Toward end-to-end quantum simulation for protein dynamics

TL;DR

This work presents end-to-end quantum algorithms for simulating protein dynamics, including initialization, connectivity loading, time evolution via normal-mode models (e.g., Gaussian network models and all-atom normal modes), and read-out of observables. It introduces efficient Gaussian random-amplitude initial-state preparation and a polylog-depth quantum read-only memory (QROM) based loading of the connectivity matrix, enabling scalable end-to-end simulations. The dynamics are implemented across harmonic-oscillator, inhomogeneous-forced, and Langevin settings, with concrete quantum algorithms and complexity analyses for state evolution, ODE solving, and open-system simulations, along with methods to extract energies, vibrational spectra, displacements, and control parameters. Classical numerical experiments on density-of-states estimation for Crambin and LQR-based control for Chignolin validate the proposed speedups and demonstrate the practical potential of quantum protein dynamics on both early-stage and fault-tolerant quantum devices.

Abstract

Modeling and simulating the protein folding process overall remains a grand challenge in computational biology. We systematically investigate end-to-end quantum algorithms for simulating various protein dynamics with effects, such as mechanical forces or stochastic noises. A major focus is the read-in of system settings for simulation, for which we discuss (i) efficient quantum algorithms to prepare initial states--whether for ensemble or single-state simulations, in particular, the first efficient procedure for preparing Gaussian pseudo-random amplitude states, and (ii) the first efficient loading of the connectivity matrices of the protein structure. For the read-out stage, our algorithms estimate a range of classical observables, including energy, low-frequency vibrational modes, density of states, displacement correlations, and optimal control parameters. Between these stages, we simulate the dynamic evolution of the protein system, by using normal mode models--such as Gaussian network models (GNM) and all-atom normal mode models. In addition, we conduct classical numerical experiments focused on accurately estimating the density of states and applying optimal control to facilitate conformational changes. These experiments serve to validate our claims regarding potential quantum speedups. Overall, our study demonstrates that quantum simulation of protein dynamics represents a robust, end-to-end application for both early-stage and fully fault-tolerant quantum computing.

Figures (3)

• Figure 1: (Left) Comparison of 100 moments from exact and approximate calculations. Each marker represents a pair $(\text{Exact},\ \text{Approx})$, with the dashed line indicating perfect agreement $(y = x)$; (Right) Deviations of approximate from exact moments (on the orders of $10^2$ and $10^3$), shown by plotting $\text{Exact} - \text{Approx}$ against the moment index. The horizontal dashed line at zero provides a visual reference for the absence of error.
• Figure 2: Comparison of estimated the density of states with the histogram of the eigenvalues computed directly from $H$.
• Figure 3: (L) The total energy following the optimal control $\bm u(t)$; (R) the structural changes under the control;

Theorems & Definitions (7)

• Theorem 1
• Theorem 2: Gaussian pseudo-random amplitude state preparation
• Lemma 1: Lemma 4.8 of BDP23
• Definition 1: CBRNG
• Lemma 2: Proposal distribution
• Theorem 3
• Theorem 4