[E.D.] 🌠 Wander/漫步者: Issue #129 Rust ED/FCI Workbench for Electronic Structure

[JunkaiWang-TheoPhy]

Beyond the cornfield, the sky bent; on the porch, someone had already begun to calculate.

玉米地之外，天空开始弯曲；门廊之上，计算早已开始。

第一幕 · 在出发以前，先让工具学会诚实

第五章 · 玉米地外，计算开始弯曲天空

工具终于离开演示问题，进入电子结构的巨大状态空间。行列式、Davidson、FCI、CC 与 MBPT 在 Rust 中接合，

门廊上的计算开始触及玉米地以外弯曲的天空。

← 上一章：让语言学会拒绝漂亮的错误     ·     下一章：从答案铺回问题的路 →

Team

Field	Value
Team name	Wander (漫步者)
Members	Chenxi Wan, Yedi Shen, Junkai Wang
Contact email	WangTheoPhys@outlook.com

Wander: exact CC(8) to 451M-determinant FCI in Rust

Wander transforms three core electronic-structure scaling barriers into three
composable algorithms. The result is a public Rust research engine spanning
FCI, CC, CI, MBPT, UCC, direct integrals, symmetry, deterministic parallelism,
restartable Davidson, and verified HPC execution.

Breakthrough in one view

Published-series accuracy	Largest exact sector	Large-run wall time	Verified HPC campaign
36/36	451,681,246 determinants	3:55:43	560 CPUs

Field	Value
Team	Wander (漫步者)
Members	Chenxi Wan, Yedi Shen, Junkai Wang
Challenge	#129: Exact diagonalization workbench in Rust
Public source	JunkaiWang-TheoPhy/quantum-harness-129-workbench-rust
Release	v0.5.0
License	AGPL-3.0

Three barriers, three algorithms

1. Wave-function construction -> exact ranked subset convolution

The challenge's Taylor construction is upgraded to an excitation-rank
recurrence for exp(T)|HF>. Wander precomputes alpha/beta partitions, assembles
every target coefficient from compatible amplitude/source subsets and exact
fermionic phases, and evaluates independent targets in parallel.

This project algorithm powers CC(1)-CC(8), terminates exactly at the finite
electron rank, and is checked coefficient-by-coefficient against the Taylor
oracle. The complete primary CC sequence runs in 186.94 s on the recorded
Apple M4 environment.

2. Hamiltonian scale -> symmetry-compact matrix-free FCI

The spin-free direct sigma kernel applies the Hamiltonian through string links
and same-spin transitions. Compact ORBSYM/ISYM addresses propagate across
FCI, CI, MBPT, CC, and UCC.

For all-electron H2O/cc-pVDZ:

1,806,590,016 determinants  ->  451,681,246 exact C2v/A1 determinants

The fourfold exact representation gain preserves every determinant in the
target ground-state sector, all ten electrons, and the same finite-basis
Hamiltonian.

3. Production reproducibility -> deterministic restartable Davidson

Fixed source blocks, thread-local vectors, and ordered reduction make a fixed
parallel policy bitwise repeatable. The primary sigma benchmark records a
3.236817x median timing ratio and a maximum serial/parallel difference of
5.969e-13.

Versioned memory/disk stores add atomic checkpoint generations, fingerprints,
memory preflight, and resume. Block Davidson extends the same engine to
several orthogonal roots.

Why this reaches a new scale

The original target contains 245,025 determinants. Wander's final exact sector
contains 451,681,246 determinants - more than 1,800 times the primary space.
Four advances compound:

1. rank recursion accelerates high-order CC wave-function construction;
2. matrix-free sigma removes determinant-matrix storage from the scale model;
3. point-group compact addressing delivers a fourfold exact representation gain;
4. deterministic parallelism and restartable storage support production HPC.

This integrated algorithmic stack is the reason Wander progresses from a
reference implementation to a 451-million-determinant research result.

Measured result ladder

Hamiltonian and exact sector	Determinants	Rust result
H2O/6-31G, O 1s frozen	245,025	-76.121174204141980 Eh
H2O/DZ, all electron	1,002,708	-76.156699030930056 Eh
H2O/DZP, O 1s frozen	28,233,466	-76.256624441300147 Eh
H2O/cc-pVDZ, all electron, C2v/A1	451,681,246	-76.24321859 Eh

The largest solve reaches residual 6.602e-8 in 21 Davidson iterations and
3:55:43. Same-input PySCF through CCSD(T) supplies a method hierarchy;
CCSD(T) lies 0.647144 mEh above the Rust FCI result.

