{"id":"68a0fdbe-e927-45d5-909e-f55b95e3b8d9","arxiv_id":"2608.08739","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"DA-CASE reconstructs subspace, Hamiltonian, and observable matrices from one cached Pauli expectation bank, reducing retained measurement width on H4 from 7371 to 2240 words without changing the solved subspace.","lead":"This paper introduces DA-CASE, a quantum subspace method that reconstructs all needed matrices from Pauli measurements on a single reference state, and uses that reuse to shrink the measurement bank while keeping the same subspace. It also provides a resource ledger that separates state preparations, measurement settings, shot counts, circuit depth, and retries, and demonstrates the trade-offs on small molecules and spin chains.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central H4 counts (same subspace, retained banks 7371 vs 2240) come from a private artifact; they are self-consistent but not independently auditable as presented.","rationale":"The paper is unusually careful: it states the central claim as a small-instance exact demonstration, separates exact/oracle/heuristic evidence, and explicitly prices or excludes omitted costs (selection cache, QND, routing, noise). The internal algebra of Sections II.A-II.C appears sound, and the H4 Hamiltonian and mapped sector energy are cross-checked against PySCF and OpenFermion. Given that support, the strongest remaining concern is not a technical inconsistency but the evidentiary status of the headline numbers. The claimed identity of the two nine-dimensional subspaces, the machine-precision energy equality, and the retained-bank counts 7371 and 2240 all come from the private clifford_qc codebase. The JSON/digest checker verifies self-consistency, not correctness. An independent reader cannot rerun the selection, the principal-angle comparison, or the word-universe enumeration. The reader's QND/post-selection worry is real but already disclosed in Section V and does not affect the sharp-determinant H4 contract; it is a scope limitation, not a hidden assumption in the main result. Therefore the most load-bearing concern is verification: the central numerical claim is currently uncheckable without the artifact. The offered access-controlled snapshot would settle it. If it reproduces, the CONDITIONAL verdict can be upgraded; if not, the central demonstration is unsupported.","tokens_in":9106,"tokens_out":23507,"duration_ms":268732,"concrete_test":"Obtain the access-controlled frozen snapshot offered in Section VII, run its generator and structural checker, and independently recompute Table I's DA-CASE (determinant) and DA-CASE (word) rows: retained W/G (7371/913 and 2240/465), energies (3.019 mHa for both), and the nine principal angles. If the artifact reproduces these numbers, the central demonstration is supported; if counts or angles differ, the claimed equivalence is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central demonstration—two generator resolutions reaching the identical nine-dimensional subspace with identical energy to machine precision while the retained Pauli bank changes from 7371 to 2240—is generated by a private codebase. The internal JSON/digest checker verifies that tables are generated from committed records, but not that the records are correct; the Hamiltonian energy is cross-checked against PySCF and OpenFermion, but the subspace-equality claim, the principal angles, and both retained-bank counts have no independent construction. As the paper stands, the load-bearing numerical evidence is not publicly verifiable. This is a verification gap, not an internal inconsistency. The reader's QND/post-selection concern is a disclosed scope limitation (Section V) that does not affect the sharp-determinant H4 contract, so I do not treat it as the decisive weakness.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces DA-CASE, a single-reference quantum subspace eigensolver in which basis states are virtual Clifford-algebra directions A_i|ψ⟩ and the projected overlap, Hamiltonian, and observable matrices are reconstructed from one cached set of Pauli expectations on |ψ⟩. The central numerical contract is a frozen eight-qubit H4 Hamiltonian: determinant-resolution and word-resolution generator families both reach a nine-dimensional subspace with energy error 3.019 mHa and energy difference 4×10^-16 Ha, while the retained Pauli bank shrinks from 7,371 to 2,240 words and the QWC setting count from 913 to 465. The paper also proposes a reference-conditioned sector-leakage certificate, a dyadic block-commuting measurement hierarchy that reduces QWC settings to 64 fully commuting settings at explicit logical-CX cost, and finite-shot diagnostics on a four-qubit TFIM bank in which covariance-aware allocation reduces a variance target by 68.9% and mode-wise overlap regularization trades