Collaborative Research: EAGER-QSA: Variational Monte-Carlo-Inspired Quantum Algorithms for Many-Body Systems and Combinatorial Optimization

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Simulation of many-body quantum systems is an extremely challenging scientific problem that pushes the limits of existing and foreseeable classical computing capabilities. The ability to simulate such systems efficiently would open the possibility of resolving longstanding scientific questions in high-temperature superconductivity as well as facilitating the design of new drugs and materials. General-purpose solvers for quantum systems in greater than one spatial dimension are beyond the reach of classical hardware and are natural candidate problems for exploiting quantum resources. This project investigates how recent progress in variational Monte Carlo simulation can be used to inspire new quantum simulation techniques. The project will also undertake educational, mentoring, and outreach activities that are integrated with the research effort. This project will capitalize on recent intellectual bridges formed between the fields of variational quantum algorithms, variational Monte Carlo methods, and quantum information geometry. It consists of three research thrusts focused on fermionic systems simulation, combinatorial optimization, and quantum information geometry. Specifically, this project will design variational quantum algorithms that avoid nonlocal fermion-qubit mappings by exploiting first-quantized and gauge-theoretic reformulations of fermionic systems. Efficient methods for imposing constraints in quantum-inspired solvers for combinatorial optimization problems will be explored. Building upon classical numerical analysis tools, acceleration techniques for the quantum natural gradient will be developed by exploiting higher-order invariance of the Riemannian metric. Because the real-time evolution process by which physical states evolve according to the Schrodinger equation is of fundamental importance, the project will furthermore investigate generalization of the quantum natural gradient from imaginary to real time.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.