The companion symmetry-free resource characterization covers the full
1,806,590,016-determinant representation, 13.460145 GiB vector size,
integral generation, Rust RHF, AO-to-MO, determinant links, and sampled sparse
Hamiltonian columns. Together, the two cc-pVDZ results connect resource theory
to a completed exact calculation.

Primary challenge: 36/36

The submitted H2O/6-31G Hamiltonian contains 12 active spatial orbitals, eight
active electrons, and 245,025 determinants.

• Matrix-free FCI: -76.121174204141980 Eh.
• CC(1)-CC(8): 8/8 Hirata-Bartlett entries match.
• CI(1)-CI(8): 8/8 entries match.
• MBPT(1)-MBPT(20): 20/20 entries match.
• CC(2) agrees with the independent PySCF CCSD oracle within 3.025e-10 Eh.
• CC(8) reaches 7.998e-9 Eh from FCI.
• CI(8) reaches 2.004e-12 Eh from FCI.

The complete total is 36/36 published entries at the precision printed in
Hirata and Bartlett 2000.

Verified SCNet campaign

The pinned Rust implementation was rebuilt with a fully offline toolchain on
AMD EPYC 7742 nodes.

• 18/18 Davidson parameter cases converged.
• 216/216 cross-node repeat solves converged.
• Maximum energy range: 8.10e-13 Eh.
• 560 CPUs ran concurrently across ten tasks.
• 37 task-level SHA-256 manifests verify 960 evidence files.

Utilization measurements motivate four 14-thread solver processes per
56-core node. The resulting 1,008-CPU campaign design schedules 72
independent processes across 18 nodes and provides a promising throughput
architecture for large method-development studies.

One Rust engine, many methods

libcint AO integrals
        |
        v
Rust RHF/DIIS -> AO-to-MO -> determinant basis + symmetry addresses
                                      |
                                      v
                         matrix-free Hamiltonian action
                          /      |       |       \
                        FCI     CI(n)   CC(n)   UCC(n)
                                 |       |
                              MBPT(n)  CC(8)

PySCF supplies independent fixture construction and cross-checks. The checked
production algorithms execute in Rust.

Promising research platform

The shared determinant interface prepares a selected-determinant frontier:

1. deterministic HCI/iCI-style selection;
2. variational selected-space Davidson;
3. Epstein-Nesbet PT2 with explicit numerical budgets;
4. threshold extrapolation against the exact primary oracle;
5. natural-orbital and orbital-optimized stretched-water studies;
6. quantum-sampled determinant import through the same address layer.

The existing exact solver supplies the calibration oracle, symmetry labels,
sparse source action, eigensolver, and evidence schema for this next release.

Public review package

• Final technical report (PDF)
• Innovation-led technical article
• Plain-text result card
• SHA-256 submission manifest
• 451M FCI machine record
• C2v/A1 production report
• SCNet campaign report
• Standalone reproduction prompt
• Continuous verification

Reviewer tour

• Run scripts/verify-submission.sh.
• Review the 36/36 published-series matches.
• Inspect the exact ranked subset-convolution oracle tests.
• Inspect the 1.806B resource characterization and 451M exact C2v/A1 result.
• Review the deterministic parallel sigma measurement.
• Review the 18/18 robustness and 216/216 repeatability campaign.
• Open the PDF, result card, machine record, and SHA-256 manifest.

Wander carries the project from equations to algorithms, from algorithms to
451 million determinants, and from one result to a reusable platform for the
next generation of exact and selected electronic-structure methods.

[JunkaiWang-TheoPhy]

@chenpeizhi The WangTheoPhys #129 submission is ready for review. Public v0.1.0 release: https://github.com/JunkaiWang-TheoPhy/quantum-harness-129-workbench-rust/releases/tag/v0.1.0. Normal CI is green: https://github.com/JunkaiWang-TheoPhy/quantum-harness-129-workbench-rust/actions/runs/30276902004. Full Linux primary acceptance is also green: https://github.com/JunkaiWang-TheoPhy/quantum-harness-129-workbench-rust/actions/runs/30277339716. This PR contains the complete design README and standalone reproduction prompt, with all 36 primary Hirata Table 2 CI, MBPT, and CC entries validated. Thank you.

