Code, results and tests for end-to-end studies of chemical reactions on qubits, from molecular integrals to the 32-bit instruction stream a hardware state-vector simulator executes. Circuits and electronic structure: PySCF active spaces from CCSD natural orbitals, optionally embedded in point charges, mapped to qubits by Jordan-Wigner; UCCSD-VQE and fermionic ADAPT-VQE with analytic adjoint gradients; compilation to Pauli exponentials, a peephole optimiser, a 32-bit instruction set, and bit-accurate 18-bit fixed-point emulation of the qsim-pynq FPGA datapath (PYNQ-Z2). Every circuit energy is checked against exact diagonalisation in the same space. Reaction energetics: transition-state theory rates, Wigner and Eckart tunnelling, and composite levels combining CCSD(T) with the circuit result in the same active space. Applications. Proton-transfer tautomerism of formamide and 5-fluorouracil. Hydride transfer in thymidylate synthase from a 96-atom active-site cluster built from PDB 1TLS, with a GFN2-xTB reaction scan, a frozen-atom-aware P-RFO saddle search, finite-difference Hessians, H/D/T kinetic isotope effects, DFT single points and ONIOM layering. A lattice protein-folding benchmark on the diamond lattice with Miyazawa-Jernigan contact energies and the dense turn encoding. New in 1.2.0. Prolyl cis/trans isomerisation of capped Xaa-Pro dipeptides, including the phosphorylation effect. Ligand-binding pocket clusters cut from crystal structures with in-silico alanine truncation, applied to CFTR with lumacaftor and acetylcholinesterase with donepezil. Amyloid steric-zipper interfaces as cluster models, for tau, alpha-synuclein and SOD1 segments, benchmarked against deposited structures. A six-system chalcogen S_N2 ladder separating nucleophile from electrophile effects in thiol-disulfide and selenium-sulfur exchange, with its numerical precision floor measured from closed thermodynamic constraints rather than asserted. Shrake-Rupley solvent accessibility, and geometric feasibility analyses of the buried Cys57-Cys146 disulfide of SOD1: solvent accessibility, backside attack geometry, side-chain rotamer scans and the displacement required to open the attack site. These are geometric and semiempirical analyses, not completed energetic determinations. New in 1.3.0. A reproducible epitope map for conformation-specific antibodies against misfolded SOD1: per-residue Shrake-Rupley accessibility of the native holo dimer against the middle layer of a three-layer stack of the wild-type fibril, which is the difference such an antibody needs, since an epitope exposed on both states binds normal protein in every cell that makes SOD1. Eleven residues are buried natively and exposed on the aggregate. The published rationale of a recent conformation-specific antibody is tested against it. A residue-accessibility bound catches summed alternate conformers and colliding residue numbers. Crystal structures for this work are fetched from RCSB like the rest. Also packaged in this release, and absent from 1.2.0: the FastAPI service is now actually installed by the package, which it was not, and the continuous integration fixes that followed. New in 1.4.0. The SOD1 geometric analyses of 1.2.0 are completed and replicated, and the energetic determination they were waiting for is here. The attack geometry is measured across three crystal forms rather than one -- 2C9U at 1.24 A, 1HL5 at 1.80 A and 7FB9 at 2.70 A -- keeping every (chain, altloc) as its own set of atoms rather than resolving alternate conformers by occupancy, which gives thirty-seven chains, thirty-four of them modelling a formed disulfide. The backside attack angle at Cys146 spans 131.9 to 146.8 degrees and reaches the 150-degree collinearity floor in none of them; the attack site 3.3 A beyond the sulfur is occupied in all thirty-seven, with main-chain atoms among the occupants in all thirty-seven. The identity of the occupying residues does not replicate -- two of them in a single chain each, against Cys146 in all thirty-seven and Gly147 in thirty-six -- which is the result that matters for what can be claimed: the obstruction is the main chain of the neighbouring strands and not any named side chain, so no rotamer rearrangement removes it. All four intramolecular routes any free SOD1 cysteine could take to the disulfide are measured, not only the one the literature names, which closes the relay objection: SOD1 has four cysteines, two of them are the bond, and there is no spare thiol to resolve an intermediate. The conformational work is now determined and not pending. Bringing Cys6 to 3.12 A of Cys146 at a 175-degree approach, in a 259-atom cluster with the outer shell held and the local backbone free, costs +131.02 kcal/mol at GFN2-xTB with ALPB solvation. Inverting Eyring at 310.15 K with the full k_B.T/h prefactor allows 25.18, 28.82 and 31.23 kcal/mol for one event per day, per year and per fifty years, so the approach alone exceeds the fifty-year ceiling by a factor of 4.2 before any bond-forming barrier is added, and crosses it at about 6.5 A with 3.3 A still to travel. Every covalent bond of that series was measured at every scan point against the relaxed reference: none is stretched by more than 11 per cent, and that one is the attacked disulfide lengthening from 2.02 to 2.24 A as the nucleophile closes. No complementary upper bound is reported, and the reason is recorded rather than omitted. Held rigid, the fold does not yield elastically to contact: it breaks a covalent bond. Restraining the backbone alone ruptured the Cys57-Cys146 disulfide between 6.27 and 5.92 A, with the nucleophile still 5.9 A away and taking no part in it. Restraining that bond at its relaxed length as well moved the failure instead of removing it, to the Cys57 CB-SG bond at the same step. Both runs are archived in results/ with the diagnosis that retires them, because each added restraint relocates the rupture and a constraint set chosen until the curve behaves is chosen for its effect on the result. What the two agree on is reported: a rigid fold