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arXiv:2512.20828

Using bosons to improve resource efficiency of quantum simulation of vibronic molecular dynamics

Henry L. Nourse, Vanessa C. Olaya-Agudelo, Ivan Kassal

quant-phSubmitted Dec 23, 2025• Announced Dec 25, 2025• 0 citations
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Abstract

Simulating chemical dynamics is computationally challenging, especially for nonadiabatic dynamics, where numerically exact classical simulations scale exponentially with system size, becoming intractable for even small molecules. On quantum computers, chemical dynamics can be simulated efficiently using either universal, qubit-only devices or specialized mixed-qudit-boson (MQB) simulators, which natively host electronic and vibrational degrees of freedom. Here, we compare the quantum resources required for a qubit-only approach to achieve the same accuracy as an MQB device at simulating nonadiabatic molecular dynamics. We find that MQB simulations require orders-of-magnitude fewer quantum operations than qubit-only simulations, with a one-gate MQB circuit requiring a qubit-equivalent circuit volume of over 400,000 when simulating an isolated molecule, which increases to over ten million when environmental effects are included. These estimates assume perfect qubits and gates, and would increase by additional orders of magnitude if error correction were used for fault tolerance. When errors are small, the advantage of MQB simulators becomes even larger as system size increases. Our results highlight the enormous resource advantages of representing non-qubit chemical degrees of freedom natively, rather than encoding them into qubits.