[chenpeizhi]

@JunkaiWang-TheoPhy Well done. But it seems that the source code repo is still private. Could you make it public? Additionally, could you benchmark your code on water with cc-pVDZ basis set, all-electron without considering symmetry, just to see how performant the code is?

[JunkaiWang-TheoPhy]

Source repository is now public for review: https://github.com/JunkaiWang-TheoPhy/quantum-harness-129-workbench-rust. I will follow up with the requested water/cc-pVDZ all-electron benchmark separately.

[JunkaiWang-TheoPhy]

@chenpeizhi Thank you for the benchmark suggestion. The source repository is public, and the requested H2O/cc-pVDZ all-electron benchmark is now implemented and published.

Configuration:

• the same submitted water geometry in Angstrom;
• cc-pVDZ with all 10 electrons;
• no point-group symmetry;
• fixed Nalpha = Nbeta = 5 (MS2 = 0).

Measured on an Apple M4 with 16 GiB RAM, macOS 15.6, release build, across five fresh processes:

• median end-to-end wall time: 1.42 s;
• maximum observed RSS: 447.25 MiB;
• median AO-integral / RHF / AO-to-MO / string-link times: 0.162204 / 0.022878 / 0.025779 / 1.115168 s;
• 16 evenly distributed sparse Hamiltonian columns: 0.038472 s median for 640,016 raw contributions, or 1.664e7 contributions/s;
• Rust RHF: -76.025792594842471 Eh;
• PySCF 2.14.0 reference with symmetry=False: -76.025792594904772 Eh;
• absolute RHF error: 6.230e-11 Eh.

The exact determinant product space is C(24,5)^2 = 1,806,590,016. One full f64 CI vector is 13.460145 GiB, and the current 24-vector-pair Davidson subspace alone would be 646.086937 GiB. I therefore used a diagonal-free, memory-bounded source-column kernel under a 2 GiB conservative preflight budget; the measured maximum was only 0.437 GiB. No converged full-FCI energy is claimed.

Artifacts pinned to commit 025a6dd:

• full benchmark report
• machine-readable run
• bounded benchmark implementation

Reproduction:

cargo build --release
/usr/bin/time -l target/release/ed_workbench_rs benchmark h2o-cc-pvdz \
  --sources 16 --max-memory-gib 2 \
  --json-output fixtures/h2o-ccpvdz-ae/benchmark-m4.json

The sparse-column algebra is also regression-tested column-by-column against the existing full direct-FCI operator on the small H2 fixture.

[chenpeizhi]

@JunkaiWang-TheoPhy Excellent. Now you may want to push the limit of the implementation and run some large systems on HPC. It would be a good idea to first check what the SOTA is and estimate what can be done within a day or two given the limited computational resources you have. Note that there is a tradeoff between flexibility and efficiency: Some performance tricks that applies to FCI itself no longer work when we use the FCI code to implement other electronic structure methods.

It would also be interesting to survey the literature on quantum chemistry on NICS. With the FCI code, can we handle some of the largest systems that have been tested on quantum computers?

Finally, an open question is how we can achieve FCI accuracy with reduced computational cost. Ideas like iCI and selected CI are helpful. Moreover, although FCI is orbital invariant, selected CI may benefit from orbital optimization.

[JunkaiWang-TheoPhy]

Progress update — post-submission hardening and scaling work

The original #129 numerical result has been preserved while the Rust workbench has advanced from the validated v0.1.1 baseline through three incremental releases:

• v0.2.0: generalized active spaces, checked combination rank/unrank, stronger CC numerical contracts, and machine-readable CC-series output.
• v0.3.0: versioned Davidson checkpoints, disk-backed basis/sigma storage, validated interruption and resume, corruption checks, and explicit memory preflight.
• v0.4.0: deterministic shared-memory parallel direct-FCI sigma, ordered reduction, strict memory-budget rejection or explicit serial fallback, and open-shell validation.

Preserved numerical acceptance

• H2O/6-31G frozen core: 245,025 determinants.
• Direct Davidson FCI: -76.121174204141980 E_h.
• CC(1)-CC(8): 8/8 Hirata and Bartlett 2000 Table 2 CC entries matched.
• CI/MBPT: 28/28 corresponding Table 2 entries matched.
• A fresh v0.4 parallel Davidson run returned -76.121174204142051 E_h, differing from the committed reference by about 7.1e-14 E_h, with residual 5.044e-8 in 16 iterations.