median error for tail-risk control. The authors explicitly limit the claims to small-instance exact and Monte Carlo results and disclaim scaling, hardware, or quantum-advantage claims.","tokens_in":9276,"tokens_out":9274,"duration_ms":102212,"significance":"If the central numerical contract is correct, the paper makes a useful conceptual point: generator resolution is an independent resource variable that can change the measurement bank without changing the solved subspace, and fixed-reference reconstruction separates state contexts from settings, shots, and depth. The strengths are real: exact projected eigensolves are checked against independent PySCF and OpenFermion constructions; the finite-shot study uses 200 Monte Carlo replicas with grouped resampling; evidence labels (exact, oracle-sampled, finite-sample, heuristic) are carried through the records; and the limitations are unusually candid, including no scaling result and no end-to-end advantage claim. The main weakness is that the headline H4 numbers are produced by a private codebase, with only the Hamiltonian energy and Pauli-term expansion cross-checked externally; the subspace-equality and retained-bank counts are not independently auditable as presented.","major_comments":[{"comment":"The central H4 contract—identical nine-dimensional span, principal angles zero, retained banks 7,371 vs 2,240—is generated by the private clifford_qc repository. The internal digest checker verifies only that printed tables match committed JSON records; it does not certify that the records are correct, and the external cross-checks (PySCF/OpenFermion) cover the mapped energy and 185-term Hamiltonian, not the subspace-equality or bank-count claims. Since these counts are the paper's headline result, the frozen artifact should be made publicly available with a persistent identifier, or a minimal independent script should be included that builds the two generator families from the FCIDUMP and recomputes principal angles and retained word universes. Without such an audit path, the load-bearing numerical evidence is not independently verifiable.","section":"§VII Reproducibility; §IV.B"},{"comment":"The statement that the two resolutions reach the same subspace 'to machine precision' is not quantified: the nine principal angles are reported only as zero to numerical precision, and the claimed energy difference is 4×10^-16 Ha but no numerical tolerance or actual maximum angle is given. Please report the largest principal angle (or equivalently the smallest singular value of the overlap between the two spans), the exact energy difference, and the thresholds used for rank and overlap. The entire generator-resolution conclusion rests on this equality, so the evidence should be quantitative in the text rather than asserted qualitatively.","section":"§IV.B"},{"comment":"The reference-conditioned certificate in Eqs. (8)–(9) and the exactness of the reconstructed matrices presume a sector-sharp reference, or a post-selected ρ_q obtained via a quantum non-demolition measurement of N and Sz whose ancilla, gate, and latency costs are explicitly unpriced. The warm-start rows of Table I use algebraic post-selection, so their unchanged setting counts do not reflect the physical cost of realizing ρ_q. Please state explicitly that these rows are conditional on a QND sector measurement being available at negligible overhead, or extend the ledger with a lower-bound cost model for that measurement.","section":"§II.C; §V"}],"minor_comments":[{"comment":"The header 'ArmMError' runs the arm and error columns together; separate the column headings to avoid ambiguity.","section":"Table I"},{"comment":"The abbreviation 'Rot.' in the table header is not defined in the text; define it in the caption, for example as preparation rotors corresponding to Dprep.","section":"Table I"},{"comment":"In Eq. (5), the symbol W denotes both the word-universe set and its cardinality; use a distinct symbol for the set and write W=|W_set| to avoid confusion.","section":"§II.A"},{"comment":"In Eq. (7), the eigenvalue variable λ is introduced without a label; clarify that it is the smallest root of the generalized 2×2 pencil used in the candidate score.","section":"§II.B"}],"recommendation":"major_revision","confidential_remarks":"The reproducibility gap is the main risk to acceptance. I recommend requiring the authors to deposit a frozen, publicly accessible artifact (code, FCIDUMP, benchmark records) or an independent verification script before acceptance. The snapshot offered to referees is a good step, but if it is not made public, the headline numbers cannot be checked by the community. The internal digest checker is good practice but should not substitute for an external check of the central H4 claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before you read it. First, this is not an accuracy or scaling pitch; it is a measurement-accounting paper for quantum subspace methods, and the novelty is real. Second, the headline numbers that carry the paper — identical nine-dimensional subspace, energy match to 4e-16 Ha, retained bank dropping from 7371 to 2240 Pauli words — come from a private codebase. I found no internal inconsistency, but independent verification is blocked until the frozen artifact snapshot is shared.