cannot be pushed past 5.9 A, and arrives there having spent 2.7 times the fifty-year ceiling on strain alone. Validation gains the check that would have caught the above at the first bad point rather than eleven hours later. covalent_stretch is the longest covalent bond of a restrained geometry over its length in the relaxed reference, with the bond list built once from that reference so a broken bond cannot be re-derived as simply absent; it is fatal, and replayed over the three runs it passes the reported series and stops both discarded ones at their first ruptured point. Long scans now checkpoint per point and resume from the last one, rather than holding a stage in memory until it ends. A correction: the epitope map named a residue as occluding the attack trajectory which occludes nothing, absent from every occupancy list at both probe radii and from all thirty-seven chains; the claim is corrected in place and dated, and no computed value changed. Validation. A physical-bounds module carrying 37 checks, each with the reason it exists written into the code; an auditor that recomputes them from stored geometry and separates recorded dead ends from open faults; a stall detector deriving its unit list from systemd; and a 101-case self-test that exercises every bound in both directions, using archived real failures as labelled positives. Long runs are resumable systemd units with atomic checkpoints and per-point resume. A FastAPI module serves the cases and their instruction streams. A Dockerfile pins the exact versions the results were produced with. Crystal structures are fetched from RCSB rather than redistributed. Educational; not for clinical use. New in 1.4.1. The derivation behind the TDP-43 charge-step result is deposited rather than only its numbers: scripts/tdp43_charge_steps.py converts the published conversion percentages of a charge-variant series to rate constants and reports the multiple each step of motif net charge buys, under both the binned-observation and the authors' fitted-line conventions, because the first step depends on which is used while the ordering does not. It reads its constructs from tdp43_frailty.py rather than carrying a second copy. Writing it corrected a number: the conversion hazard had been described as flat to 4 per cent across a four-fold range of time, which is the coefficient of variation of the three estimates, but read as a bound on any one estimate it understates by more than a factor of two, the worst point being 6.0 per cent from the mean and lowest to highest 10.1 per cent. All three measures are now reported so that a sentence quoting one cannot be read as another. The SOD1 attack-site replication is also recorded at the second probe distance: the cross-crystal analysis defines the ideal attack point 3.0 A beyond the leaving sulfur in the methods and computed it at 3.3 A, so both were run and both are archived. Nothing the exclusion rests on moves -- thirty-seven chains, thirty-four with a formed disulfide, the site occupied in all thirty-seven with main-chain atoms among the occupants in all thirty-seven, no chain reaching the 150-degree floor -- while the identity of the occupying residues does move, which is the quantity already reported as not replicating. Tooling: the Markdown-to-PDF renderer draws the thirteen characters outside Latin-1 that the built-in PDF fonts cannot, which had been emitting filled squares where the manuscripts write Greek, reaction arrows and angle brackets, and it now reports what it had to borrow. A sibling renders the same Markdown subset to .docx. CITATION.cff, which still read 1.3.0 in the 1.4.0 release, is corrected. New in 1.4.2. The SOD1 cysteine work gains the assay that would settle it, and the reason no existing dataset can. Published SOD1 proteomic surveys run carbamidomethyl on cysteine as a fixed modification, so every cysteine is reduc
Code, results and tests for end-to-end studies of chemical reactions on qubits, from molecular integrals to the 32-bit instruction stream a hardware state-vector simulator executes. Circuits and electronic structure: PySCF active spaces from CCSD natural orbitals, optionally embedded in point charges, mapped to qubits by Jordan-Wigner; UCCSD-VQE and fermionic ADAPT-VQE with analytic adjoint gradients; compilation to Pauli exponentials, a peephole optimiser, a 32-bit instruction set, and bit-accurate 18-bit fixed-point emulation of the qsim-pynq FPGA datapath (PYNQ-Z2). Every circuit energy is checked against exact diagonalisation in the same space. Reaction energetics: transition-state theory rates, Wigner and Eckart tunnelling, and composite levels combining CCSD(T) with the circuit result in the same active space. Applications. Proton-transfer tautomerism of formamide and 5-fluorouracil. Hydride transfer in thymidylate synthase from a 96-atom active-site cluster built from PDB 1TLS, with a GFN2-xTB reaction scan, a frozen-atom-aware P-RFO saddle search, finite-difference Hessians, H/D/T kinetic isotope effects, DFT single points and ONIOM layering. A lattice protein-folding benchmark on the diamond lattice with Miyazawa-Jernigan contact energies and the dense turn encoding. New in 1.2.0. Prolyl cis/trans isomerisation of capped Xaa-Pro dipeptides, including the phosphorylation effect. Ligand-binding pocket clusters cut from crystal structures with in-silico alanine truncation, applied to CFTR with lumacaftor and acetylcholinesterase with donepezil. Amyloid steric-zipper interfaces as cluster models, for tau, alpha-synuclein and SOD1 segments, benchmarked against deposited structures. A six-system chalcogen S_N2 ladder separating nucleophile from electrophile effects in thiol-disulfide and selenium-sulfur exchange, with its numerical precision floor measured from closed thermodynamic constraints rather than asserted. Shrake-Rupley solvent accessibility, and geometric feasibility analyses of the buried Cys57-Cys146 disulfide of SOD1: solvent accessibility, backside attack geometry, side-chain rotamer scans and the displacement required to open the