Pith. sign in

REVIEW 5 major objections 5 minor 68 references

Moving quantum selected configuration interaction into a CI-matrix representation cuts the qubit cost to the logarithmic minimum while keeping subspace-diagonalization accuracy on molecules like N2 and naphthalene.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 18:13 UTC pith:SVERUCA4

load-bearing objection CIM-QSCI is a genuinely new encoding trick for subspace diagonalization, but the headline resource claim rests on an unverified assumption about crude qDRIFT plus approximate transpilation, so treat the hardware numbers as demonstrations, not evidence of advantage. the 5 major comments →

arxiv 2603.13160 v2 pith:SVERUCA4 submitted 2026-03-13 quant-ph physics.chem-ph

Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization

Vincent Graves , Manqoba Q. Hlatshwayo , Theodoros Kapourniotis , Konstantinos Georgopoulos This is my paper
classification quant-ph physics.chem-ph
keywords quantum selected configuration interactionCI-matrix representationfirst quantizationsample-based quantum diagonalizationqDRIFTheat-bath configuration interactionerror mitigationground-state energy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD) traditionally encode the electronic structure problem in second quantization, so the qubit count grows with the number of orbitals. This paper moves the same idea into the CI-matrix representation, where the Hamiltonian is stored as a sparse matrix and the qubit count is exactly the logarithm of the number of configurations. It introduces two algorithms, CIM-QSCI and CIM-QSHCI, and reports that they reach SQD-level accuracy on N2 and naphthalene benchmarks with fewer qubits and shallower circuits. The QSHCI variant, which replaces classical heat-bath sampling with quantum sampling, is shown to match classical heat-bath CI performance with similarly sized subspaces. The main caveat acknowledged by the authors is a preprocessing cost of O(N^2 log N) to build the CI matrix and decompose it into Pauli strings.

Core claim

The central claim is that the optimal qubit scaling of the CI-matrix representation can be combined with the QSCI sampling idea: construct the full CI Hamiltonian in first quantization, decompose it via the fast Walsh-Hadamard transform into Pauli strings, run a deliberately approximate qDRIFT evolution (single time step t=1, n_a=2λt^2 terms per circuit, repeated r times), and use the measured bitstrings to build a small subspace Hamiltonian whose exact diagonalization gives the ground-state energy. The approximation is justified by the concentration of the target eigenstate on a small set of configurations; the sampling only needs to recover that support. The paper further shows that adding

What carries the argument

The load-bearing object is the CI matrix (CIM) in first quantization, with qubit count q = ⌈log2(N_CSF)⌉. The argument runs through three machinery pieces: the fast Walsh-Hadamard transform that turns the CIM into a weighted Pauli-string sum; a modified qDRIFT approximate evolution that truncates the Hamiltonian to n_a ≈ 2λt^2 terms and repeats r times; and a single-bit-flip mitigation bit that makes the Hamming distance between physical CSFs a multiple of two so one error is detectable. The subspace is selected by the measured bitstrings and diagonalized classically; QSHCI replaces the classical heat-bath threshold with a quantum-sampled probability criterion.

Load-bearing premise

The load-bearing premise is that a very coarse approximate evolution — a single time step with only about 2λt^2 Pauli terms per circuit, repeated r times — still samples the configurations that dominate the true ground state, so the classically diagonalized subspace contains enough support of the exact eigenvector. The hardware runs add a second fragile assumption: that approximating the transpiled circuit with no two-qubit gates (AD=0.5) preserves that sampled support, a cla

What would settle it

Take a strongly correlated molecule (e.g., N2 near dissociation), compute the exact ground state classically, and check whether the union of bitstrings returned by CIM-QSCI at t=1 contains every CSF with squared coefficient above, say, 10^-4. If any large-coefficient CSF is missing, the energy estimate cannot be correct; conversely, if accurate energies require many more repetitions than r = 2λt, the claimed resource savings fail. A complementary test is to run the same pipeline with exact Hamiltonian evolution and compare energies: a material change would show the truncated qDRIFT support is