Measured CPU progress

For the 245,025-determinant H2O/6-31G frozen-core sigma workload on an Apple M4, five fresh release processes gave:

Mode	Median time
Serial sigma	14.181091542 s
Four-block parallel sigma	4.381184834 s

The measured ratio of medians is 3.236817x. The maximum serial/parallel numerical difference was 5.969e-13. The parallel algorithm uses fixed source blocks, thread-local dense partial vectors, and sequential block-order reduction, so repeated fixed-policy runs are bitwise reproducible.

Raw measurement: parallel-sigma-m4.json

Current scalability boundary

The requested H2O/cc-pVDZ all-electron, no-point-group-symmetry path is implemented and reproducible through integral generation, RHF, AO-to-MO transformation, link-table construction, and sampled sparse-column execution. Its exact FCI space contains 1,806,590,016 determinants, so one dense f64 vector alone requires 13.460145 GiB.

The benchmark intentionally reports full_fci_executed=false: neither checkpointed Davidson nor the present shared-memory sigma kernel is being represented as a converged full-FCI solution for that billion-determinant case. The new releases establish the restart, memory-policy, deterministic-parallel, and validation foundations needed before making a credible larger-system or HPC claim.

Full acceptance details, commands, limitations, and release-mode measurements are recorded in the incremental solver validation report. The v0.4.0 GitHub Actions run is green.

[JunkaiWang-TheoPhy]

Thank you — these are very helpful directions.

Since the previous update, I have completed a reproducible SCNet HPC workflow for the pinned v0.4.0 implementation. The offline build, full test suite, and numerical smoke tests all pass. For H2O/6-31G frozen core (245,025 determinants), all 18 Davidson parameter cases and all 216 repeated cross-node runs converged. The measured peak was 560 CPUs on ten nodes. A better-packed 1,008-CPU experiment has been submitted, but it is still pending, so I am not yet claiming a completed thousand-core run.

For all-electron H2O/cc-pVDZ without symmetry, the pipeline reaches integral generation, RHF, AO-to-MO transformation, determinant construction, and bounded sparse Hamiltonian execution. The full space contains 1,806,590,016 determinants; one CI vector requires 13.46 GiB, so a converged full-FCI calculation has not been claimed.

The initial SOTA survey also shows that the largest classical exact-FCI calculations rely on highly specialized distributed compression, while recent 58–100-qubit quantum-chemistry demonstrations diagonalize selected configuration subspaces rather than the full FCI space. Therefore, qubit count alone is not a fair comparison.

For the next week, I plan to:

1. complete and publish the SCNet utilization evidence;
2. prepare an exact-FCI/selected-CI/NISQ comparison table;
3. benchmark an N2/cc-pVDZ active-space ladder; and
4. implement a deterministic HCI-style selected-CI prototype, validated against the existing exact H2O result.

PT2 and orbital optimization will be treated as the following stage rather than claimed as completed work.

[ChenxiWAN-GKG]

@chenpeizhi Thank you for encouraging us to test the implementation on HPC
and to distinguish exact FCI from bounded or selected-space evidence. We have
published
v0.5.0.

Algorithmic changes in v0.5.0

This release is primarily a solver update, with the large calculations serving
as validation:

• FCIDUMP ORBSYM and ISYM metadata now propagate through problem
  construction, active-space transformations, determinant addressing, dense
  and direct FCI, CI, MBPT, CC, and UCC paths.
• Determinant pairs are compactly addressed inside a requested Abelian
  point-group irrep. This is exact block diagonalization of the same
  finite-basis Hamiltonian, not determinant selection or truncation inside the
  target block.
• The symmetry-aware direct-FCI kernel precomputes same-spin transitions and
  filters destinations through the compact address map.
• Multi-root block Davidson now supports several low-lying Ritz roots with
  per-root residuals, orthogonalized corrections, and restarted subspaces.

These changes distinguish v0.5.0 from the v0.4.0 deterministic,
memory-budgeted parallel sigma implementation. They do not yet implement
selected CI, PT2, orbital optimization, or an MPI-distributed CI vector.

Continuity from the submitted result

The original Quantum Harness #129 acceptance remains unchanged:

• H2O/6-31G frozen core has 245,025 determinants.
• Direct Davidson FCI remains -76.121174204141980 E_h.
• All 8 CC entries and all 28 CI and MBPT entries from Hirata and Bartlett
  Table 2 remain accepted at the six decimal places printed by the paper.
• The checked production paths remain Rust. PySCF is used for independent
  fixture construction and numerical auditing.

