(578b) Bayesian Optimization-Aided Ground-State Molecular Calculation in Current Quantum Computers

In modern materials and chemistry research, computational simulations of electronic structures play a pivotal role in understanding molecular behaviors. Quantum chemistry, in particular, is used to understand molecular structures, dynamics, and reactivity, which aid in the development of novel materials and technologies. However, the computational challenge of calculating exact molecular energies requires brute-force methods, which is inherently intractable. To address this, computational chemists have devised clever approximate simulation algorithms over the decades, enabling groundbreaking scientific discoveries.

Quantum computing is an optimistic avenue for advancing molecular simulation, offering the potential for precise and efficient energy calculations of molecular systems. Despite the optimism surrounding quantum computers, the current state-of-the-art is still defined as noisy and intermediate-scale quantum (NISQ) devices. The intermediate scale restricts the size of problems that can be solved, whereas the presence of noise undermines the reliability of quantum-computed energies.

The variational quantum eigensolver (VQE) algorithm offers a promising approach to alleviate the intermediate-scale limitations of current quantum computers by leveraging a classical machine to iteratively optimize a parameterized trial wave function, which is simulated in the quantum device for a given Hamiltonian [1]. Formally, the VQE represents the trial wave function as a quantum circuit parameterized by rotation angles, which are used to modify the quantum state. The VQE algorithm thus entails a feedback loop in which the quantum computer simulates the molecular system for a given set of parameters, while the classical side uses measurements of the quantum simulation to select circuit parameters that drive the system to the ground state, using data-driven optimization.

Noise arising from quantum circuit observations arises from three sources: quantum uncertainty, environmental disturbances, and hardware limitations [2]. Although quantum uncertainty is intrinsic to quantum mechanics, it can be controlled by repeated measurements of the final quantum state, known as shots. Noise introduced by environmental disturbances and hardware limitations is not as easily addressed and poses a significant challenge to the practical application of NISQ devices in scientific discovery.

While noise and error mitigation is the subject of ongoing research, a more immediate solution is to use a classical optimization algorithm that can gracefully navigate noisy observations.
Bayesian optimization is a particularly well-suited algorithm for solving the parameter setting problems for the VQE in NISQ devices due in part to the Gaussian process model's unparalleled capacity for uncertainty quantification. Specifically, modifications to the standard Bayesian optimization algorithm have shown that cheaper (and noisier) low-shot measurements can be leveraged to construct a topological prior for optimization of the high-shot circuit of interest [3].

In this work, we build on our previously proposed algorithm [3] by using sparse Gaussian process models to construct the topological prior. The proposed modifications are benchmarked against several standard optimizers on a variety of small molecular systems on simulators with high-fidelity noise models. Experiments in physical quantum hardware are also presented. Optimization trajectories generated by searching the high-fidelity noise simulators and NISQ devices are compared to coherent (i.e., subject to only quantum uncertainty) simulators and show that the proposed algorithm is capable of finding near-optimal parameters in the presence of noise. Through this analysis, we show that while current NISQ devices have a tendency to dampen the true values of the simulated energies, they can still be used more efficiently to optimize circuit parameters, which can be validated via classical quantum information processing.

REFERENCES
[1] M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J.
Coles, “Variational quantum algorithms,” Nature Reviews Physics, vol. 3, pp. 625–644, 2020.
[2] T. Ayral, F.-M. L. Régent, Z. Saleem, Y. Alexeev, and M. Suchara, “Quantum divide and compute: Exploring the effect of different
noise sources,” SN Computer Science, vol. 2, p. 132, Mar 2021.
[3] F. Sorourifar, D. Chamaki, N. M. Tubman, J. A. Paulson, and D. E. Bernal Neira, “Bayesian optimization priors for efficient variational
quantum algorithms,” Computer Aided Chemical Engineering, 2024.