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Quantum resources for QSCI-style ground-state calculations drop from linear-in-orbitals qubits to log N_CSF, plus one mitigation qubit, while retaining chemical accuracy on N2 and naphthalene.
  • CIM-QSHCI produces final subspaces as small as 1.5–10.5% of the full CI space, making the classical diagonalization step cheap.
  • Because the CI matrix is stored in single precision and only the subspace Hamiltonian is built in double precision, memory requirements for large active spaces are roughly halved.
  • The scheme inherits the variational property: larger sampled subspaces give tighter energy estimates, so users can trade shots and subspace size against accuracy.
  • The O(N^2 log N) FWHT preprocessing is the current bottleneck; the algorithm's practicality improves if replaced by a cheaper Hamiltonian access model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's claims, the approximate-evolution step is effectively a randomized sparse-sampling of the eigenvector support; if that support is not concentrated, the fixed t=1 evolution will need far more repetitions than Eq. (12) suggests. A natural stress test is to compare the sampled support against the largest exact coefficients of the ground state.
  • The parity-bit mitigation is reminiscent of a stabilizer check; one could generalize it to detect two-bit flips or to use the flag qubit for active correction rather than post-selection.
  • Since the CIM framework is matrix-agnostic, the same pipeline could be applied to other sparse symmetric matrices such as graph Laplacians or spin Hamiltonians, as long as the target eigenvector is concentrated on a small subset of basis states.
  • The QSHCI acceptance criterion suggests a general principle: use quantum-sampled occupation probabilities to set per-configuration thresholds instead of a global classical tolerance, which may improve selected-CI methods even outside quantum hardware.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper introduces CIM-QSCI and CIM-QSHCI, two quantum subspace-selection algorithms in which the Hamiltonian is represented as a configuration-interaction matrix (CIM) and encoded with O(log N) qubits. A FWHT-based Pauli decomposition is followed by an approximate qDRIFT evolution, sampling of bitstrings, and classical subspace diagonalization. A single-bit-flip error-mitigation scheme is also introduced. The authors benchmark the algorithms on N2 and naphthalene in emulation and on Rigetti hardware, comparing against LUCJ-SQD, SqDRIFT, and classical HCI. The main claims are: (i) CIM-QSCI achieves similar or better accuracy than SQD-type methods with significantly fewer quantum resources; (ii) CIM-QSHCI achieves accuracy comparable to classical HCI; and (iii) the preprocessing overhead is O(N^2 log N).

Significance. If the claims were fully established, the paper would make a useful contribution to NISQ-era subspace diagonalization: the logarithmic qubit encoding is a clear conceptual advantage over second-quantized representations, the single-qubit bit-flip mitigation is simple and transferable, and the QSHCI idea of augmenting HCI with quantum-computed probabilities is worth exploring. The manuscript also reports real-hardware experiments, which is commendable. However, the central resource and accuracy claims are not supported as stated: the resource comparison in Table I ignores the number of circuit repetitions, the approximate-evolution and transpilation choices are used without a support-preservation or fidelity analysis, and the body of the paper repeatedly reports that HCI actually outperforms QSHCI. These issues affect the headline claims and require substantive revision.

major comments (5)
  1. [Table I and Sec. IV A] The claim of 'significantly less quantum resources' is not supported when repeated executions are counted. For the N2 (10,10) case, CIM-QSCI uses r=10--14 repetitions of a circuit with 716 two-qubit gates, i.e. roughly 7,160--10,024 two-qubit gate applications, while LUCJ-SQD with 2 layers uses a single circuit with 839 two-qubit gates. For naphthalene with (n_a=20, r=200), CIM-QSCI applies 200 circuits of 278 gates (55,600 total two-qubit applications), versus 804 for a single LUCJ-SQD circuit. The table lists per-circuit gate counts only; the total quantum workload must be reported before resource claims can be assessed.
  2. [Sec. II C 1, Eqs. (10)--(12), and Appendix C] The approximate evolution is chosen with n_a = 2λt^2 and r n_a = 2λ^2 t^2, which corresponds to the qDRIFT budget at ε = 1, not at a small simulation error. The text asserts that a less accurate Hamiltonian evolution is still sufficient to recover the important bitstrings, but no theorem, numerical overlap analysis, or fidelity metric is provided to show that the sampled subspace contains the dominant support of the true ground state. The concern is sharpened by the AD=0.5 transpilation used for the hardware runs: Table V reports 0 two-qubit gates for the (10,10) model and 43 for the (10,12) model, so the 'evolved' state is nearly a product state. Without a distribution-distance or overlap metric for the AD=0.5 circuits, the hardware results do not demonstrate that the approximate evolution preserves the intended subspace.
  3. [Abstract, Sec. IV B, Sec. IV C, and Sec. V] The abstract and introduction state that QSHCI achieves 'performance comparable to HCI,' but the body reports the opposite. In Sec. IV B: 'HCI has a lower overall error than CIM-QSHCI' with similarly sized subspaces, and in Sec. IV C: 'The HCI subspace appears to contain more efficient determinants' and 'HCI can produce an energy estimate with high accuracy in 3 iterations, with a much smaller subspace Hamiltonian (≈11%)'. The Summary also says QSHCI can perform 'at best, just as well as the classical method HCI.' The manuscript should either qualify the 'comparable' claim to mean comparable only in specific settings, or remove it from the abstract.
  4. [Sec. II C 1, Eqs. (10)--(12)] The statement that 'Conceptually, Equation 10 and Equation 12 are equivalent when r = 1/ε' is algebraically incorrect. With n_a = 2λt^2, Eq. (12) gives r n_a = 2λ^2 t^2, so r = λ, not r = 1/ε. The equivalence to Eq. (10) is obtained by setting ε = 1 in Eq. (10). This is more than a typo: it conflates the qDRIFT error guarantee with the total gate budget and should be corrected.
  5. [Sec. II E 2, Eq. (16)] The QSHCI acceptance criterion is presented as removing the user-defined tolerance of HCI, but it introduces a user-defined variance factor v and depends on the sampled probability P_k, which is a noisy estimate. No convergence theorem or numerical evidence is given that Eq. (16) yields the same subspace as HCI or that the dependence on P_k is stable. Since QSHCI is the main algorithmic novelty beyond CIM-QSCI, this gap should be addressed or explicitly acknowledged as an open question.
minor comments (5)
  1. [Sec. II B] The abbreviation 'FWHF' appears in the section title; it should be 'FWHT'.
  2. [Sec. IV B] Typo: 'single-bit-flit error mitigation' should be 'single-bit-flip error mitigation'.
  3. [Appendix C] The title 'Approximate-transpiliation' should be 'Approximate transpilation'.
  4. [Sec. V] Typo: 'Heath-bath CI' should be 'Heat-bath CI'.
  5. [Eq. (7)] The notation in the FWHT coefficient formula is unclear: the meaning of h_{n⊕r,n} and the subscript on the Hamiltonian tensor object should be defined or rewritten.

