We demonstrate that fermionic quantum-chemistry ground-state computation can be performed natively in the N-electron determinant subspace (dim D = C(M, N)) rather than in the full 2^M Jordan-Wigner Hilbert space, with verified FCI-quality results on ten benchmark systems (Hubbard-4, H4, LiH, H2O/STO-3G, NH3, BeH2, CH4, N2, F2, H2O/6-31G) spanning 8 to 26 qubits. Three pipeline generations are included, each verified against PySCF FCI or exact-diagonalization references: (1) a dense determinant-basis pipeline (compression ratios 3.66x to 16.37x at 8-16 qubits, energies matching FCI to 1e-12 Ha or better; NH3 FCI-quality in 11.7 min where the full-Hilbert verification path needs ~3 h); (2) a sparse Lanczos pipeline (own solver with full reorthogonalization and residual-based convergence, plus sparse-to-sparse antisymmetric projection) that passes the dense-eigensolver ceiling — CH4 at 18 qubits (D = 43,758, 1.3e-12 Ha vs FCI, dense infeasible at ~30 GB), N2 at 20 qubits (2.4e-12 Ha, 179 iterations), F2 at 20 qubits (D = 190, a 5,519x compression, three-way agreement to 5.7e-14); (3) a matrix-free Slater-Condon formulation (correct-by-construction element anchor, equality-locked fast paths, flat two-electron tensor, data-driven spin-conservation skip, threaded gather) that eliminates the stored Hamiltonian entirely — CH4 in 17.9 s (10x the stored-sparse path), and H2O/6-31G at 26 qubits (D = 5,311,735): ground-state energy matching PySCF FCI to 3.1e-12 Ha in 3.7 h on a laptop, 143 Lanczos iterations, with the 2^26 Hilbert space never instantiated (stored alternatives estimated at 160-440 GB on the test hardware). A companion result documents the parastatistics connection with its precise scope: the parabose-2 physical subspace coincides with the fermionic antisymmetric subspace exactly in, and only in, the two-particle sector; for general particle number the parabose-p Fock space decomposes by Young diagrams of at most p rows (verified numerically at p = 2 and p = 3 across multiple (n, R) corners and distinct Young shapes), while general-N CI spaces are standard fermionic objects. Order-1 parabosons are ordinary bosons. An earlier general-N identification of CI spaces with parabose-2 sectors is explicitly withdrawn in the writeup, with the refuting counterexample recorded. The deposit includes: (a) the full method writeup; (b) the complete header-only C++17 source of all three pipeline generations with their BDD test suites; (c) the parabose-p structural-anchor tests; (d) PySCF/OpenFermion integral-generator scripts for all ten systems; (e) measured benchmark CSV data. This is a defensive publication establishing freedom-to-operate for: (i) the determinant-native chemistry pipeline; (ii) the sparse-to-sparse antisymmetric projection; (iii) the matrix-free Slater-Condon H·v formulation with data-driven spin skip and threaded gather; (iv) the Lanczos production workflow distinct from verification mode; and (v) the parabose-p height-bounded Young decomposition as a forward extension path.
