Quantum Computing Innovation for Off-Road Mobility

Project #1.A73 began Sep. 2020 for 2 years as an exploratory effort and was completed Dec. 2023 in the core portfolio.

An important consideration in quantum algorithm design is the ability to perform fault-tolerant quantum computation, which necessarily incurs an overhead in the requisite number of physical qubits that are well beyond the near-term capabilities for problem sizes of technological importance. Interest has thus shifted to hybrid quantum-classical algorithms which involve the optimization of parameters of a variational quantum circuit to prepare a desired target quantum state (see figure). These variational algorithms exploit the advantages of a Quantum Processing Unit (QPU) for state preparation as well as a Classical Processing Unit (CPU) for optimization purposes. The interaction of a QPU and CPU in this way can plausibly deliver a quantum advantage and variational algorithms have been designed for solving hard combinatorial optimization as well as quantum chemistry problems.

A theoretical obstacle facing variational quantum algorithms is that they involve the introduction of a stochastic optimization problem as part of the classical outer loop. This optimization problem is generically non-convex, which greatly complicates the asymptotic complexity analysis. Although asymptotic speedups appear out of reach, it is nevertheless plausible that hybrid quantum-classical algorithms could provide valuable heuristics for solving problems of practical interest. Moreover since they involve stochastic optimization, they exhibit noise robustness and can be implemented on noisy intermediate-scale quantum computers with limited number of qubits.

The primary objective is to develop Quantum algorithms for tackling hard computational problems arising in the field of autonomous ground vehicle systems research. In particular, we explored the quantum approximate optimization landscape through the lens of information geometry, exploiting the strong analogy between quantum circuit architectures and deep neural networks. Specifically, we will draw on a toolbox of recently developed quantum-information-geometric optimization tools which have proven successful in Machine Learning and digital quantum computation.

In parallel, we pursued classical algorithms for enabling the simulation of our quantum algorithms on foreseeable quantum hardware. The main tool we utilized is Variational Monte Carlo (VMC), which simulates variational quantum states using neural networks. The use of VMC as a stepping stone will yield valuable lessons about the optimization dynamics, which can be imported to the quantum computing literature upon the availability of quantum hardware.

1.A73