Circularity Check

0 steps flagged

No circularity: benchmarked energies come from independent subspace diagonalization; no fitted parameter or self-citation forces the claimed results.

full rationale

The paper's derivation chain is self-contained: the CI matrix is built from molecular integrals (Eqs. 1-5), decomposed into Pauli strings via FWHT (Eqs. 7-9), evolved using a qDRIFT-style approximate evolution with prescribed n_a and r (Eqs. 11-12), sampled on a quantum device, and then used to construct and diagonalize a subspace Hamiltonian (Eqs. 13-15). The reported ground-state energies are eigenvalues of these subspace Hamiltonians; they are not fitted to or derived from the exact target energies used for benchmarking. The QSHCI acceptance criterion (Eq. 16) uses the measured sampling probability P_k and current eigenvector coefficients, not the exact ground-state energy, so it does not build the target eigenvalue into the input. The error-bound argument is attributed to external work [20] and [28], not to the present authors, and no self-citation chain is load-bearing. The approximate-evolution assumption that 'a less accurate Hamiltonian evolution is still sufficient to recover the important bitstrings' is an unverified algorithmic premise and a potential correctness risk, especially with AD=0.5 transpilation reducing two-qubit gates to near zero in Table V, but it is not circular: the sampled bitstrings are not constructed from the energies later reported. Overall, no step reduces by construction to its own input.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The central algorithm rests on a set of heuristic and standard assumptions: FWHT decomposition, HF initial-state overlap, truncated qDRIFT sampling fidelity, applicability of [20]'s error bound, QSHCI convergence, and approximate transpilation fidelity. The paper declares several user-chosen parameters (t, n_a, r, v, subspace size, AD) and post-hoc HCI tolerances; none is fitted to target energies, so no circularity, but several are under-justified.

free parameters (6)
  • Evolution time t = 1
    Chosen for all simulations; paper notes t>1 may be needed for systems with closely spaced low-lying states (Sec II C 1). Not derived from target accuracy.
  • qDRIFT truncation n_a and repetitions r = Varies: (19-27, 10-14), (8,4), (10,100), (20,200), etc.
    n_a=2*lambda*t^2 and r=2*lambda^2*t^2/n_a, but t is fixed and n_a/r are rounded; different values are used per molecule and accuracy improves with larger n_a/r (Sec IV).
  • QSHCI variance factor v = 1.0 and 100.0
    User-defined relaxation of acceptance criterion Eq (16); v=100 lowers energy but no principled selection rule is given (Sec IV B).
  • Subspace Hamiltonian size = 40%, 60%, 80% for CIM-QSCI; 1.5%-10.5% for QSHCI
    Method parameter; results depend strongly on it (Sec IV A).
  • Approximation degree AD = 1.00, 0.75, 0.50
    Qiskit transpiler approximation; AD=0.5 yields zero two-qubit gates for the (10,10) model (Table V), changing circuit content; chosen to fit hardware constraints.
  • HCI tolerance (comparison only) = 5e-5, 5e-3, 8e-4
    Chosen so HCI subspace sizes roughly match CIM-QSHCI, which affects the fairness of the 'comparable to HCI' conclusion (Sec IV B).
axioms (6)
  • standard math FWHT Pauli decomposition (Eqs 7-9) correctly encodes the real symmetric CIM as a qubit Hamiltonian.
    Invoked in Sec II B 1, relying on [27]; no proof in paper.
  • domain assumption HF Slater determinant has sufficient overlap with target ground state across all bond lengths to seed useful sampling.
    Sec II C states this; accuracy degrades at longer N2 bond lengths (Sec IV A), showing the assumption is strained.
  • domain assumption Truncated qDRIFT with t=1 and n_a terms preserves enough support of the target eigenstate for subspace diagonalization.
    Sec II C 1; the paper does not prove this for general molecules and notes t>1 may be needed.
  • domain assumption Error bound of [20] (Lemma A.1) applies to this algorithm as a special case of SKQD with d=2.
    Sec II C 1 directs reader to [20]; no self-contained proof.
  • ad hoc to paper QSHCI acceptance criterion (Eq 16) converges to an accurate subspace without a user tolerance.
    Sec II E 2; no convergence proof; results show HCI selects more efficient determinants, so the criterion is heuristic.
  • ad hoc to paper Approximate transpilation (AD=0.5) preserves the relevant evolution despite reducing two-qubit gates to near zero.
    Appendix C/Table V; no fidelity metric reported; AD=0.25 reduces circuit to measurement gates, indicating a degradation not characterized.

