0.002. The authors interpret the associated eigenvalue changes as magnitude scaling while Pauli mixing remains gate-derived.
Linear-fit frontier velocities varied by topology and noise level. On heavy-hex, the values were 0.376 hops per cycle in the noiseless case, 0.145 at gamma = 1, and 0.152 at both gamma = 2 and gamma = 3. On rectangular 7 by 7, they were 0.448, 0.382, 0.248 and 0.097 hops per cycle in the same order.
Arrival delays were not monotonic across the two layouts. On rectangular, mean delay increased with gamma, but the gamma = 3 mean was lower than the gamma = 2 mean. The paper attributes that result to survivorship: gamma = 3 reached only 25 sites, while gamma = 2 also reached 12 harder, more distant sites. Heavy-hex delays were non-monotone.
The hardware-matrix comparison was different
The heavy-hex hardware-PTM comparison produced a different numerical result. Only 21 of 68 sites were reached. The best noisy sample had a mean loss of 7.962, while frontier MPF and entropy MPF both had 9.532. The reported improvement was 0%.
Because the analysis was computational, this result concerns simulated matrices rather than a hardware run.
Constraints exposed a fitting trade-off
The analysis compared an unconstrained optimizer with one using the Lieb-Robinson constraint. On rectangular 7 by 7, the unconstrained optimizer reached a mean loss of -0.69 and was described in the paper as a causality violation. The constrained result was +2.68.
Another reported comparison allowed alpha to adapt over time or distance. Time-adaptive alpha(t) had the best reported values: a mean loss of 0.481 on heavy-hex depolarizing noise and 1.276 on rectangular 7 by 7, corresponding to reported reductions of 55% and 65%. Two distance-adaptive alpha(d) options had heavy-hex and rectangular losses of 1.218 and 6.007 for one option, and 1.050 and 5.808 for the other.
The time-adaptive fit also had a practical boundary. In a 20-cycle heavy-hex 3 by 3 uniform-noise run, the frontier emptied after cycle 13. Alpha(t) became ill-conditioned, with a mean loss of 4.206, and performed worse than the best gamma sample.
A numerical result with a narrow reach
The supplied analysis reports no confidence intervals or replicate variability for the reported comparisons. The percentages and mean losses are therefore reported values from the stated numerical configurations.
The document identifies itself as an [arXiv preprint, 2608.25254v1](https://arxiv.org/abs/2608.25254), dated 26 August 2026. Its front matter lists Advanced Micro Devices, Inc. as the author's affiliation and supplies no funding statement.
Paper data and sources
Original title: The Pauli Lightcone: Information-Theoretic Error Mitigation Beyond the Autocorrelation
Authors: Paolo D'Alberto
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text