attack site. These are geometric and semiempirical analyses, not completed energetic determinations. New in 1.3.0. A reproducible epitope map for conformation-specific antibodies against misfolded SOD1: per-residue Shrake-Rupley accessibility of the native holo dimer against the middle layer of a three-layer stack of the wild-type fibril, which is the difference such an antibody needs, since an epitope exposed on both states binds normal protein in every cell that makes SOD1. Eleven residues are buried natively and exposed on the aggregate. The published rationale of a recent conformation-specific antibody is tested against it. A residue-accessibility bound catches summed alternate conformers and colliding residue numbers. Crystal structures for this work are fetched from RCSB like the rest. Also packaged in this release, and absent from 1.2.0: the FastAPI service is now actually installed by the package, which it was not, and the continuous integration fixes that followed. New in 1.4.0. The SOD1 geometric analyses of 1.2.0 are completed and replicated, and the energetic determination they were waiting for is here. The attack geometry is measured across three crystal forms rather than one -- 2C9U at 1.24 A, 1HL5 at 1.80 A and 7FB9 at 2.70 A -- keeping every (chain, altloc) as its own set of atoms rather than resolving alternate conformers by occupancy, which gives thirty-seven chains, thirty-four of them modelling a formed disulfide. The backside attack angle at Cys146 spans 131.9 to 146.8 degrees and reaches the 150-degree collinearity floor in none of them; the attack site 3.3 A beyond the sulfur is occupied in all thirty-seven, with main-chain atoms among the occupants in all thirty-seven. The identity of the occupying residues does not replicate -- two of them in a single chain each, against Cys146 in all thirty-seven and Gly147 in thirty-six -- which is the result that matters for what can be claimed: the obstruction is the main chain of the neighbouring strands and not any named side chain, so no rotamer rearrangement removes it. All four intramolecular routes any free SOD1 cysteine could take to the disulfide are measured, not only the one the literature names, which closes the relay objection: SOD1 has four cysteines, two of them are the bond, and there is no spare thiol to resolve an intermediate. The conformational work is now determined and not pending. Bringing Cys6 to 3.12 A of Cys146 at a 175-degree approach, in a 259-atom cluster with the outer shell held and the local backbone free, costs +131.02 kcal/mol at GFN2-xTB with ALPB solvation. Inverting Eyring at 310.15 K with the full k_B.T/h prefactor allows 25.18, 28.82 and 31.23 kcal/mol for one event per day, per year and per fifty years, so the approach alone exceeds the fifty-year ceiling by a factor of 4.2 before any bond-forming barrier is added, and crosses it at about 6.5 A with 3.3 A still to travel. Every covalent bond of that series was measured at every scan point against the relaxed reference: none is stretched by more than 11 per cent, and that one is the attacked disulfide lengthening from 2.02 to 2.24 A as the nucleophile closes. No complementary upper bound is reported, and the reason is recorded rather than omitted. Held rigid, the fold does not yield elastically to contact: it breaks a covalent bond. Restraining the backbone alone ruptured the Cys57-Cys146 disulfide between 6.27 and 5.92 A, with the nucleophile still 5.9 A away and taking no part in it. Restraining that bond at its relaxed length as well moved the failure instead of removing it, to the Cys57 CB-SG bond at the same step. Both runs are archived in results/ with the diagnosis that retires them, because each added restraint relocates the rupture and a constraint set chosen until the curve behaves is chosen for its effect on the result. What the two agree on is reported: a rigid fold cannot be pushed past 5.9 A, and arrives there having spent 2.7 times the fifty-year ceiling on strain alone. Validation gains the check that would have caught the above at the first bad point rather than eleven hours later. covalent_stretch is the longest covalent bond of a restrained geometry over its length in the relaxed reference, with the bond list built once from that reference so a broken bond cannot be re-derived as simply absent; it is fatal, and replayed over the three runs it passes the reported series and stops both discarded ones at their first ruptured point. Long scans now checkpoint per point and resume from the last one, rather than holding a stage in memory until it ends. A correction: the epitope map named a residue as occluding the attack trajectory which occludes nothing, absent from every occupancy list at both probe radii and from all thirty-seven chains; the claim is corrected in place and dated, and no computed value changed. Validation. A physical-bounds module carrying 37 checks, each with the reason it exists written into the code; an auditor that recomputes them from stored geometry and separates recorded dead ends from open faults; a stall detector deriving its unit list from systemd; and a 101-case self-test that exercises every bound in both directions, using archived real failures as labelled positives. Long runs are resumable systemd units with atomic checkpoints and per-point resume. A FastAPI module serves the cases and their instruction streams. A Dockerfile pins the exact versions the results were produced with. Crystal structures are fetched from RCSB rather than redistributed. Educational; not for clinical use. New in 1.4.1. The derivation behind the TDP-43 charge-step result is deposited rather than only its numbers: scripts/tdp43_charge_steps.py converts the published conversion percentages of a charge-variant series to rate constants and reports the multiple each step of motif net charge buys, under both the binned-observation and the authors' fitted-line conventions, because the first step depends on which is used while the ordering does not. It reads its constructs from tdp43_frailty.py rather than