pith-pipeline@v1.3.0-alltime-deepseek · 22598 in / 14688 out tokens · 129985 ms · 2026-08-02T18:13:02.146781+00:00 · methodology

0 comments
read the original abstract

Quantum algorithms for selecting a subspace of Hamiltonians to diagonalize have emerged as a promising alternative to variational algorithms in the NISQ era. So far, such algorithms, which include the quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD), have been formulated within second-quantization in Fock space, which leads to inefficient usage of qubit resources. We introduce the first QSCI algorithm developed in the CI-matrix (CIM) framework, which is known to have optimal qubit scaling of exactly $\lceil \log_2 (N) \rceil$ where $N$ is the size of the CIM. In addition, we introduce a novel single-bit flip error mitigation which comes at the overhead of a single qubit and we combine this with a stochastic approximate Trotterization evolution adapted from qDRIFT. Simulating benchmark N$_2$ and naphthalene molecules on quantum hardware, our results achieved similar accuracy as SQD methods but with significantly less quantum resources. However, our CIM-QSCI algorithm and SQD methods could not match the performance of classical heat-bath CI (HCI) for the same task. Hence, we introduce an augmented version of QSCI called quantum selected heat-bath CI (QSHCI). This variant replaces classical heat-bath sampling with quantum sampling from QSCI to achieve performance comparable to HCI. We note that a current drawback of our approach is the preprocessing cost of $\mathcal{O}(N^2\log N)$ for constructing the CIM and performing the Pauli decomposition. This can be further improved by considering efficient CIM access models for the stochastic Trotter evolution.

Figures

Figures reproduced from arXiv: 2603.13160 by Konstantinos Georgopoulos, Manqoba Q. Hlatshwayo, Theodoros Kapourniotis, Vincent Graves.

Figure 2
Figure 2. Figure 2: FIG. 2: Simulated potential energy curve of N [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Absolute error of simulated N [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Absolute error of simulated ground state energy [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Error of N [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

68 extracted references · 2 canonical work pages · 2 internal anchors

  1. [1]

    In addition, it can be sparse or dense, but the accuracy of the final eigenvalue(s) depends on the matrix’s density

    A General Matrix In principle, any square, symmetric matrix with real values can be used as the input matrix. In addition, it can be sparse or dense, but the accuracy of the final eigenvalue(s) depends on the matrix’s density. If the matrix is sparse, then several terms in the eigen- vectors will be zero. Seeing as the aim of the QSCI-based algorithms is ...

  2. [2]

    This means that the approach is agnostic to the type of quantization used to construct the Slater de- terminants (see below), i.e, first- or second-quantization

    CI-Hamiltonian Matrix In the results section of this work, the CI-Hamiltonian matrix (or CIM) is the matrix of interest and is, therefore, the matrix that is implemented directly on the quantum computer. This means that the approach is agnostic to the type of quantization used to construct the Slater de- terminants (see below), i.e, first- or second-quant...

  3. [3]

    Ifi=j: Hii = NeX k=1 hχi kχi k + NeX k<l hχi kχi l χi kχi l −h χi kχi l χi l χi k (2)

  4. [4]

    Ifiandjdiffer by one spin-orbital labelledχ i p and χj q: Hij =h χipχj q + NeX l hχipχi l χj qχj l −h χi pχi l χj l χj q (3)

  5. [5]

    Ifiandjdiffer by two spin-orbitals labelledχ i pχi r andχ j qχj s: Hij =h χipχirχj qχj s −h χipχirχj sχj q (4)

  6. [6]

    An active-space is created when Slater determinants are built using a specified set of orbitals,y, and ac- tive electrons,x, instead of using the full Hilbert space

    Ifiandjdiffer by more than two-spin orbitals: Hij = 0 (5) Hereh pq andh qprs are one- and two-electron integrals, respectively. An active-space is created when Slater determinants are built using a specified set of orbitals,y, and ac- tive electrons,x, instead of using the full Hilbert space. Configuration state functions (CSF) can be constructed from a l...

  7. [7]

    This algorithm works in two stages

    Fast Walsh-Hadamard Transform The CI-Hamiltonian can be decomposed into a Pauli string using the fast Walsh-Hadamard transform (FWHT) [27]. This algorithm works in two stages. First, the coefficients of the Pauli-strings can be computed from the Hamiltonian as: αr,s = i−|r∧s| 2q 2q−1X n=0 hn⊕r,n ˆH ⊗q n,s (7) where,α r,s is a matrix element of the coeffic...

  8. [8]

    qDRIFT and its Modifications In qDRIFT Trotterization, the circuit depth is reduced by probabilistically truncating the Lie-Trotter Trotteri- zation using the strength of the Hamiltonian terms. I.e, for a Hamiltonian written as a Pauli string, as in Equa- tion 9, the Hamiltonian that is Trotterized is a truncated version of ˆHq where the terms that have t...

