The Modular Quantum Emulator: Chemically Accurate, Polynomial-Cost Simulation of Multi-Step Metalloenzyme Catalysis in a Dissipative Protein Environment
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.
(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 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.
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.
The quantum computation of electronic energies can break the curse of dimensionality that plagues manyparticle quantum mechanics.It is for this reason that a universal quantum computer has the potential to fundamentally change computational chemistry and materials science, areas in which strong electron correlations present severe hurdles for traditional electronic structure methods.Here we present a state-of-the-art analysis of accurate energy measurements on a quantum computer for computational catalysis, using improved quantum algorithms with more than an order of magnitude improvement over the best previous algorithms.As a prototypical example of local catalytic chemical reactivity we consider the case of a ruthenium catalyst that can bind, activate, and transform carbon dioxide to the high-value chemical methanol.We aim at accurate resource estimates for the quantum computing steps required for assessing the electronic energy of key intermediates and transition states of its catalytic cycle.In particular, we present quantum algorithms for double-factorized representations of the four-index integrals that can significantly reduce the computational cost over previous algorithms, and we discuss the challenges of increasing active space sizes to accurately deal with dynamical correlations.We address the requirements for future quantum hardware in order to make a universal quantum computer a successful and reliable tool for quantum computing enhanced computational materials science and chemistry, and identify open questions for further research.
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.