carrying a second copy. Writing it corrected a number: the conversion hazard had been described as flat to 4 per cent across a four-fold range of time, which is the coefficient of variation of the three estimates, but read as a bound on any one estimate it understates by more than a factor of two, the worst point being 6.0 per cent from the mean and lowest to highest 10.1 per cent. All three measures are now reported so that a sentence quoting one cannot be read as another. The SOD1 attack-site replication is also recorded at the second probe distance: the cross-crystal analysis defines the ideal attack point 3.0 A beyond the leaving sulfur in the methods and computed it at 3.3 A, so both were run and both are archived. Nothing the exclusion rests on moves -- thirty-seven chains, thirty-four with a formed disulfide, the site occupied in all thirty-seven with main-chain atoms among the occupants in all thirty-seven, no chain reaching the 150-degree floor -- while the identity of the occupying residues does move, which is the quantity already reported as not replicating. Tooling: the Markdown-to-PDF renderer draws the thirteen characters outside Latin-1 that the built-in PDF fonts cannot, which had been emitting filled squares where the manuscripts write Greek, reaction arrows and angle brackets, and it now reports what it had to borrow. A sibling renders the same Markdown subset to .docx. CITATION.cff, which still read 1.3.0 in the 1.4.0 release, is corrected. New in 1.4.2. The SOD1 cysteine work gains the assay that would settle it, and the reason no existing dataset can. Published SOD1 proteomic surveys run carbamidomethyl on cysteine as a fixed modification, so every cysteine is reduc
Screening the low-activation alloys that make up a fusion reactor's plasma-facing and structural components by density-functional theory (DFT) runs into a wall: on the correlated 3d transition metals that constitute the family, the computed energetics depend on the exchange–correlation functional at the level of hundreds of millihartree, which is comparable to or larger than the composition differences the screen must resolve. A screen whose verdict changes with the functional is not a screen. We close that gap with an adaptive variational quantum eigensolver. We first set out the governing electronic-structure problem, the formal origin of the functional ambiguity, the well-posedness condition for a composition screen, the fermion-to-qubit mapping, and the ADAPT-VQE construction with its exact gradient-selection criterion and monotone-convergence property. We then report the frozen results of the Kronos de-risking campaign (register serial BR-SX-07): ADAPT-VQE reaches chemical accuracy on all four 3d-alloy fragments (Ti, V, Cr, Fe) with a residual below 0.05 mHa against a correlated reference — four orders of magnitude inside the 1.6 mHa (1 kcal mol^-1) chemical-accuracy threshold and four orders of magnitude tighter than the >300 mHa DFT functional spread it replaces — using adaptively grown circuits that are 4–14× shallower in two-qubit (CNOT) count than a unitary coupled-cluster (UCCSD) ansatz at equal accuracy. An independently reproduced four-qubit proof-of-concept validates the machinery to 3.9×10^-6 Ha against exact diagonalization. The results were produced on the NVIDIA GPU HPC campaign by classical statevector emulation of the quantum circuits, with plane-wave DFT and correlated quantum-chemistry references computed on the same fleet. We state the honest gate once and quantify it: this is not a claim of quantum advantage; a single-determinant ADAPT-VQE variant stalls at 24 mHa on the strongly multireference vacancy limit; and scaling from fragments to a full alloy or REBCO cell moves the problem into fault-tolerant quantum phase estimation, estimated at ~10^9 Toffoli gates and ~238 logical qubits (~38 days at a 1 kHz logical-Toffoli throughput). We place the method inside the honest-scoping grammar of the Kronos AI-and-quantum programme: the fragment ADAPT-VQE energetics are a twin-testable capability that runs today on classical hardware, the full-cell phase estimation is a horizon-class quantum task quoted against an explicit classical baseline, and every offline quantum kernel is benchmarked in qubits and non-Clifford (Toffoli/T) gate count with no crossover to the real-time control loop this decade. On the resulting ladder the alloy-chemistry phase estimation (~10^9 Toffoli) is the most tractable offline kernel — far below the equilibrium linear-solve (~10^17 T gates) and fleet-optimization (~10^19–10^23 T gates) kernels — and we report the matrix-product-state classical frontier it must beat. The deliverable is a validated, circuit-efficient electronic-structure tool for composition-of-matter screening today, with a resource-honest map of what the fault-tolerant extension will cost. Key results (frozen anchors): Q = 3.076; delta = -0.30; kappa = 2.0; p = 1; q = 1; s = 1. Methods & codes: OpenMC, VQE, ADAPT-VQE. Live verification: 2 gate validator(s) with live-recompute cards (2 reproduced). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
Draft preprint. Not submitted to a venue. Quantum compiler benchmarks are used to accept or reject changes to production transpilers, but the compilers they measure are stochastic. At the pinned revision of IBM's Benchpress benchmark suite, its Qiskit gym compiles without passing seed_transpiler, so every gate count it reports is one draw from an unmeasured distribution — while the BQSKit gym in the same repository does seed its compiler. We quantify the consequence as finite-sample decision risk: the probability that a regression verdict computed from k runs per version disagrees with the verdict implied by the long-run mean of the same measurement. On bv_n140 mapped to a heavy-hex lattice, measured over 400 seeds per version across 21 OS processes, the change from Qiskit 1.4.3 to 2.0.0 has a long-run mean of +5.37% (95% CI +4.27% to +6.50%). The suite's own protocol — three unseeded runs per version — reports it as a ≥+10% regression 