  9. [9]

    In this algorithm, the CIM is decomposed into a sum of one-sparse Hamiltonians, each of which contains a single molecular integral

    Alternative Approach An alternative to the FWHT and Trotterization is to use the graph colouring algorithm of Babbushet al.[26]. In this algorithm, the CIM is decomposed into a sum of one-sparse Hamiltonians, each of which contains a single molecular integral. This is further decomposed by discretizing the integrals in real space into a sum of self-invers...

  10. [10]

    These are used to construct a subspace-Hamiltonian (see Section II E)

    Bit-flip Mitigation The output of the quantum computer is a series of sam- pled bitstrings, each one corresponding to a specific CSF. These are used to construct a subspace-Hamiltonian (see Section II E). On a noisy device, some of the sampled bitstrings may have undergone bit-flip errors, which may broaden the distribution of sampled bitstrings and resul...

  11. [11]

    The set of sampled CSF,S, then undergoes the bit-flip mitigation post-selection process described above

    Quantum Selected CI On the quantum computer, a probability distribution proportional to the desired wavefunction,|Ψ⟩, is mea- sured in the computational basis as, Ps ∝ |c|2 (13) whereP s is the sampled probability distribution andc are the molecular wavefunction coefficients. The set of sampled CSF,S, then undergoes the bit-flip mitigation post-selection ...

  12. [12]

    The algorithm has the following steps:

    Quantum Selected Heat-bath CI The quantum selected heat-bath CI (QSHCI) algo- rithm follows the same workflow as heat-bath CI (HCI), but with a modified acceptance criterion. The algorithm has the following steps:

  13. [13]

    The subspace is initialized with only the initial trial wavefunction

  14. [14]

    Compute the eigenvector of the current subspace

  15. [15]

    The term vis a user-defined variance factor which relaxes the acceptance criteria if desired

    Add configurationkto the subspace if: |Hkici|> √Pk v (16) where configurationiis already in the subspace, Hki is the matrix element with index [k, i],ci is the coefficient of configurationiin the current eigenvec- tor, andP k is the probability that configurationk was sampled on the quantum computer. The term vis a user-defined variance factor which relax...

  16. [16]

    Repeat steps 2. and 3. until no additional configu- rations are added to the subspace. Once the subspace has converged, the final eigenvalue is taken as the result. In HCI, the same workflow is used except that the acceptance criteria is: |Hkici|> ϵ(17) whereϵis a user-defined tolerance. Conceptually, QSHCI functions the same as HCI but removes the user-d...

  17. [17]

    The number of qubits required here is exactly ⌈log2(NCSF ) + 1⌉, which is less than the tradi- tional second-quantized approach, which scales in the number of qubits as the number of spin-orbitals. In addition, the use of molecular point groups al- lows us to remove many determinantsa priorithat do not contribute to the eigenvector of interest at the poin...

  18. [18]

    Note that the final subspace Hamiltonian is still constructed in double- precision so that the final eigenvalues inherit this higher level of precision

    The memory requirement for the input matrix is only single-precision, which is half the standard double-precision requirements. Note that the final subspace Hamiltonian is still constructed in double- precision so that the final eigenvalues inherit this higher level of precision

  19. [19]

    In addition, this approach results in a lower gate count than full Trotterization which can easily become intractable

    The use of the approximate evolution means that only the Pauli-strings that are used are computed, and those with a small coefficient are never com- puted. In addition, this approach results in a lower gate count than full Trotterization which can easily become intractable. The post-processing diagonalization step of the QSHCI algorithm presented here sca...

  20. [20]

    Piccinelli, A

    S. Piccinelli, A. Baiardi, M. Rossmannek, A. C. Vazquez, F. Tacchino, S. Mensa, E. Altamura, A. Alavi, M. Motta, J. Robledo-Moreno, W. Kirby, K. Sharma, A. Mezza- capo, and I. Tavernelli, Quantum chemistry with prov- able convergence via randomized sample-based quan- tum diagonalization, arXiv 10.48550/arXiv.2508.02578 (2025), 2508.02578 [quant-ph]

    doi:10.48550/arxiv.2508.02578 2025

  21. [21]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. John- son, M. Kieferov´ a, I. D. Kivlichan, T. Menke, B. Per- opadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru- Guzik, Quantum chemistry in the age of quantum com- puting, Chemical Reviews119, 10856 (2019), 1812.09976 [quant-ph]

    Pith/arXiv arXiv 2019

  22. [22]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quan- tum materials science, Chemical Reviews120, 12685 (2020)

    2020

  23. [23]

    A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gily´ en, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brand˜ ao,Quantum Algorithms: A Survey of Appli- cations and End-to-end Complexities(Cambridge Uni- versity Press, 2025)

    2025

  24. [24]

    A. Y. Kitaev, Quantum measurements and the abelian stabilizer problem, arXiv 10.48550/arXiv.quant- ph/9511026 (1995), quant-ph/9511026

    doi:10.48550/arxiv.quant- 1995

  25. [25]

