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

TL;DR

This work tackles the challenge of simulating nonadiabatic vibronic molecular dynamics by comparing resource requirements of mixed-qudit-boson (MQB) simulators against qubit-only quantum computers at equal accuracy. By framing the comparison with memory-time quantum volumes and matching error metrics, the authors show that MQB devices, which natively encode electronic states as qudits and vibrational modes as bosons, require orders of magnitude fewer quantum operations than qubit-only approaches, both in isolated molecules and in open environments. The pyrazine example demonstrates substantial resource savings, and scaling analyses indicate the MQB advantage grows with system size, suggesting near-term MQB hardware could tackle classically intractable vibronic dynamics. Overall, the paper argues that representing non-qubit degrees of freedom natively is a principled design choice for quantum chemistry simulations, with significant practical implications for open-system chemistry and beyond.

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.

Figures (5)

• Figure 1: Simulated population dynamics of the pyrazine bright state $\pi\pi^*$ subject to different sources of error, using an LVC model with two electronic states and two vibrational modes. (a) Dynamics in an MQB simulator, subject to pure vibrational dephasing with rate $\gamma_d^{\mathrm{err}}$ on both vibrational modes. (b) Dynamics on a qubit-only simulator, subject to first-order Trotter error due to discretization to $N$ steps.
• Figure 2: Matching errors between MQB and qubit-only simulations of isolated pyrazine. (a) MQB error of the excited-state population $P_1$ as a function of the vibrational pure-dephasing rate $\gamma_d^{\mathrm{err}}$. (b) Same error for a qubit-only simulator, as a function of the Trotter number $N$. Arrows depict an example of error matching between MQB and qubit-only simulations: for $\gamma_d^{\mathrm{err}} = 0.1\per s$, the MQB simulation error of $\varepsilon_1 = 1.6e-4$ is matched to the same qubit-only error, which occurs at $N=61000.0$. Dashed line is extrapolation.
• Figure 3: MQB simulation requires orders of magnitude fewer quantum resources compared to qubit-only simulation with the same error. Shown is the equivalent computational cost, in logical CNOT gates, on a qubit-only computer for simulating the vibronic dynamics of (a) isolated pyrazine and (b) pyrazine in an environment (with $\gamma_d = 2.1e12\per s$). The equivalent cost is defined by matching the error $\varepsilon_1$ or infidelity $\varepsilon_{\mathcal{F}}$ on the MQB simulator, which arise from pure vibrational dephasing $\gamma_d^{\mathrm{err}}$ in (a) and vibrational heating $\gamma_h^{\mathrm{err}}$ in (b). Typical ranges of these rates in trapped-ion simulators are $\gamma_d^{\mathrm{nat}} \in [e0, e2]$ and $\gamma_h^{\mathrm{nat}} \in [e-1, e1]$Brownnutt2015macdonell2023predictingvalahu2023directOlaya_2025lucas2007Talukdar2016Jarlaud2021. Dashed lines are extrapolation.
• Figure 4: The advantage of MQB simulators over qubit-only simulators grows with system size, even as MQB errors increase. (a,c): MQB errors increase with the number of modes $M$ for both an isolated molecule and when in an environment (with $\gamma_d = 2.1e12\per s$) because each mode experiences noise. Infidelity increases monotonically because it is a global error, whereas the population error is a local observable and can be non-monotonic. (b,d): The advantage $A$---the ratio of qubit-only to MQB volume---increases with system size. Here, $\gamma_d^{\textrm{err}} = 30\per s$ and $\gamma_h^{\textrm{err}} = 0.2\per s$ for the isolated and in environment molecule, respectively.
• Figure A1: Resource requirements for first- and second-order Trotterizations are comparable in qubit-only simulations when targeting (a) population error and (b) infidelity for isolated pyrazine at error levels typically achieved by MQB simulators (shaded region). The legend labels the $p$th-order Suzuki-Trotter decomposition.