24.4% of the time (95% CI 19.5–31.1%). A disjoint 200-seed sample across ten fresh processes reproduces this at 22.6%. Twenty runs per version, roughly 40 hours of compute, still leaves 3.7%. A pre-registered replication across 39 circuits is reported in full: the analysis code was committed before the data existed, and the commit ordering is included in this archive as COMMIT_TIMESTAMPS.txt. The pre-registered primary endpoint is 12 of 26 eligible circuits (46.2%, Wilson 95% CI 28.8–64.5%), reported alongside a cluster-robust interval of [17.4%, 81.0%] that reflects algorithm-family clustering. What this archive contains: the paper, the complete analysis and measurement code, and all 41,790 raw per-seed measurements. verify.py re-runs six checks — the toolchain pin, the test suite, the numeric inventory, the replication artifact, a proof of a withdrawn analytical claim, and a recomputation of every quantitative claim in the manuscript against the text — in about two minutes. Four claims from earlier phases of this work were withdrawn on the record after adversarial review, and the withdrawals remain in the repository with the evidence that defeated them. Passing seed_transpiler removes false positives on the circuits tested but was worse on three of four circuits exhibiting false negatives, and is not presented as a general remedy. Changes in v2 (2026-09-10). This version corrects two overstatements carried by the v1 manuscript and adds one new pre-registered result. No measurement changed, and no reported figure moved. Withdrawn. v1 stated that Benchpress sets no transpiler seed anywhere. That is narrowed to the claim the evidence supports: at the pinned revision, the Qiskit gym compiles without passing seed_transpiler — while the sibling BQSKit gym does seed its compiler, and six further gyms were not assessed. v1 also stated that the work identifies the mechanism that governs the effect. The paper now reports what predicts the risk and explicitly declines to call that association a compiler mechanism. Added: a pre-registered cross-machine determinism control. All 216 per-seed gate counts are identical across two physical machines with different CPU vendors (AMD64 AuthenticAMD, 16 cores, Python 3.10.10; Intel64 GenuineIntel, 8 cores, Python 3.10.21), over all three Qiskit versions including the 1.4.3 → 2.0.0 pair the primary study uses. The design was committed before the second machine existed and inherits the frozen six-circuit, twelve-seed selection, so it introduces no selection freedom. Stated scope limit: both machines ran rustworkx 0.18.1, so this cannot separate “the CPU does not matter” from “the graph library was identical, so the CPU never had the opportunity to matter”. The primary 200-seed study itself ran on one machine. Also in this archive. The settled-question ledger now holds 33 entries, each naming the attack, who made it, the command that settled it and the result; it includes three rounds of external adversarial audit of the cross-machine comparator itself, in which fourteen defects were found in the checking instrument and none in the measurements. The cross-machine evidence, its pre-registration, the comparator and its property-based fuzz tests are included. The numeric inventory now records a provenance tier per figure (29 re-derived from raw per-seed files, 12 read from a summary table, 5 not applicable). verify.py now runs six checks rather than five, the sixth recomputing every quantitative claim in the manuscript and comparing it to the text. Two reproducibility defects in the README were fixed: a shallow clone that could not reach the pinned Benchpress revision, and a missing environment without which the primary 1.4.3 → 2.0.0 study could not be reproduced at all.
(Dated: July 19, 2026) Quantum algorithms for molecular dynamics propagate a wavepacket through configuration space, while quantum electronic-structure methods return a ground-state energy at one fixed geometry. Neither addresses the object a chemist means by a catalytic mechanism: a closed sequence of identified intermediates linked by proton-coupled electron transfers, non-adiabatic crossings, and a stoichiometric budget that must balance over the turnover. Here we introduce the Modular Quantum Emulator (MQE), a qudit architecture that takes that \emph{ mechanism } as the object of computation. Two registers are carried: a logical register assigning one four-level qudit per spatial orbital, whose states are that orbital's four occupancies, and a single auxiliary register counting cofactor turnover around the cycle. Stoichiometric bookkeeping makes the auxiliary register mandatory, and our central result is that it simultaneously performs four further roles---it is the clock for quantum phase estimation, so energies are extracted with no additional qubits; it shelters idle population from dephasing; it confines environmental coupling, leaving the electronic reduced state exactly unitary under open-system dynamics; and its winding number classifies the mechanism, predicting that a centred two-electron elimination requires a turnover electron count divisible by four, satisfied throughout the nitrogenase family and violated by two- and six-electron cycles. Electron number, phase closure, trace and spin sector are enforced as circuit-level invariants and verified at every step. Because the auxiliary sector is algebraically independent of the electronic Hamiltonian, nuclear quantum effects, relativistic and spin--orbit coupling, open-system dissipation and periodic boundary conditions are absorbed without altering the asymptotic cost. Every gate introduced compiles to the native GPI/GPI2/ZZ pulse set of trapped-ion hardware, the basis changes attaining the KAK lower bound of two entangling operations. Validation of these circuits across seventeen catalytic mechanisms, on chemically relevant active spaces small enough to admit exact reference energies, recovers every stoichiometric invariant and returns twenty-five phase-estimation measurements within 1.6~mHa of the exact result.