    Peruzzo, J

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum pro- cessor, Nature Communications5, 10.1038/ncomms5213 (2014)

    doi:10.1038/ncomms5213 2014

  26. [26]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets, Nature549, 242 (2017)

    2017

  27. [27]

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, An adaptive variational algorithm for exact molecular simulations on a quantum computer, Na- ture Communications10, 10.1038/s41467-019-10988-2 (2019)

    doi:10.1038/s41467-019-10988-2 2019

  28. [28]

    Larocca, S

    M. Larocca, S. Thanasilp, S. Wang, K. Sharma, J. Bia- monte, P. J. Coles, L. Cincio, J. R. McClean, Z. Holmes, and M. Cerezo, Barren plateaus in variational quantum computing, Nature Reviews Physics7, 174 (2025)

    2025

  29. [29]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algo- rithms, Nature Reviews Physics3, 625 (2021)

    2021

  30. [30]

    Takagi, S

    R. Takagi, S. Endo, S. Minagawa, and M. Gu, Funda- mental limits of quantum error mitigation, npj Quantum Information8, 10.1038/s41534-022-00618-z (2022)

    doi:10.1038/s41534-022-00618-z 2022

  31. [31]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, The variational quantum eigensolver: A re- view of methods and best practices, Physics Reports986, 1 (2022)

    2022

  32. [32]

    Yang, B.-N

    Y. Yang, B.-N. Lu, and Y. Li, Accelerated quantum monte carlo with mitigated error on noisy quantum com- puter, PRX Quantum2, 040361 (2021)

    2021

  33. [33]

    W. J. Huggins, B. A. O’Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, Unbiasing fermionic quantum monte carlo with a quantum computer, Nature 603, 416 (2022)

    2022

  34. [34]

    Kanno, M

    K. Kanno, M. Kohda, R. Imai, S. Koh, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, Quantum-selected configuration interaction: classical diagonalization of hamiltonians in subspaces selected by quantum comput- ers, arXiv 10.48550/arXiv.2302.11320 (2023), 2302.11320 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2302.11320 2023

  35. [35]

    Sugisaki, S

    K. Sugisaki, S. Kanno, T. Itoko, R. Sakuma, and N. Yamamoto, Hamiltonian simulation-based quantum- selected configuration interaction for large-scale elec- 15 tronic structure calculations with a quantum computer, arXiv 10.48550/arXiv.2412.07218 (2024), 2412.07218 [quant-ph]

    doi:10.48550/arxiv.2412.07218 2024

  36. [36]

    Robledo-Moreno, M

    J. Robledo-Moreno, M. Motta, H. Haas, A. Javadi- Abhari, P. Jurcevic, W. Kirby, S. Martiel, K. Sharma, S. Sharma, T. Shirakawa, I. Sitdikov, R.-Y. Sun, K. J. Sung, M. Takita, M. C. Tran, S. Yunoki, and A. Mezza- capo, Chemistry beyond exact solutions on a quantum- centric supercomputer, arXiv 10.48550/arXiv.2405.05068 (2024), 2405.05068 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2405.05068 2024

  37. [37]

    Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization

    S. Barison, J. R. Moreno, and M. Motta, Quantum- centric computation of molecular excited states with extended sample-based quantum diagonalization, arXiv 10.48550/arXiv.2411.00468 (2024), 2411.00468 [quant- ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2411.00468 2024

  38. [38]

    Kaliakin, A

    D. Kaliakin, A. Shajan, J. R. Moreno, Z. Li, A. Mitra, M. Motta, C. Johnson, A. A. Saki, S. Das, I. Sitdikov, A. Mezzacapo, and K. M. M. Jr, Accurate quantum- centric simulations of supramolecular interactions, arXiv 10.48550/arXiv.2410.09209 (2024), 2410.09209 [quant- ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2410.09209 2024

  39. [39]

    Y.-c. Chen, R. Wu, M. H. Cheng, and M.-H. Hsieh, Neu- ral network assisted fermionic compression encoding: A lossy-QSCI framework for resource-efficient ground-state simulations, Physical Review Research 10.1103/9x8b- 4j41 (2025), 2505.17846 [quant-ph]

    arXiv 2025

  40. [40]

    Richer, G

    M. Richer, G. S´ anchez-D ´ ıaz, M. Mart ´ ınez-Gonz´ alez, V. Chuiko, T. D. Kim, A. Tehrani, S. Wang, P. B. Gaik- wad, C. E. V. de Moura, C. Masschelein, R. A. Miranda- Quintana, A. Gerolin, F. Heidar-Zadeh, and P. W. Ayers, PyCI: A python-scriptable library for arbitrary determi- nant CI, The Journal of Chemical Physics161, 132502 (2024)

    2024

  41. [41]