\n\nWhat is actually new: the explicit separation of generator resolution from basis construction, and the resource ledger that refuses to conflate state contexts, measurement settings, shot counts, circuit depth, and post-selection retries. The generator-resolution result is concrete: determinant excitations and their Pauli-word components reach the same span and energy to machine precision, while the final bank changes. If that survives audit, benchmark reports in this subfield should start using these units. The reference-aware symmetry certificate is also well designed. It correctly distinguishes an operator that globally conserves sector from a direction that is sector-safe for one reference, and the negative control (global filter alone leaves them stuck at identity with 56 mHa) makes the point cleanly. The dyadic grouping table shows the full logical-CX cost of trading settings for entangling depth, which is more transparent than most measurement-grouping papers.\n\nThe paper is honest about scope. Exact eigensolves checked against PySCF and OpenFermion, 200-replica Monte Carlo with reported intervals, evidence labels, and no scaling or hardware claims. The finite-shot section reports the bias/tail trade without spinning it: mode-wise regularization removes catastrophic estimates but doubles median error. That is the kind of result you can actually use.\n\nSoft spots, in order. The private artifact is the main concern. The digest checker proves only that tables match committed JSON records, not that the records are correct. The subspace-equality claim and the 7371/2240 counts have no independent construction; only the Hamiltonian energy is cross-checked externally. This is a verification gap rather than a detected error, but it sits exactly on the load-bearing claim. The QND post-selection issue is disclosed in Section V and priced as unpriced; it affects warm-start applications but not the sharp-determinant H4 contract, so I do not treat it as decisive. Minor: the overlap cutoff is explicitly heuristic, which is acceptable, and the ADAPT-VQE comparison is carefully labeled as not equal-precision but still easy to over-read.\n\nWho this is for: anyone comparing subspace methods, designing measurement grouping, or writing benchmark methodology. It deserves a serious referee. My recommendation: send it to review, and make the artifact snapshot part of the review agreement.","headline":"Careful, well-scoped measurement-accounting paper whose central bank-size result rests on private code; deserves peer review if the artifact snapshot actually gets provided.","tokens_in":9769,"tokens_out":3553,"would_cite":true,"duration_ms":36850,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P68","65F15"],"pacs":[],"model":"deepseek-v4-flash","headline":"DA-CASE shows that one cached Pauli bank can rebuild all subspace matrices, and that generator resolution alone cuts the retained bank from 7,371 to 2,240 words on H4.","keywords":["adaptive quantum subspace eigensolver","measurement reuse","Pauli expectation bank","generator resolution","reference-conditioned symmetry","dyadic commuting hierarchy","finite-shot covariance allocation","overlap regularization"],"falsifier":"Take a reference with known sector weight below 1 (for instance, a superposition across particle-number sectors) and run the word-resolution pipeline: if the reconstructed $S$ and $H$ matrices deviate from the exact sector-projected matrices by more than numerical tolerance, or if the computed $\\ell_B$ from Eq. (9) fails to match direct projection of the retained Ritz vectors, the single-bank exactness claim is refuted for sector-mixed references.","tokens_in":8923,"feed_emoji":"⚛️","tokens_out":10650,"duration_ms":100953,"temperature":0.7,"pith_summary":"This paper tries to establish a measurement architecture for quantum subspace diagonalization in which every projected quantity—overlap, Hamiltonian, and observables—is reconstructed by linear combinations of one cached set of Pauli expectations on a single reference state. The paper argues that the dominant costs of such methods are not raw basis size, but measurement contexts, settings, shots, circuit depth, and post-selection retries, and it builds a resource ledger to keep those units separated. On a frozen eight-qubit H4 Hamiltonian, it shows that two generator resolutions, determinant-level and Pauli-word-level, converge to the same nine-dimensional subspace