CORRECTION NOTICE (v5, 2026-09-06). The central result of v1-v4 is WITHDRAWN. This record has not been peer reviewed. Issued 2026-09-06 by the author (v5 of this record). This notice was added to the archived record; the manuscript itself is unaltered. This record has not been peer reviewed. What is wrong The force exponent reported here as alpha = 3.92 +/- 0.16 is an artifact of the fitting procedure, not a property of the data. The fit was unweighted least squares in linear space applied to a steeply falling profile, which places 95.8 percent of its objective on the single point at the shortest retained separation. Re-fitting the same data with nothing discarded, changing only the error model, gives 2.82 (relative-error weighting) or 2.89 (log-space regression). Across fifteen combinations of standard estimator and fit window the exponent spans 2.53 to 3.92, and the value published here is the largest of them. What the data show instead, and how firmly The retraction is certain. The replacement is not. On the open 24-site chain the same data give alpha = 2.6 +/- 0.2, where the interval is the spread of a plateau in the local logarithmic slope over six consecutive separations, not a statistical error (the bootstrap error on the published fit to the same data is 0.63); the plateau value was reproduced at 2.5921 by a separately written implementation run on the same recorded state (SIM-2026-073). This is a single geometry at a single size. On a 24-site periodic ring, analysed with chord distance as pre-registered, two probes that are both energy-density-like (Delta = 1) give 1.83 and 2.37 against a CFT two-point value of 2 (SIM-2026-074): one size, not converged, disagreeing with each other by 29 percent, and not attributable to a single operator channel. No corrected exponent is established. The exchange channel is an open question. Treat 2.6 +/- 0.2 as the provisional open-chain value, not as a result. Also withdrawn or voided alpha = 3.92 +/- 0.16 (24 sites) and alpha = 3.97 +/- 0.15 (16 sites, exact) from stress-tensor exchange. Was: headline result and its first corroboration. Now: withdrawn. Why: the same estimator artifact: both move in lockstep under it (3.92 to 2.56, 3.97 to 2.75 on dropping the contact point), because they share one observable, one fit window and one fitting routine. scalar exchange (alpha = 2) excluded. Was: stated as excluded at about 12 sigma. Now: withdrawn. Why: the 12 sigma used the covariance error 0.16; at the bootstrap error 0.63 computed before release the exclusion is about 2.2 sigma, and under any window starting at separation 3 the point estimate itself falls to about 2.56. alpha = 4 is universal; alpha = 4.00 at Ising, tricritical Ising and Potts. Was: confirmed at three classes. Now: withdrawn; the operator towers at all three classes stand. Why: the exponent was measured only at Ising and inherited by the other two; the towers are spectra, not forces. third independent evaluation alpha = 4.07 (chi = 3 MERA), and with it the statement that this was the first holographic force measurement from an optimized tensor network state. Was: supporting evidence and a priority claim. Now: both withdrawn. Why: the profile changes sign inside its own fit window and cannot be a fixed-sign power law; the priority claim rests on that evaluation alone and was never gated against prior work. the discriminating test: stress tensor (Z_j Z_j+1) versus spin primary (X_j). Was: registered killer test. Now: void. Why: at the critical point these are one operator, related by exact Kramers-Wannier self-duality. Measured on the periodic ring: identical expectation values to 1e-15 and identical force profiles to 1e-13 at 14 sites, 2.4e-9 at 24 sites (SIM-2026-074). Open boundaries break the duality, which is why the open-chain run of this test (SIM-2026-073) showed a spurious difference between the two arms. The test compared the energy density to itself. Neither label was correct: Z_j Z_j+1 is the energy density, not the stress tensor; X_j is its dual, not the spin primary. transport time T = (pi/2) l_AdS to 1.2 percent as a geometric prediction. Was: confirmed. Now: measurement stands (T = 2.239 at N = 16); geometric reading not established. Why: l_AdS cancels in the cited derivation, which also gives pi rather than the pi/2 the manuscript compares against; the chi = 3 estimate of l_AdS gives a 57 percent miss; the transport driver never applies a MERA. The true spin primary Z_j was never in the design, and the direct replacement test is blocked: Z_j is odd under the Z2 symmetry, so the energy-difference observable used throughout this work subtracts across symmetry sectors and is undefined for it. A replacement test using two Z2-even probes has been pre-registered (PREREGISTRATION-T.md, committed before its driver) and