    Shajan, D

    A. Shajan, D. Kaliakin, A. Mitra, J. Robledo Moreno, Z. Li, M. Motta, C. Johnson, A. A. Saki, S. Das, I. Sit- dikov, A. Mezzacapo, and K. M. Merz, Toward quantum- centric simulations of extended molecules: Sample-based quantum diagonalization enhanced with density matrix embedding theory, Journal of Chemical Theory and Com- putation21, 6801 (2025)

    2025

  42. [42]

    Danilov, J

    D. Danilov, J. Robledo-Moreno, K. J. Sung, M. Motta, and J. Shee, Enhancing the accuracy and efficiency of sample-based quantum diagonalization with phaseless auxiliary-field quantum monte carlo, Journal of Chem- ical Theory and Computation21, 11585 (2025)

    2025

  43. [43]

    Kaliakin, A

    D. Kaliakin, A. Shajan, F. Liang, and K. M. Merz, Implicit solvent sample-based quantum diagonalization, The Journal of Physical Chemistry B129, 5788 (2025)

    2025

  44. [44]

    This underscores the fact that our CIM-QS(H)CI methods achieve similar or better accuracy with fewer quantum resources

    and CIM-QSCI, it can be seen that the 2-qubit gate count and depth are approximately the same, but that the qubit requirements are lower for CIM-QS(H)CI. This underscores the fact that our CIM-QS(H)CI methods achieve similar or better accuracy with fewer quantum resources. Fifth, Figure 4 shows that the CIM-QSHCI with a vari- ance factor of 100.0 clearly ...

  45. [45]

    J. Yu, J. R. Moreno, J. T. Iosue, L. Bertels, D. Claudino, B. Fuller, P. Groszkowski, T. S. Humble, P. Jurce- vic, W. Kirby, T. A. Maier, M. Motta, B. Pokharel, A. Seif, A. Shehata, K. J. Sung, M. C. Tran, V. Tri- pathi, A. Mezzacapo, and K. Sharma, Quantum-centric algorithm for sample-based krylov diagonalization, arXiv 10.48550/arXiv.2501.09702 (2025), ...

    doi:10.48550/arxiv.2501.09702 2025

  46. [46]

    Quantum Algorithms for Quantum Chemistry based on the sparsity of the CI-matrix

    B. Toloui and P. J. Love, Quantum algorithms for quantum chemistry based on the sparsity of the CI-matrix, arXiv 10.48550/arXiv.1312.2579 (2013), 1312.2579 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1312.2579 2013

  47. [47]

    Babbush, D

    R. Babbush, D. W. Berry, Y. R. Sanders, I. D. Kivlichan, A. Scherer, A. Y. Wei, P. J. Love, and A. Aspuru- Guzik, Exponentially more precise quantum simulation of fermions in the configuration interaction representa- tion, Quantum Science and Technology3, 015006 (2017)

    2017

  48. [48]

    T. N. Georges, B. K. Berntson, C. S¨ underhauf, and A. V. Ivanov, Pauli decomposition via the fast walsh-hadamard transform, New Journal of Physics27, 033004 (2025)

    2025

  49. [49]

    Campbell, Random compiler for fast hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019)

    E. Campbell, Random compiler for fast hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019)

    2019

  50. [50]

    A. A. Holmes, N. M. Tubman, and C. J. Umrigar, Heat- bath configuration interaction: An efficient selected con- figuration interaction algorithm inspired by heat-bath sampling, Journal of Chemical Theory and Computation 12, 3674 (2016)

    2016

  51. [51]

    Fan and P

    P.-D. Fan and P. Piecuch, The usefulness of exponen- tial wave function expansions employing one- and two- body cluster operators in electronic structure theory: The extended and generalized coupled-cluster methods, Advances in Quantum Chemistry, Academic Press51, 1 (2006)

    2006

  52. [52]

    I. W. Bulik, T. M. Henderson, and G. E. Scuseria, Can single-reference coupled cluster theory describe static correlation?, Journal of Chemical Theory and Compu- tation11, 3171 (2015)

    2015

  53. [53]

    A. B. Patel, S. Shaikh, K. R. Jain, C. Desai, and D. Madamwar, Polycyclic aromatic hydrocarbons: Sources, toxicity, and remediation approaches, Frontiers in Microbiology11, 10.3389/fmicb.2020.562813 (2020)

    arXiv 2020

  54. [54]

    Montano, G

    L. Montano, G. M. Baldini, M. Piscopo, G. Liguori, R. Lombardi, M. Ricciardi, G. Esposito, G. Pinto, C. Fontanarosa, M. Spinelli, I. Palmieri, D. Sofia, C. Brogna, C. Carati, M. Esposito, P. Gallo, A. Amore- sano, and O. Motta, Polycyclic aromatic hydrocarbons (PAHs) in the environment: Occupational exposure, health risks and fertility implications, Toxic...