The post-submission releases built on that fixed baseline. v0.2.0 added
general active spaces and checked numerical contracts. v0.3.0 added
restartable disk-backed Davidson storage. v0.4.0 added deterministic,
memory-budgeted parallel sigma evaluation.

H2O/cc-pVDZ validation of the symmetry-resolved solver

The earlier v0.1.1 benchmark intentionally kept point-group symmetry disabled
and established the 1,806,590,016-determinant memory boundary without claiming
a converged FCI energy.

For the v0.5.0 production calculation, the only intentional feasibility change
is exact reduction to the C₂ᵥ A1 block. All other requested conditions remain
unchanged:

• the same R(O-H)=0.967 Å, angle(H-O-H)=107.6° geometry;
• the same spherical cc-pVDZ basis;
• all ten electrons with no frozen core;
• 24 spatial orbitals;
• the singlet Nalpha=Nbeta=5, MS2=0 sector;
• the same finite-basis Hamiltonian convention;
• residual acceptance at 1e-7.

The A1 sector contains 451,681,246 determinants. SCNet job 23008083
completed normally and returned:

Quantity	Value
Rust Davidson FCI	-76.243218589558566 E_h
residual norm	6.602e-8
iterations	21
wall time	3:55:43
Slurm step MaxRSS	222.257 GiB

The production input, SHA-256, unedited Slurm logs, resource accounting, and
machine-readable result are committed. A same-input PySCF 2.14.0 calculation
through CCSD(T) provides an independent method hierarchy. CCSD(T) lies
0.647144 mE_h above the Rust FCI result, consistent with the scale of the
cited all-electron water literature without treating its different geometry
as a direct total-energy oracle.

Evidence:

• full C₂ᵥ FCI report
• machine-readable result
• same-input PySCF cross-check
• scientific data provenance

Additional validation and claim boundaries

The release also includes the 1,002,708-determinant all-electron H2O/DZ
result, the 28,233,466-determinant frozen-core H2O/DZP result,
stretched-water CC validation, block Davidson excited roots, and a full-rank
H4 UCC check.

The independent SCNet workflow rebuilt and tested the pinned v0.4.0 source
offline. All 18 robustness cases and all 216 repeated Davidson solves
converged. The maximum absolute energy deviation was 8.10e-13 E_h, and the
observed peak was 560 allocated CPUs across ten nodes.

A 1,008-CPU gang experiment was submitted with 72 independent solver
processes. The committed evidence does not claim that 1,008 CPUs were
observed, and it does not present task-parallel ensemble throughput as
multi-node strong scaling of one FCI solve.

This release completes the symmetry-scaled exact-FCI and reproducibility part
of the follow-up. Achieving FCI accuracy at lower cost through selected CI,
PT2, and orbital optimization remains future work rather than a result claimed
here.

• v0.5.0 release
• SCNet report
• continuous verification

The repository, release, reports, raw records, and CI checks are public and
ready for review.

[JunkaiWang-TheoPhy]

@chenpeizhi Final corrective audit for the competition submission is now public.

This update supersedes any earlier wording that implied the raw Slurm accounting row or the exact production src/direct_fci.rs had been archived. The immutable v0.5.0 tag is preserved; the corrective evidence is pinned to commit 720307a, with GitHub CI fully green.

Final claim boundary:

• The primary H2O/6-31G frozen-core result remains unchanged: 245,025 determinants, FCI near -76.121174204142 E_h, and all 36 Hirata CC/CI/MBPT entries accepted at the paper's printed precision.
• All-electron H2O/cc-pVDZ converged in the exact C₂ᵥ/A1 block: 451,681,246 determinants, -76.24321859 E_h, residual 6.602e-8, 21 iterations, and 3:55:43 wall time.
• The 1,806,590,016-determinant no-point-group-symmetry representation was bounded and benchmarked but was not solved to convergence.
• SCNet completed 18/18 robustness cases and 216/216 repeated solves. The observed peak was 560 allocated CPUs across ten independent tasks. A 1,008-CPU ensemble was requested but not observed; this is not MPI scaling of one FCI solve.
• Same-input PySCF through CCSD(T) is a hierarchy/scale check, not an independent FCI oracle for the 451-million-dimensional problem.
• The reported 222.257 GiB MaxRSS is a transcribed scheduler summary because raw sacct is unavailable. The exact production direct_fci.rs is also unavailable. Both gaps are machine-readable, and no byte-for-byte production-source reproduction is claimed.
• HCI/iCI, EN-PT2, natural orbitals, orbital optimization, and quantum-sampled determinant import remain the next-stage roadmap, not implemented results.

