Modeling stochastic chemical kinetics on quantum computers

The Chemical Master Equation (CME) provides a highly accurate yet extremely resource-intensive representation of stochastic chemical reaction networks and their kinetics due to the exponential scaling of its possible states with the number of reacting species. In this work, we investigate how quantum computing can be employed to model stochastic chemical kinetics as described by the CME using the Schlögl model of a trimolecular reaction network as an illustrative example. We analyze the mono- and bistable regimes of the Schlögl model, identifying the bistable regime as more suitable for quantum computation due to the availability of a Hermitian operator form that preserves eigenvalues and eigenvectors. Employing the Variational Quantum Deflation (VQD) algorithm, we compute the smallest-magnitude eigenvalues, λ0, and λ1. We use VQD and a combination of Quantum Phase Estimation (QPE) and Variational Quantum Singular Value Decomposition (VQSVD) to estimate the zeromode (non-equilibrium steady state) of the bistable case. Our results from noiseless quantum simulations (VQD) and quantum hardware (QPE + VQSVD) agree within a few percent with the classically computed eigenvalues and zeromodes of up to 4-qubit operators. We show that achieving an exact solution requires at least 5 qubits, which is within reach of near-term quantum computers.