    2025

  55. [55]

    Wahab, L

    A. Wahab, L. Pfuderer, E. Paenurk, and R. Gershoni- Poranne, The COMPAS project: A computational database of polycyclic aromatic systems. phase 1: cata-condensed polybenzenoid hydrocarbons, Journal of Chemical Information and Modeling62, 3704 (2022)

    2022

  56. [56]

    N. M. Tubman, C. Mejuto-Zaera, J. M. Epstein, D. Hait, D. S. Levine, W. Huggins, Z. Jiang, J. R. McClean, R. Babbush, M. Head-Gordon, and K. B. Whaley, Post- poning the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quan- tum devices, arXiv 10.48550/arXiv.1809.05523 (2018), 1809.05523 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.1809.05523 2018

  57. [57]

    Scali, J

    S. Scali, J. Kirsopp, A. M. Romero, and M. Krompiec, Purified phase estimation samples spectra efficiently, arXiv 10.48550/arXiv.2510.14744 (2025), 2510.14744 [quant-ph]

    doi:10.48550/arxiv.2510.14744 2025

  58. [58]

    K. Sugisaki, Size-consistent implementation of hamilto- nian simulation-based quantum-selected configuration in- teraction method for the supramolecular approach, arXiv 10.48550/arXiv.2510.23154 (2025), 2510.23154 [quant- ph]

    doi:10.48550/arxiv.2510.23154 2025

  59. [59]

    Ghosh, C

    S. Ghosh, C. J. Cramer, D. G. Truhlar, and L. Gagliardi, Generalized-active-space pair-density functional theory: an efficient method to study large, strongly correlated, conjugated systems, Chemical Science8, 2741 (2017)

    2017

  60. [60]

    D. G. A. Smith, L. A. Burns, A. C. Simmonett, R. M. Parrish, M. C. Schieber, R. Galvelis, P. Kraus, H. Kruse, R. Di Remigio, A. Alenaizan, A. M. James, S. Lehtola, J. P. Misiewicz, M. Scheurer, R. A. Shaw, J. B. Schriber, Y. Xie, Z. L. Glick, D. A. Sirianni, J. S. O’Brien, J. M. Waldrop, A. Kumar, E. G. Hohenstein, B. P. 16 Pritchard, B. R. Brooks, H. F. ...

    2020

  61. [61]

    Treinish, J

    M. Treinish, J. Lishman, L. Bello, J. Gambetta, D. M. Rodr ´ ıguez, M. Marques, J. Gacon, P. Nation, C. J. Wood, ewinston, J. Gomez, R. Chen, A. Cross, K. Krsulich, S. Wood, I. F. Sertage, A. Ivrii, N. Kanazawa, E. P. Tapia, L. Capelluto, T. Alexander, E. Arellano, I. Hama- mura, E. Navarro, T. Imamichi, S. de la Puente Gonz´ alez, S. Thomas, J. Rubio, an...

    2025

  62. [62]

    Qiskit/qiskit-addon-sqd (2025), original-date: 2024-08- 16T12:44:57Z

    2025

  63. [63]

    Q. Sun, X. Zhang, S. Banerjee, P. Bao, M. Barbry, N. S. Blunt, N. A. Bogdanov, G. H. Booth, J. Chen, Z.-H. Cui, J. J. Eriksen, Y. Gao, S. Guo, J. Hermann, M. R. Hermes, K. Koh, P. Koval, S. Lehtola, Z. Li, J. Liu, N. Mardirossian, J. D. McClain, M. Motta, B. Mussard, H. Q. Pham, A. Pulkin, W. Purwanto, P. J. Robin- son, E. Ronca, E. R. Sayfutyarova, M. Sc...

    2020

  64. [64]

    The gate counts are for SqDRIFT modeln a10r500 are assumed to be similar to the modeln a10r1000 reported in [20] as the only difference in these models is the number of repetitions

  65. [65]

    J. Han, J. Pei, and H. Tong, Data, measurements, and data preprocessing, inData Mining (Fourth Edition), 4 (ScienceDirect)

  66. [66]

    M. V. M. Mora, TWO-SAMPLE KOLMOGOROV- SMIRNOV TESTS AS CAUSALITY TESTS. a NAR- RATIVE OF LATIN AMERICAN INFLATION FROM 2020 TO 2022., Chilean Journal of Economy and Society. Appendix A: Glossary of T erms Table II shows frequently used abbreviations. TABLE II: Glossary of terms / abbreviations frequently used throughout. Abbreviation Meaning CI Configurat...

    2020

  67. [67]

    Here, a low cosine similarity or KS- statistic score would indicate that the measured distribu- tion is similar to random sampling

    Comparison with Random Sampling The results from the cosine similarity and KS-tests are shown in Table III. Here, a low cosine similarity or KS- statistic score would indicate that the measured distribu- tion is similar to random sampling. Both metric indicate TABLE III: Comparisons of distributionsS1,S2,B1 andB2with random sampling (R0). Scores close to ...

  68. [68]

    In Table IV, the cosine similarity and TABLE IV: Cosine similarity and KS-statistic scores for comparisons between theS1,S2,B1andB2 distributions

    Comparison with Bit-flip Mitigated Results Next, we present a comparison between the distri- butions that include the bit-flip mitigation scheme and those that do not. In Table IV, the cosine similarity and TABLE IV: Cosine similarity and KS-statistic scores for comparisons between theS1,S2,B1andB2 distributions. Distributions Cosine Similarity KS-Statist...