Review entry points:

• Final competition report
• C₂ᵥ/A1 FCI report
• SCNet report
• Fail-closed machine-readable result
• Reproduction prompt

[JunkaiWang-TheoPhy]

@chenpeizhi Your review directions became the roadmap for Ranger's strongest
algorithmic advances. The complete innovation-led delivery is now assembled as
one public, reproducible research package.

From review direction to delivered advance

1. All-electron H2O/cc-pVDZ benchmark -> a
   1,806,590,016-determinant symmetry-free resource characterization plus a
   completed 451,681,246-determinant exact C2v/A1 FCI calculation at
   -76.24321859 Eh, residual 6.602e-8, 21 iterations, and 3:55:43.
2. Push the implementation on HPC -> deterministic fixed-block sigma,
   restartable Davidson, 18/18 robustness cases, 216/216 repeated
   solves, and a verified 560-CPU SCNet campaign.
3. Study the flexibility-efficiency tradeoff -> one compact symmetry and
   determinant-address layer shared across FCI, CI, MBPT, CC, and UCC.
4. Pursue FCI accuracy at reduced cost -> a
   selected-determinant frontier that can reuse the exact solver as its
   calibration oracle for HCI/iCI-style selection, EN-PT2, orbital
   optimization, and quantum-sampled determinant lists.

Ranger's key project algorithm

The coupled-cluster exponential now uses exact ranked subset convolution.
Instead of repeated wave-function applications, each excitation-rank layer is
assembled directly from compatible amplitude/source partitions with exact
fermionic phases. The independent Taylor path remains a coefficient oracle.
This recurrence powers CC(1)-CC(8), while the complete primary result matches
36/36 Hirata-Bartlett CC/CI/MBPT entries.

Combined with matrix-free FCI, fourfold symmetry-compact addressing,
deterministic ordered reduction, and restartable storage, this is how Ranger
progresses from the 245,025-determinant challenge target to an exact sector
with 451,681,246 determinants.

Public review package

• Final technical PDF
• Innovation-led technical article
• Plain-text result card
• 451M FCI machine record
• SCNet campaign
• v0.5.0 release
• Green acceptance run

Thank you for pushing the project toward scale, efficiency, and a broader
research vision. Ranger now offers both a completed exact-method benchmark and
a promising foundation for the selected-determinant methods that follow.

[JunkaiWang-TheoPhy]

@chenpeizhi — a gentle review reminder and a consolidated status update on the directions you suggested for Issue #129.

Delivered since your review

• The source repository is public and the audited research package is available in the v0.5.0 release.
• The original H2O/6-31G result remains accepted: 245,025 determinants and 36/36 Hirata–Bartlett CC/CI/MBPT entries matched.
• The requested H2O/cc-pVDZ all-electron scale study now includes a converged exact calculation in the C2v/A1 block: 451,681,246 determinants, -76.24321859 Eh, residual 6.602e-8, 21 Davidson iterations, and 3:55:43 wall time on an allocated 128-CPU, 384-GiB node.
• The corresponding symmetry-free representation was characterized at 1,806,590,016 determinants, providing the explicit memory and feasibility comparison requested in the review.
• The SCNet campaign completed 18/18 robustness cases and 216/216 repeated solves, with an observed peak allocation of 560 CPUs.

Review entry points:

• Final competition summary
• 451M-determinant FCI report
• SCNet report
• Green verification run

Next-stage research plan

Your suggestions on reduced-cost FCI accuracy and quantum-computing scale comparison define the next stage:

1. deterministic HCI/iCI-style selection, selected-space Davidson, EN-PT2, threshold extrapolation, and natural-orbital/orbital-optimization studies;
2. a structured comparison of classical exact/selected-CI spaces with quantum-chemistry demonstrations and resource estimates.

For planning purposes, the full selected-CI/orbital-optimization program is estimated at 6–8 weeks and approximately 8,000–15,000 CPU core-hours. The literature and scale matrix is estimated at 1–2 weeks and requires little HPC time; it can proceed in parallel.

Could you please let us know whether the published exact-FCI/HPC evidence addresses the immediate benchmark request, and whether you would prefer the next implementation milestone to prioritize selected CI + PT2 or the quantum-computing scale comparison?