The Modular Quantum Emulator: Chemically Accurate, Polynomial-Cost Simulation of Multi-Step Metalloenzyme Catalysis in a Dissipative Protein Environment
(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.
(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.
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.
Summary. Enzymes are four-billion-year-evolved coherence-preserving machines operating at room temperature with rate enhancements of 10⁶–10¹⁷. Quantum computing pursues the same goal — preserved coherent transitions — at near-absolute-zero with extraordinary isolation requirements. This paper asks what biology has learned about coherence engineering that quantum computing has not, and turns the answer into testable predictions. Empirical core. Twelve enzymes spanning all six Enzyme Commission classes are decomposed into a universal five-operation set {R, F, T, P, S}: spinor rotation (R), frequency shift (F), amplitude transfer (T), phase alignment (P), substrate coupling (S). Across sixty-eight individual catalytic steps, every step decomposed into one of the five operations; zero steps required a sixth. Five of the six cross-class validation enzymes — selected from independent literature without reference to the framework — collapse to the exact canonical sequence R · F · T · P · S. P (phase alignment) appears immediately before S (substrate release) in 11 of 12 enzymes (recognition before release). Two enzymes whose chemistry is entirely different (serine protease and ATP synthase) share the identical abstract gate sequence F · R · R · T · T · P · S, evidence that the decomposition captures operations on coherence itself rather than chemical substrate. Five lessons for quantum computing. (1) Five operations suffice — biology's longest coherence-engineering programme converged on a five-gate set. (2) P-penultimate as a scheduling principle — verify-before-emit is universal in biology. (3) Closed-pentachoron verification — gate-set completeness, not per-gate fidelity. (4) Substrate coupling as a first-class operation — measurement is just another gate, controllable in time and amplitude. (5) Result-becomes-substrate — chained substrate-becoming computation as a first-principle architecture. Geometric reading. The five-gate count is forced from two independent geometric directions. The pentachoron (4-simplex) has by definition exactly five tetrahedral cells, and the cube admits a minimum tetrahedral decomposition of exactly five tetrahedra. The same five gates are the pentachoron's bounding 3-cells (4D top-down) and the cube's interior simplicial floor (3D bottom-up); biology's empirical 5 is the geometric minimum from both directions simultaneously. Hardware programme. The merkabit ternary architecture instantiates {R, F, T, P, S} as quantum operations on the Eisenstein lattice. Five pre-registered hardware predictions on IBM Quantum (Eagle r3 + Heron r2), instantiating the four interior gates R/F/T/P, have all passed (5/5). The S gate is currently confirmed in simulation only and is the subject of a pre-registered 19-qubit Pentachoric Verification Protocol on Google Willow Phase 2. Five falsifiable predictions. §9.1 Biological: no future-characterised enzyme will require a sixth fundamental operation. §9.2 Cross-domain: the Pentachoric Verification Protocol passes on Google Willow. §9.3 Structural: the P-penultimate signature persists at ~90% across additional enzymes. §9.4 Threshold: product-release kinetics for canonical-cycle enzymes follow stretched-exponential decay with KWW exponent α = 4/3 ± 0.07. §9.5 Molecular instantiation: PSII OEC turnover under coherent driving shows a resonance enhancement at the Coxeter-h = 12 frequency, with a 5-state Kok-cycle simulation reproducing rate(T = 12) ≈ 1.8 × rate(T = 11) ≈ 2.1 × rate(T = 13). Reproducibility. All simulation code, raw JSON output, and figure-generation scripts are deposited at https://github.com/SelinaAliens/enzymes_5_gates_merkabit (MIT-licensed). The Cirq simulations supporting §6.5 (forward direction), §7.7 (bidirectionality and round-trip closure), and §9.5 (PSII OEC h=12 resonance) are deterministic with fixed gate parameters, run in under one second on a standard laptop, and use only NumPy + Cirq + Matplotlib. Source data: the twelve-enzyme decomposition is derived directly from peer-reviewed mechanism literature with no proprietary or unpublished biological inputs.
Accurately simulating molecular dynamics during chemical reactions remains a central challenge in computational chemistry. These processes are inherently quantum mechanical, involving coupled electronic and nuclear motion and non-adiabatic effects. A fully quantum description is therefore required, yet the associated computational cost grows exponentially with system size. Even with modern supercomputers, storing and evolving a molecular wavefunction rapidly becomes intractable, limiting exact simulations of chemical dynamics. Quantum simulation offers a promising alternative by using controllable quantum systems to directly reproduce molecular dynamics. However, fully digital, qubit-based approaches remain impractical for chemistry due to limited qubit numbers, coherence times, and gate fidelities. This motivates the exploration of more resource-efficient quantum architectures. In this thesis, we demonstrate that mixed-qudit-boson (MQB) quantum simulators provide a practical platform for simulating chemical dynamics in the quantum regime. In MQB devices, multilevel qudits encode electronic states while bosonic modes natively represent vibrational degrees of freedom, avoiding costly qubit encodings of nuclear motion and substantially reducing resource requirements. The thesis makes three main contributions. First, it reports the direct observation of geometric-phase interference in non-adiabatic dynamics using an MQB simulation of the Jahn–Teller model. Second, it extends the MQB framework to open-system chemical dynamics through programmable Lindblad dissipation. Third, it presents a resource analysis showing that MQB simulators can reduce resource costs by several orders of magnitude relative to qubit-only approaches. Together, these results establish MQB quantum simulators as a promising route for studying chemical dynamics beyond the reach of classical computation.
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.
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
(Dated: July 14, 2026) Simulating the dynamical trajectories of complex metalloenzymes, such as the nitrogenase FeMo-cofactor, remains classically intractable due to real-time entanglement growth and non-adiabatic surface crossings. Here, we introduce the Modular Quantum Emulator (MQE), a polynomialcomplexity quantum architecture designed for the chemically accurate emulation of multi-step fermionic catalysis. The MQE employs a universal four-dimensional qudit encoding that natively absorbs fermionic exchange signs. This entirely eliminates the Jordan-Wigner parity string bottleneck, reducing the entangling gate count from quartic to quadratic scaling. To track multi-step stoichiometry, the emulator utilizes a dual-manifold design: a logical register for electronic structure and a virtual register for coherent cofactor phase accumulation. We prove a structural isomorphism wherein this virtual register natively functions as the phase clock for Quantum Phase Estimation, enabling exact energy extraction with zero ancilla overhead. Finally, we establish strict polynomial resource bounds for complete catalytic trajectories and demonstrate that the architecture seamlessly accommodates eight systematic physical extensions—including open-system dissipation and relativistic kinematics—without altering its asymptotic complexity class. Validated across seventeen biochemical mechanisms, this framework fundamentally shifts the computational paradigm from static variational minimization to exact, polynomially-bounded dynamical emulation.