and the same energy to machine precision, while the retained measurement bank falls from 7,371 to 2,240 Pauli words. The contribution is a demonstration of measurement reuse with an explicit ledger, explicitly limited to small exact and Monte Carlo instances.","feed_headline":"Pauli bank shrinks 7,371 to 2,240 with no subspace change","feed_subtitle":"One cached Pauli expectation set rebuilds all subspace matrices from a single reference.","key_machinery":"The load-bearing object is the single-reference Pauli expectation bank: for a reference $\\rho$, each matrix element of $S$, $H$, and $Q$ is expanded in the Hermitian Pauli basis, and all entries are assembled from expectations $\\langle P_w\\rangle$ on the same $\\rho$. Three mechanisms carry the argument. Generator resolution is the choice between scoring a candidate as a complete determinant excitation or as its component Pauli words; this changes the retained word universe and setting count without changing the solved span. The reference-conditioned symmetry certificate, $\\ell_B=\\lambda_{\\max}(L,S)$ with $L_{ij}=\\operatorname{Tr}[\\rho A_i^\\dagger(1-P_q)A_j]$, certifies sector leakage of every normalized combination in the retained subspace, even when individual words fail an operator-global commutator test. The dyadic block-commuting hierarchy groups Pauli words that commute on each contiguous block, interpolating from qubit-wise commuting at block size 1 to full Pauli commutation at block size $n$, and trades setting count for logical-CX depth.","core_discovery":"The central claim is that for a fixed reference $\\rho$, the projected matrices $S_{ij}=\\operatorname{Tr}(\\rho A_i^\\dagger A_j)$, $H_{ij}=\\operatorname{Tr}(\\rho A_i^\\dagger H A_j)$, and observable matrices $Q_{ij}=\\operatorname{Tr}(\\rho A_i^\\dagger Q A_j)$ can all be reconstructed from the same cached Pauli expectations on $\\rho$, with no separately prepared basis states and no Hadamard tests. The paper then claims that generator resolution is a real resource variable: resolving a determinant excitation into component Pauli words, rather than scoring it as one operator, reaches the same retained subspace and energy on H4—energies agree to about $4\\times10^{-16}$ Ha—while the retained word universe drops from 7,371 to 2,240 and the qubit-wise-commuting setting count from 913 to 465. The narrower bank is licensed by a reference-conditioned sector certificate, $\\ell_B=\\lambda_{\\max}(L,S)$, which bounds leakage of the whole retained span even when individual Pauli words fail the global commutator test. The paper also reports auxiliary trades: a dyadic block-commuting hierarchy reduces settings from 913 to 64 at the price of logical CX gates, and covariance-aware shot allocation lowers a projected-matrix variance target by 68.9% in a four-qubit finite-shot diagnostic.","pith_inferences":["A testable extension is to reuse the wide selection cache across a family of related Hamiltonians, such as nearby geometries or embedding parameters, which the paper lists as a possible next step but does not test; the retained-bank ratios on H4 and the 2x2 Hubbard plaquette hint that the saving is system-dependent.","If QND post-selection for sector-mixed references turns out to be expensive on real hardware, the warm-start rows of the ledger would grow by more than the stated retry factor, potentially reversing the apparent advantage over multi-reference methods; the paper explicitly leaves that circuit unpriced.","Adopting the paper's accounting rule—keep contexts, settings, shots, depth, and retries as separate ledger columns—would make future subspace-method comparisons more informative than basis-dimension or energy-error comparisons alone.","The exact span coincidence between determinant and word resolutions is striking but only shown on small systems; a natural check is to test whether the two resolutions continue to converge to the same subspace on larger molecules, which would let cost alone decide the resolution choice."],"forward_implications":["A single cached bank can serve overlap, Hamiltonian, and multiple observable matrices, so subsequent solves or observable evaluations on the same reference reuse the same set of physical shots rather than requiring new prepared basis states.","Generator resolution becomes a practical tuning knob: word-level scoring can shrink the final measurement bank by roughly a factor of three on H4 while preserving the solved subspace, at the cost of more extensive selection work.","A reference-conditioned certificate can admit Pauli directions that a global symmetry filter rejects, provided the reference is sharp in the declared sector, and it certifies the full retained span rather than individual words.","The dyadic commuting hierarchy gives a monotone family of operating points from 913 settings to 64 settings on the retained H4 bank, with