[MSRudolph]

Continuous-time Pauli propagation (CTPP) steps reuse their storage, and candidate selection for the support is modularized. With the default streaming proposer, the measured ladder cases run 18–32% faster and use 61–65% less peak memory than the original main baseline. On the dephased ring, peak memory falls by 67%, with no measurable runtime improvement. The optional shortlist proposer reduces runtime by 28–46% and peak memory by 57–76% across these cases.

Streaming remains the default. Shortlist is faster on the larger cases, but uses more memory than streaming on the ladder and changes the retained support. Both use magnitude-based retention.

Design

• Single main storage: candidates are collected in the over-allocated slots of the main string and coefficient arrays. Coefficients are updated in place.
• Modularized proposers: CandidateProposer is the interface for selecting which candidate strings to admit. Callers can supply a strategy through the existing step methods.
  • Alternative: ShortlistScoreProposer shortlists candidates by individual Hamiltonian contributions, then ranks them by full signed leakage.
  • Default: StreamingProposer remains the default. General dissipators use it automatically.
• Automatic reuse: LindbladSpec reuses candidate lookup tables, source-order storage, generator connections, and exponential work arrays across step calls. Callers can own this storage through PcStepWorkspace.
• General-coupling connection cache: connections identify the parent string and Hamiltonian term. Coefficients are read from the model, so unequal couplings need no special case.
• Paired connection cache: without general dissipators, the Hamiltonian part of the generator is antisymmetric. If string i reaches j through term k, then j reaches i through k with the opposite sign. The cache stores each connected pair once, using 6-byte entries when Hamiltonian term IDs fit in 16 bits and 8-byte entries for larger term lists. The product applies each pair in both directions.
• Compact Pauli strings: ppvm-lindblad's Word stores only the X and Z bit planes, 32 bytes at 128 qubits instead of 48. The number of qubits comes from the model. Hashes are computed when needed and match the general PauliWord's hashes and ordering, so hash-table order is unchanged. ppvm_pauli_sum symmetry routines still take the general type, exposed as GeneralWord, with conversions at that boundary.

Benchmarks vs the original main baseline

Measured on 2026-11-09 after removing forward-looking retention: median of three fresh, interleaved runs per implementation, Apple arm64 on AC power, mimalloc (the allocator the Python extension uses), 6 threads, MIMALLOC_PURGE_DELAY=0. Each case uses dt=0.1, retained support limit B and admission cap 3B. Times measure propagation; build time is excluded. Memory is OS-reported peak RSS.

The baseline is the original PR control at 342e3234. Both current proposers use the same binary built from the reverted working tree. Both models evolve a magnetization operator in the Heisenberg picture.

• Ladder: 2 × 41 sites, open boundaries, no dissipation. H = Σ⟨ij⟩ (XᵢXⱼ + YᵢYⱼ) over nearest-neighbour bonds on a ladder topology. Observable is the average of Z on the two sites in the middle.
• Ring: 61 sites with all-to-all couplings. H = Σᵢ<ⱼ Jᵢⱼ (XᵢXⱼ + YᵢYⱼ), with Jᵢⱼ ∝ rᵢⱼ^−1.1 (ring distance), normalized so that Σⱼ Jᵢⱼ² = 1. Each site also has Z dephasing at rate γ = 8. Observable is Z on the center site.

Default: streaming

Values show baseline → current.

Model	String limit B	Propagation time	Peak RSS
82-spin ladder, Jt=0→5	2^17	13.42 → 9.17 s (−32%)	300 → 105 MiB (−65%)
82-spin ladder, Jt=0→5	2^19	78.24 → 64.32 s (−18%)	940 → 367 MiB (−61%)
61-spin dephased ring, Jt=0→2	2^19	276.90 → 277.20 s (unchanged)	1,885 → 629 MiB (−67%)

Optional: shortlist-and-score

Values show the same baseline → current with shortlist selected.

Model	String limit B	Propagation time	Peak RSS
82-spin ladder, Jt=0→5	2^17	13.42 → 9.73 s (−28%)	300 → 130 MiB (−57%)
82-spin ladder, Jt=0→5	2^19	78.24 → 50.61 s (−35%)	940 → 392 MiB (−58%)
61-spin dephased ring, Jt=0→2	2^19	276.90 → 149.14 s (−46%)	1,885 → 453 MiB (−76%)

For comparison across string representations, S = 56·B bytes: 7 MiB at B=2^17 and 28 MiB at B=2^19. Differences below about 5% are not treated as resolved performance gains.

Numerical agreement

These comparisons measure agreement with the original baseline, rather than accuracy against an exact reference. Neither current proposer is bit-identical to that baseline. All three repeats reproduce identical numerical trajectories within each implementation and case.

• Ring: streaming differs by about 2e-11 in final MSD, and shortlist by 9e-6. The largest absolute density-profile differences over all recorded times are 4.7e-12 and 2.1e-9, respectively.
• Ladder: final MSD at B=2^19 is 35.711 for the baseline, 35.692 for streaming and 35.276 for shortlist. At B=2^17 it is 35.213, 35.267 and 35.130, respectively. Changing the retained support changes the approximation; runtime and memory gains alone do not establish improved accuracy.
• Revert check: the current streaming ladder trajectories match the previous streaming benchmarks with forecasting disabled bit for bit, including state hashes.

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[Roger-luo]

I think this is better to be merged after the main refactor gets in - the new trait system gives more flexibility in choosing different PauliWord data structures