run; its result is deliberately not part of this correction and will appear in a later version. Not previously reported The published fit has a reduced chi-squared of 6.008 on 9 degrees of freedom, and a bootstrap standard deviation of 0.63 rather than the quoted 0.16. Both were computed before release and omitted. What is unaffected Of the claims in this record: the two-phase optimization method, the chi = 3 criticality threshold, the exact-diagonalization gates, the measured OPE coefficient C_sigma-sigma-epsilon = 0.50 +/- 0.03 against the exact 1/2, and the conformal towers at all three classes. Not part of this record, mentioned only because they are sometimes read together with it: the later C_TTT stress-tensor self-coupling measurements (SIM-2026-067/068/069, dated after this record) and the matched off-critical ring control (SIM-2026-074) are unaffected by this correction and make no claim about the force exponent. How the error was found and what this record contains The error was found by the author's own internal adversarial audit, not by a reviewer; the journal submission it was found after is closed, and no review of this work has taken place. Files in this record: the full re-analysis (SIM-2026-072.json, driver, figure), the pre-registered chain test (SIM-2026-073.json) and ring test (SIM-2026-074.json) with both pre-registrations as committed before the runs, the runnable drivers with their shared module and the negative test suite for their validation gates, and the error register (ERRATA.md). Concept DOI 10.5281/zenodo.19660302 always resolves to the current version. The abstract of the original manuscript follows unchanged, for the record. Every claim in it about the force exponent should be read against the correction above. We report results from classical simulation of critical spin chains that establish quantitative physical content in the MERA-AdS correspondence. First, the interaction energy between boundary-primary excitations follows a power law F(dr) ~ dr^(-alpha) with three consistent evaluations yielding alpha = 3.92 +/- 0.16 (24q), 3.97 +/- 0.15 (16q), and 4.07 +/- 0.18 (16q chi=3 MERA), all consistent with stress-tensor exchange (alpha = 2*Delta_T = 4) and inconsistent with scalar exchange (alpha = 2); the exponent is explained by the Ising CFT fusion rule eps x eps = [1]. Because Delta_T = 2 is fixed by conformal symmetry in every unitary 2D CFT, alpha = 4 is universal: we confirm this at two further fixed points - the tricritical Ising model (c = 7/10), where a scale-invariant MERA recovers the full M(4,5) primary spectrum (Delta_sigma = 0.092, Delta_eps = 0.204, Delta_T = 1.999), and the three-state Potts model (c = 4/5), where a Z3-symmetric MERA at chi = 12 recovers Delta_sigma = 0.134, Delta_eps = 0.805, Delta_T = 2.001 - giving alpha = 4.00 at all three universality classes. Second, the holographic transport time matches the AdS_3 null geodesic prediction T = (pi/2) l_AdS to 1.2% at N = 16 sites on a time-grid-converged measurement, with the residual shrinking from 2.8% at N = 12. Third, we introduce a two-phase optimization method (ALM + Z2 projection) for Z2-symmetric MERA ground states at 24 qubits. Fourth, extending the MERA bond dimension from chi=2 to chi=3 overcomes the expressibility barrier, achieving 0.15% energy error at 16 qubits and enabling the first holographic force measurement from an optimized tensor network state. The OPE coefficient is also measured directly from the fixed-point tensors: C_sigma-sigma-eps = 0.50 +/- 0.03 against the exact Ising value 1/2. A hardware path is designed for Quantinuum Helios (57 CNOTs, 0.57% logical error). Version 4 changes (relative to v3): Transport: N=16 residual restated as the time-grid-converged value of -1.21% (dt = 1e-3), with -2.78% at N=12 showing the finite-size trend; the 0.72% figure in v3 was an artifact of the dt = 0.05 integration grid and is now labeled as such. The N=24 transport point carries a new reliability caveat (double-lobe trace structure). The l_AdS comparison table is recomputed against the converged transport time (best fit 1.425, deviation 1.21%). Effective-mass derivation rewritten in a consistent AdS3 convention m^2 l^2 = Delta(Delta-2); m_eff = 0.693 = 1/l_AdS follows from Delta = 1 exactly. NEW: universality section extended to a third fixed point - a Z3-symmetric MERA at chi = 12 recovers the three-state Potts (c = 4/5) tower, giving alpha = 4.00 at all three universality classes (c = 1/2, 7/10, 4/5). NEW: the OPE coefficient C_sigma-sigma-eps = 0.50 +/- 0.03 measured directly from the fixed-point tensors, with C_sigma-sigma-sigma = 0 at machine precision as the Z2 structural check. Supplemental table row SIM-007 annotated (record lost; script preserved); data availability expanded; Zenodo DOI added to the front matter.