explicitly counted logical-CX gates and depths, so a hardware-specific optimum can be chosen once gate and noise data exist.","Covariance-aware shot allocation and mode-wise overlap regularization reduce catastrophic finite-shot outliers and RMSE while increasing median error, indicating a tunable bias–tail-risk trade-off rather than an unconditional accuracy improvement."],"supporting_citations":[{"why":"defines quantum subspace expansion and the projected S and H matrices that the single-bank reconstruction generalizes.","marker":"[1]"},{"why":"supplies the nonorthogonal generalized eigenproblem context and the motivation for off-diagonal overlap measurement.","marker":"[2]"},{"why":"ADAPT-VQE is the main adaptive-state baseline whose context and setting counts the paper compares.","marker":"[13]"},{"why":"ADAPT-GCIM supplies the generating-function baseline with multiple state preparations and transition-matrix pairs used in the matched comparison.","marker":"[14]"},{"why":"defines the FCIDUMP interchange format that binds the frozen Hamiltonian data and reproducibility records.","marker":"[19]"},{"why":"provides an independent Hamiltonian construction check for the H4 contract.","marker":"[20]"},{"why":"provides an independent Pauli-term reconstruction check over 185 terms.","marker":"[21]"},{"why":"introduces qubit-wise commuting grouping, the endpoint of the dyadic hierarchy and the baseline for setting counts.","marker":"[22]"},{"why":"supplies Clifford circuits for simultaneous diagonalization of commuting Pauli groups, used by the dyadic measurement hierarchy.","marker":"[23]"}],"fun_headline_variants":["One cached Pauli set cuts measurement bank from 7,371 to 2,240","Same subspace, 2,240 Pauli words instead of 7,371","Single reference, cached Pauli expectations, no extra state prep","Measurement bank shrinks 69% with no subspace loss","Same energy to machine precision with 69% fewer measurements"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole reconstruction and symmetry certificate assumes the reference state is a sharp eigenstate of the particle-number and $S_z$ sector projectors; when the reference is sector-mixed, exactness requires a QND post-selection whose ancilla, gate, and latency costs the paper does not price.","fun_headline_variants_meta":{"raw":{"variants":["One cached Pauli set cuts measurement bank from 7,371 to 2,240","Same subspace, 2,240 Pauli words instead of 7,371","Single reference, cached Pauli expectations, no extra state prep","Measurement bank shrinks 69% with no subspace loss","Same energy to machine precision with 69% fewer measurements"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000812,"raw_usage":{"total_tokens":3658,"prompt_tokens":1142,"completion_tokens":2516,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":758,"completion_tokens_details":{"reasoning_tokens":2422}},"tokens_in":758,"tokens_out":2516,"duration_ms":17041,"temperature":1.0,"reasoning_tokens":2422,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:25:02.534398+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a reference with known sector weight below 1 (for instance, a superposition across particle-number sectors) and run the word-resolution pipeline: if the reconstructed $S$ and $H$ matrices deviate from the exact sector-projected matrices by more than numerical tolerance, or if the computed $\\ell_B$ from Eq. (9) fails to match direct projection of the retained Ritz vectors, the single-bank exactness claim is refuted for sector-mixed references.","supporting_citations":[{"cited_title":"This removes separately prepared basis states but can enlarge the Pauli universe","cited_arxiv_id":null,"evidence_quote":"defines quantum subspace expansion and the projected S and H matrices that the single-bank reconstruction generalizes."},{"cited_title":"On H4, coarse determinant excitations and their Pauli- word resolution reach the same retained subspace with widths 7371 and 2240","cited_arxiv_id":null,"evidence_quote":"supplies the nonorthogonal generalized eigenproblem context and the motivation for off-diagonal overlap measurement."},{"cited_title":"Bharti and T","cited_arxiv_id":null,"evidence_quote":"ADAPT-VQE is the main adaptive-state baseline whose context and setting counts the paper compares."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"ADAPT-GCIM supplies the generating-function baseline with multiple state preparations and transition-matrix pairs used in the matched comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"introduces qubit-wise commuting grouping, the endpoint of the dyadic hierarchy and the baseline for setting counts."},{"cited_title":"Zheng, B","cited_arxiv_id":null,"evidence_quote":"supplies Clifford circuits for simultaneous diagonalization of commuting Pauli groups, used by the dyadic measurement hierarchy."}],"review_version":1}