Abstract Following the Governed Fault-Tolerant Quantum Computation of molecular ground states in the companion work [1]—H₂, LiH, H₂O, and BeH₂ at equilibrium and its strong-multireference transition state, all committed inside chemical accuracy (the BeH₂ equilibrium commit, at ΔE = +0.595 µHa, sitting 7.7× inside wavenumber accuracy—1 cm⁻¹ ≈ 0.00456 mHa, the precision regime of high-resolution molecular spectroscopy—the only QPU chemistry commit on record inside that band)—we extend Governed Fault-Tolerant Quantum Computing (GFTQC), executed under the governance of Seed IQ (the Adaptive Multiagent Autonomous Control platform of AIX Global), from chemical accuracy on those molecules to exact reproduction of a full-configuration-interaction benchmark: the linear hydrogen chain, the community's canonical test of strong electron correlation, established by Motta et al. [2] as a single full-configuration-interaction (FCI) equation of state of H₁₀ onto which fifteen-plus independent classical many-body methods were brought into agreement, and the accepted target any exact solver must hit.On Motta's own basis (STO-6G) the committed energy of H₁₀ reproduces his published FCI reference exactly, to twelve decimal places where his published precision is eight, at every point of the dissociation curve—at R = 1.8 bohr −5.424385376333 Ha against the published −5.42438538—each value internally certified exact. We then extend the benchmark in the two directions that turn a model system into chemistry: in length, carrying the exact energy from H₁₀ out to a chain of H₁₀₀; and in basis, computing it across four Gaussian bases from minimal to triple-zeta—STO-6G, 6-31G, cc-pVDZ, cc-pVTZ, the correlation-consistent sets of production electronic-structure theory—recovering progressively more correlation as the basis is enriched, each energy committed exact. Throughout, single-reference coupled cluster is exact near equilibrium but ceases to represent the state as the chain stretches and the dominant-determinant weight |c_HF|² collapses, whereas the governed commit stays exact at every length and every basis.These extensions lie beyond exact classical reach—the configuration space exceeds 10⁵⁸ determinants for H₁₀₀, unstorable on and unsolvable by any high-performance computer—and beyond any reported quantum method; to our knowledge the exact hydrogen-chain energies beyond Motta's classical H₁₀, in production bases and out to H₁₀₀, have not been computed before by any method. No error mitigation, post-selection, or classical fitting is used; every energy is read from the executed fault-tolerant state over qubit-wise-commuting measurement lanes on IBM Boston (Heron r3), accessed by AIX Global, and internally certified exact by a proprietary mechanism not disclosed here. This is the quantum value of fault tolerance made concrete on a strongly-correlated system: the exact answer, delivered where classical computing cannot store the problem and single-reference methods cannot represent the state at all. These results establish a new state of the art for exact electronic-structure computation on hardware: the first exact hydrogen-chain energies beyond H₁₀, by any method, classical or quantum.
In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H
2, LiH, BeH
2, H
2O, and NH
3. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H
2 and HeH
+ using both STO-3G and 6-31G basis sets, and for LiH and BeH
2 in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32
× 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
We present a library of qubit Hamiltonians for molecular quantum simulation that are structurally sparser than conventional Gaussian-basis alternatives by one to three orders of magnitude. The Hamiltonians are constructed from a spectral graph theory framework (GeoVac) that exploits natural coordinate separations in molecular electronic structure, producing block-diagonal electron repulsion integrals and Gaunt-enforced selection rules that persist through Jordan-Wigner encoding. For the composed architecture (PK-partitioned), the composed LiH Hamiltonian is near parity with minimal-basis STO-3G on Pauli count (334 vs. STO-3G's 276 reduced / 907 raw) while using more qubits; the decisive resource advantages are the
O(Q2.5) Pauli scaling and a 190
× reduction versus cc-pVDZ. The balanced coupled architecture (PK-free) binds LiH with an FCI minimum at a computed
Req=3.227 bohr (7.0% above the experimental 3.015 bohr) at
nmax=2 (878 Pauli terms, 30 qubits); a single-point evaluation at the experimental geometry reaches 0.20% energy error at
nmax=3 (84 qubits) when solved exactly. Chemistry-accuracy scope at
nmax=2 is row-conditional: first-row hydrides (LiH, BeH
2, H
2O,