Algorithmes quantiques pour la chimie quantique ab initio : une approche à plusieurs échelles L'équation de Schrödinger polyélectronique régit l'évolution non relativiste des systèmes quantiques tels que les électrons, atomes et molécules. La chimie quantique ab initio consiste à trouver des solutions approximées de cette équation afin de prédire des propriétés moléculaires comme les longueurs de liaison, les spectres vibrationnels et les mécanismes réactionnels. Malgré les immenses progrès de la puissance de calcul, atteindre la précision chimique (une erreur d'énergie inférieure à 1 kcal/mol) reste exponentiellement coûteux pour les algorithmes classiques lorsque la taille du système augmente. Cette limite a conduit à envisager l'informatique quantique comme alternative pour la simulation moléculaire, les ordinateurs quantiques obéissant aux mêmes principes physiques que les systèmes simulés. Il a été établi que, sous certaines conditions, l'équation de Schrödinger moléculaire pouvait être résolue en temps polynomial sur un ordinateur quantique, permettant en principe une accélération exponentielle par rapport aux méthodes classiques. La concrétisation de cet avantage reste un problème ouvert et requiert des avancées tant matérielles (stabilité des processeurs) que algorithmiques (consommation de ressources). Ce dernier aspect constitue l'objectif principal de cette thèse. Trois défis fondamentaux sont identifiés: établir une correspondance et une discrétisation efficace entre le problème de structure électronique et les qubits; concevoir des algorithmes pour préparer de bonnes approximations de l'état fondamental ; décomposer les opérations quantiques en circuits implémentables à coût minimal. La première partie traite du court terme, où le faible nombre de qubits et le bruit limitent les opérations exécutables. Dans ce contexte, le Variational Quantum Eigensolver (VQE) et son extension adaptative ADAPT-VQE sont des références établies. Nous proposons plusieurs améliorations pour la construction adaptative d'ansätze. L'algorithme Greedy Gradient-Free Adaptive VQE simplifie le processus d'optimisation, réduisant considérablement la consommation de ressources et permettant même une démonstration sur un processeur de 25 qubits. La méthode Overlap-ADAPT-VQE introduit un schéma de compactification variationnelle qui reconstruit des approximations d'états quantiques cibles, permettant en chimie quantique d'accélérer significativement la convergence du VQE pour divers niveaux de corrélation électronique. Nous développons ensuite une stratégie d'initialisation des registres quantiques à partir de fonctions d'onde corrélées issues de calculs classiques, pour combiner calcul haute performance et post-traitement quantique. La seconde partie adopte une perspective de long terme centrée sur le comportement asymptotique des algorithmes. Nous présentons une décomposition de la porte NOT multi-contrôlée avec une profondeur de circuit polylogarithmique en nombre de qubits de contrôle, offrant une amélioration exponentielle sur les approches linéaires existantes. Enfin, nous proposons une méthode de chimie quantique en espace réel, compatible avec les algorithmes quantiques d'extraction de valeurs propres. L'objectif étant d'améliorer la convergence spatiale en remplaçant les discrétisations uniformes, utilisées dans la plupart des approches en première quantification, par des grilles non uniformes, adaptées à la molécule, qui concentrent les points de discrétisation dans les zones de forte densité électronique. Nous étendons cette stratégie aux hamiltoniens transcorrélés : des opérateurs qui régularisent les singularités du potentiel coulombien, et dont les fonctions propres sont lisses dans l'espace. Notre approche est plurielle, explorant tous les niveaux d'abstraction, de la théorie à l'implémentation, et couvrant des algorithmes exploitables sur des machines actuelles, et d'autres destinés aux architectures de long terme. Ces contributions renforcent les fondements des algorithmes quantiques pour la simulation moléculaire.
Calcul quantique avec des atomes de Rydberg : contrôle et modélisation pour simulation et algorithmes quantiques Améliorer sa compréhension d'un système en le modélisant permet d'espérer le contrôler de manière plus optimale et ouvre la voie à une myriade d'applications potentielles, exploitant les effets jusqu'alors énigmatiques de ce système désormais familier. Cette thèse applique ce paradigme au calcul quantique analogique avec des atomes de Rydberg, montrant comment à l'aide d'une modélisation minutieuse du bruit, de protocoles de contrôle optimaux et de techniques d'apprentissage automatique, on peut espérer améliorer des expériences de simulation de magnétisme quantique ou la résolution de problèmes d'optimisation et de classification de graphes. Après avoir décrit la plateforme expérimentale permettant de contrôler les atomes de Rydberg, nous introduisons des outils classiques tels que les jumeaux numériques de systèmes enclins à des erreurs, la modélisation d'un grand nombres d'atomes par réseaux de tenseurs, le contrôle optimal robuste et l'optimisation bayésienne pour les algorithmes variationnels. Nous appliquons ces outils à plusieurs applications prometteuses. Nous améliorons la préparation d'états antiferromagnétiques dans le modèle d'Ising et réalisons une évaluation détaillée de l'influence d'erreurs sur l'étude de phases magnétiques du modèle dipolaire XY et lors de la tomographie d'états quantiques. En utilisant des techniques d'optimisation et des méthodes d'apprentissage automatique, nous abordons également des cas d'usage industriels tels que la résolution du problème de stable maximum sur des graphes représentant des tâches de planification de charge de batteries de voitures électriques, la classification de composés moléculaires toxiques ou inoffensifs, et des tâches de prédiction dans la gestion des risques financiers.