(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.
(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.
(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.
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.
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic creation-annihilation operators, and the space depends on the number of qubits used. While standard fermion encodings like Jordan-Wigner are space optimal for arbitrary fermionic systems, physical symmetries like particle conservation can reduce the number of physical configurations, allowing improved space complexity. Such space saving is only feasible if the gate overhead is small, suggesting a (quantum) data structures problem, wherein one would like to minimize space used to represent a fermionic state, while still enabling efficient rotations. We define a structure which naturally captures mappings from fermions to systems of qubits. We then instantiate it in two ways, giving rise to two new second-quantized fermion encodings of F fermions in M modes. An information theoretic minimum of I: = ⌈log₂ binom(M,F)⌉ qubits is required for such systems, a bound we nearly match over the entire parameter regime. 1) Our first construction uses I + o(I) qubits when F = o(M), and allows rotations generated by creation-annihilation operators in O(I) gates and O(log M log log M) depth. 2) Our second construction uses I + O(1) qubits when F = Θ(M), and allows rotations generated by creation-annihilation operators in O(I³) gates. In relation to comparable prior work, the first represents a polynomial improvement in both space and gate complexity (against Kirby et al. 2022), and the second represents an exponential improvement in gate complexity at the cost of only a constant number of additional qubits (against Harrison et al. or Shee et al. 2022), in the described parameter regimes.
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic creation-annihilation operators, and the space depends on the number of qubits used. While standard fermion encodings like Jordan-Wigner are space optimal for arbitrary fermionic systems, physical symmetries like particle conservation can reduce the number of physical configurations, allowing improved space complexity. Such space saving is only feasible if the gate overhead is small, suggesting a (quantum) data structures problem, wherein one would like to minimize space used to represent a fermionic state, while still enabling efficient rotations. We define a structure which naturally captures mappings from fermions to systems of qubits. We then instantiate it in two ways, giving rise to two new second-quantized fermion encodings of F fermions in M modes. An information theoretic minimum of I:=⌈log(FM)⌉ qubits is required for such systems, a bound we nearly match over the entire parameter regime. (1) Our first construction uses I+o(I) qubits when F=o(M), and allows rotations generated by creation-annihilation operators in O(I) gates and O(logMloglogM) depth. (2) Our second construction uses I+O(1) qubits when F=Θ(M), and allows rotations generated by creation-annihilation operators in O(I3) gates. In relation to comparable prior work, the first represents a polynomial improvement in both space and gate complexity (against Kirby et al. 2022), and the second represents an exponential improvement in gate complexity at the cost of only a constant number of additional qubits (against Harrison et al. or Shee et al. 2022), in the described parameter regimes.
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.