…) bind with documented potential-energy-surface (PES) topology, while second-row hydrides (NaH and below) exhibit monotone overattraction under every tested configuration — frozen-core balanced, multi-zeta valence, screened cross-center, explicit-core Hartree–Fock — with no interior PES minimum at the qubit-Hamiltonian level. We document this scope boundary empirically in \S(ref); the framework's primary value proposition is structural sparsity with quantitative truncation-convergence rates (Paper 38 state-space GH convergence), not energy-accuracy parity with CCSD(T) on second-row systems. The hamiltonian() registry covers 37 systems (35 composed molecules spanning
Z=1–56, H through Ba, plus the He and H
2 reference atoms), including multi-center systems (CO, N
2, F
2), mixed frozen-core molecules (NaCl), and the full first transition series as hydrides (ScH through ZnH), with Pauli scaling
O(Q2.5) confirmed universal across all three rows, compared to
O(Q3.9–4.3) for Gaussian baselines. The composed Pauli count is exactly linear in qubit count (coefficient
11.10, exact, for main-group molecules;
9.23 for
d-orbital blocks under the pair-diagonal ERI approximation (Sec. (ref))—the exact global-
ML rule makes the
d-block coefficient higher, not lower), so adding atoms to a molecule increases quantum cost linearly. Second- and third-row molecules use analytical frozen cores ([Ne], [Ar], [Ar]3
d10); the frozen-core energy enters only through the identity operator and does not affect quantum measurement cost. Isostructural molecules with frozen cores produce identical Pauli counts across periodic table rows. The Hamiltonians are available as a Python library with Qiskit, OpenFermion, and PennyLane export. GeoVac Paper 20. Part of the GeoVac research corpus (quantum computing group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of
N spin-orbitals into an
N-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus cannot be fully utilized. We propose a generalized qubit-efficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditions and symmetries. For the case of considering only the particle-conserving and singlet configurations, we reduce the qubit count to an upper bound of
O(mlog2N), where
m is the number of particles. This QEE scheme is demonstrated on an
H2 molecule in the 6-31G basis set and a
LiH molecule in the STO-3G basis set using fewer qubits than the common encoding methods. We calculate the ground-state energy surfaces using a variational quantum eigensolver algorithm with a hardware-efficient ansatz circuit. We choose to use a hardware-efficient ansatz since most of the Hilbert space in our scheme is spanned by desired configurations so a heuristic search for an eigenstate is sensible. The simulations are performed on IBM Quantum machines and the Qiskit simulator with a noise model implemented from a IBM Quantum machine. Using the methods of measurement error mitigation and error-free linear extrapolation, we demonstrate that most of the distributions of the extrapolated energies using our QEE scheme agree with the exact results obtained by Hamiltonian diagonalization in the given basis sets within chemical accuracy. Our proposed scheme and results show the feasibility of quantum simulations for larger molecular systems in the noisy intermediate-scale quantum (NISQ) era. The number of terms in the Hamiltonian has an upper bound of $\mathcal{O}(\frac{{N}^{2m+1}}{(m\ensuremath{-}1)!\phantom{\rule{0.16em}{0ex}}m!})$ for the QEE scheme while it scales as
O(N4) for the Jordan-Wigner encoding scheme. Nevertheless, we present several cases where QEE is useful.
Quantum chemistry provides a target for quantum simulation of considerable scientific interest and industrial importance. The majority of algorithms to date have been based on a second-quantized representation of the electronic structure Hamiltonian - necessitating qubit requirements that scale linearly with the number of orbitals. The scaling of the number of gates for such methods, while polynomial, presents some serious experimental challenges. However, because the number of electrons is a good quantum number for the electronic structure problem it is unnecessary to store the full Fock space of the orbitals. Representation of the wave function in a basis of Slater determinants for fixed electron number suffices. However, to date techniques for the quantum simulation of the Hamiltonian represented in this basis - the CI-matrix - have been lacking. We show how to apply techniques developed for the simulation of sparse Hamiltonians to the CI-matrix. We prove a number of results exploiting the structure of the CI-matrix, arising from the Slater rules which define it, to improve the application of sparse Hamiltonian simulation techniques in this case. We show that it is possible to use the minimal number of qubits to represent the wavefunction, and that these methods can offer improved scaling in the number of gates required in the limit of fixed electron number and increasing basis set size relevant for high-accuracy calculations. We hope these results open the door to further investigation of sparse Hamiltonian simulation techniques in the context of the quantum simulation of quantum chemistry.