The potential for quantum computers (QC) to solve complex problems exponentially faster than classical computers promises revolutionary advancements in data analysis, optimization, and encryption. Many problems fundamental to the disciplines of significance to society can be expressed as complex optimization problems governing the underlying relationships in large dimensions requiring exponential classical computational resources. QCs provide a revolutionary computing methodology for finding the optimal solution given these objective functions and constraints. A prominent application of QCs is a quantum simulation that has a significant impact on a multitude of scientific research areas, such as computer-aided drug design, high-energy physics, quantum chemistry, and many-body physics. For instance, simulation of the drug’s molecular structures can replace the traditional mass-scale trial-and-error design process; hence drastically speeding up computationally and thus lowering the design cost. In quantum chemistry, the main interest is in computing the molecular properties such as the energy of the ground state. The time required to obtain molecular energies scales exponentially with the system size in classical computers, whereas it is known to be polynomial in quantum computers. In the noisy intermediate-scale quantum (NISQ) regime, the variational quantum algorithms (VQA) appear as the most promising paradigm to address these applications.
In my research group, we endeavor to develop a unified framework for the crafting and analysis of computationally and physically scalable and efficient VQAs that are robust against infidelities in NISQ hardware. Data efficiency is crucial in VQAs, especially in quantum simulation, where state preparation has a high gate complexity. For example, the time dynamics of the two-dimensional Fermi-Hubbard model on an 8X8 lattice require roughly 107 Toffoli
gates. One of the aims of our research is to develop highly sample-efficient VQAs. We aim to develop a new algorithmic and computational framework of VQAs with exponential convergence rates that are implementable on NISQ hardware through insightful analytical tools such as quantum Fisher information, quantum natural gradient descent, and Fubini-Study metric.