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Simulating chemical dynamics is computationally challenging, especially for nonadiabatic dynamics, where numerically exact classical simulations scale exponentially with system size, becoming intractable for even small molecules. On quantum computers, chemical dynamics can be simulated efficiently using either universal, qubit-only devices or specialized mixed-qudit-boson (MQB) simulators, which natively host electronic and vibrational degrees of freedom. Here, we compare the quantum resources required for a qubit-only approach to achieve the same accuracy as an MQB device at simulating nonadiabatic molecular dynamics. We find that MQB simulations require orders-of-magnitude fewer quantum operations than qubit-only simulations, with a one-gate MQB circuit requiring a qubit-equivalent circuit volume of over 400,000 when simulating an isolated molecule, which increases to over ten million when environmental effects are included. These estimates assume perfect qubits and gates, and would increase by additional orders of magnitude if error correction were used for fault tolerance. When errors are small, the advantage of MQB simulators becomes even larger as system size increases. Our results highlight the enormous resource advantages of representing non-qubit chemical degrees of freedom natively, rather than encoding them into qubits.
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.
Interactions of molecules with their environment influence the course and outcome of almost all chemical reactions. However, classical computers struggle to accurately simulate complicated molecule-environment interactions because of the steep growth of computational resources with both molecule size and environment complexity. Therefore, many quantum-chemical simulations are restricted to isolated molecules, whose dynamics can dramatically differ from what happens in an environment. Here, we show that analog quantum simulators can simulate open molecular systems by using the native dissipation of the simulator and injecting additional controllable dissipation. By exploiting the native dissipation to simulate the molecular dissipation—rather than seeing it as a limitation—our approach enables longer simulations of open systems than are possible for closed systems. In particular, we show that trapped-ion simulators using a mixed qudit-boson (MQB) encoding could simulate molecules in a wide range of condensed phases by implementing widely used dissipative processes within the Lindblad formalism, including pure dephasing and both electronic and vibrational relaxation. The MQB open-system simulations require significantly fewer additional quantum resources compared to both classical and digital quantum approaches.
Accurate simulation of dynamic processes in molecules and reactions is among the most challenging problems in quantum chemistry. Quantum computers promise efficient chemical simulation, but the existing quantum algorithms require many logical qubits and gates, placing practical applications beyond existing technology. Here, we carry out the first quantum simulations of chemical dynamics by employing a more hardware-efficient encoding scheme that uses both qubits and bosonic degrees of freedom. Our trapped-ion device accurately simulates the dynamics of nonadiabatic chemical processes, which are among the most difficult problems in computational chemistry because they involve strong coupling between electronic and nuclear motions. We demonstrate the programmability and versatility of our approach by simulating the dynamics of three different molecules, as well as open-system dynamics in the condensed phase, all with the same quantum resources. Our approach requires orders of magnitude fewer resources than equivalent qubit-only quantum simulations, demonstrating the potential of using hybrid encoding schemes to accelerate quantum simulations of complex chemical processes, which could have applications in fields ranging from energy conversion and storage to biology and drug design.
Molecular quantum dynamics simulations that treat both electrons and nuclei quantum mechanically are crucial for predicting chemical reactions. With classical computation, a full wave-function representation of both types of particles requires resources that grow exponentially with their number. Oscillator-qubit processors, including trapped-ion and circuit QED devices, represent electronic states with qubits and nuclear vibrations with oscillators. Their native operations produce linear vibronic interactions, from which programmable anharmonic interactions can be built. Product-formula approaches build the corresponding phase gates by repeating small noncommuting phase steps, and quantum signal processing (QSP) approaches approximate each gate directly with a Fourier series. Simulations apply many such gates in sequence, so accumulated cost and error limit how long the dynamics can be followed. We propose near-optimal quantum primitives for molecular quantum dynamics simulation, covering the representations of both types of particles and their interactions. We synthesize nonlinear and multimode bosonic phase gates using generalized Jacobi-Anger (GJA) expansions within QSP, with a cost that grows near-optimally in both interaction strength and precision. Our interaction model and gate synthesis each have their own accuracy setting. Chosen together, these settings make our multimode benchmark circuits about one-third shorter than those of the previous direct QSP approach. We then simulate energy exchange between the stretching and bending vibrations of a simplified carbon dioxide model. With circuit-QED noise, a short simulation narrowly misses our accuracy criteria at qubit and oscillator lifetimes near 2 ms and 5 ms. These lifetimes mark a concrete checkpoint on the way to simulating anharmonic multimode molecular quantum dynamics on near-term oscillator-qubit processors.
Modern computational techniques used to simulate quantum chemistry are on the boundary of tractability due to the exponential growth of the molecular wavefunction, requiring a careful balance between molecule size and simulation accuracy. In recent years, quantum computing has risen in popularity as a potential alternative to conventional (classical) techniques; however, most methods rely on access to "digital" quantum computers composed of qubits and quantum gates, which at present are severely limited by noise. We have developed a real-time, analog approach to simulate vibronic chemical dynamics with existing quantum technology. Our approach uses an intuitive mapping of molecular electronic and vibrational degrees of freedom onto quantum resonators and qudit (d-level system) states, with controllable couplings between degrees of freedom. The measurement output can be mapped onto different time-dependent observables, including the time-domain simulation of vibronic spectra. Our approach can also incorporate controlled sources of noise to simulate system-bath interactions and dissipative dynamics at a minimal cost. We present experimental results using a trapped-ion device, thus showing the potential for near-term simulation of chemical dynamics in complex environments beyond the abilities of classical computers.
Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks down. Quantum computers could simulate quantum-chemical dynamics more efficiently than classical computers, but there is currently no complete quantum algorithm for calculating dynamical observables to within a known error. Here, we develop an efficient, end-to-end quantum algorithm for simulating chemical dynamics that avoids all uncontrolled approximations (including the Born-Oppenheimer approximation) and whose error is bounded subject to mild assumptions. To do so, we treat the nuclei and the electrons on an equal footing and simulate the full molecular wavefunction on a momentum-space grid in first quantization, including all algorithmic steps: initial-state preparation, time evolution using qubitization, and measurement of chemical observables such as reaction yields and rates. Our work gives the first algorithm for quantum simulation of chemistry whose end-to-end complexity achieves sublinear scaling in the size of the grid. We achieve this by developing an exponentially faster method for initial-state-preparation. Photochemistry is a likely early application of our algorithm and we estimate resources required for end-to-end simulations of non-adiabatic dynamics of atmospherically important molecules. Classically intractable photochemical computations could be performed using resources comparable to those required for other chemical applications of quantum computing.