Speakers
Description
Simulating non-adiabatic quantum dynamics, such as those governing photochemical processes in human vision or DNA resistance to UV, remains a major challenge [1]. Specifically, because these phenomena lie beyond the Born-Oppenheimer approximation, requiring both electrons and nuclei to be treated as an entangled quantum system, they are inherently hard to simulate classically. To describe these dynamics, we use the linear vibronic coupling model (LVCM), where $N$ electronic configurations couple to $M$ vibrational modes via vibronic couplings $\kappa_{mij}$:
\begin{equation}
H_{\text{mol}} = \sum_{i,j}^{N} \Delta_{ij} \psi_{i}^{\dagger} \psi_{j} + \sum_{m}^{M} \nu_{m} a_{m}^{\dagger} a_{m} + \sum_{m}^{M} \sum_{i,j}^{N} \kappa_{mij} \psi_{i}^{\dagger} \psi_{j} (a_{m}^{\dagger} + a_{m}).
\end{equation}
Previous simulations restricted this model to two electronic states ($N=2$) via single-qubit encodings. We overcome this bottleneck by employing qudits, directly expanding the simulation to $N=d$ configurations. Trapped ions provide an ideal mapping for this scaled architecture. The $d$-dimensional electronic space is encoded into discrete internal ion states, while the vibrational modes map naturally onto the continuous motion of a calcium-ion chain.
A key objective of this work is to assess how various algorithmic and physical error sources impact the simulation. First, since LVCM interaction terms are not natively available, we theoretically derive the necessary gate sequences for a qutrit ($d=3$) to implement short-time evolution operators, which are then combined using Trotterization. Second, we study how experimentally relevant noise sources, such as motional heating, amplitude damping, and dephasing, impact these simulated dynamics. Finally, we analyze the validity of the Lamb--Dicke approximation, quantifying the systematic errors that arise when approaching its breakdown regime. For our qutrit encoding, we aim to identify an optimal operating regime that balances these competing errors within the hardware's coherence limits.
Our work will provide concrete parameters for feasible simulations on the MILC trapped-ion platform and establish a pathway toward scaling to higher-dimensional qudits ($d>3$). Over the next five months leading up to the conference, I will extend these pulse constructions to larger qudit spaces, refine the error models, and explore noise mitigation strategies. By establishing these theoretical bounds, this work will dictate exactly which complex non-adiabatic chemical dynamics can be feasibly simulated on current trapped-ion hardware.
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M. Kang et al., Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics, Nat. Rev. Chem. 8 (2024), pp. 340–358.
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J. Whitlow et al., Quantum simulation of conical intersections using trapped ions, Nat. Chem. 15 (2023), pp. 1509–1514.
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C. H. Valahu et al., Direct observation of geometric-phase interference in dynamics around a conical intersection, Nat. Chem. 15 (2023), pp. 1503–1508.
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T. Navickas et al., Experimental quantum simulation of chemical dynamics, arXiv:2409.04044 (2024)
| Academic level | Master's Student |
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