This proposal seeks to demonstrate quantum utility by leveraging multiple quantum resources of distinct nature, including both discrete-variable (DV, qubits) and continuous-variable (CV, bosonic modes, or quantum harmonic oscillators) quantum resources for useful applications. We target one of the major problems in physical sciences, quantum simulation (also called Hamiltonian simulation) of quantum matter composed of fermion-boson mixtures, by performing end-to-end fine-grained resource estimation on multiple metrics including qubit and oscillator count, gate count, real runtime, solution accuracy, and energy-to-solution.

The design period of this program will concentrate on four intertwined activities, namely, ion trap hardware, component technologies, quantum algorithms and support software. NCSU's effort focuses on the innovation of the software expression of high level applications/algorithms to native architectural considerations such as gate protocols, connectivity, and qubit modularity. This will crucially involve the use of error mitigation strategies that exploit symmetries or structures in the application circuits themselves.

Understanding chemical reactions is of paramount importance in critical areas, including biological and life sciences, the chemical industry, environmental processes, and geosciences. The hallmark of chemical reactions is the concerted motion of electrons and atomic nuclei across multiple scales, typically ranging from femto- (electron) to pico-seconds (nuclei) in time and from electron volts (eV, electrons) to one part in a thousand eV (nuclei) in energy. On top of the vast span of energy and time scales is the correlated nature of interacting electrons and the topological aspects of nuclei-electron wave function near conical intersections. These characteristics are where the complexity of chemistry arises, and have also made the efficient simulation and prediction of chemical reaction pathways a Holy Grail for chemical science. Leveraging quantum algorithms and the recently established molecular phase space formulation, we propose efficient hybrid quantum-classical algorithms to simulate coupled electron-nuclei dynamics near molecular conical intersections.

The primary goal of the QACTI quantum system and technology demonstrator is to build an advantage-class trapped-ion quantum-computer capable of being used by the broader scientific community remotely. The secondary goals are to discover algorithms suited for near-term quantum computers, improve and democratize ion trap quantum technology, and develop a workforce capable of utilizing and building advantage-class machines.These goals only become achievable by performing device-oriented experiments at fine-grained control levels that are not available on commercial platforms, thereby contributing to the development of a combined hardware/software stack in an open-source manner.

Intrinsically Disordered Proteins (IDPs) play important roles in neurodegenerative diseases like Alzheimer's (AD) and Parkinson's (PD), which together affect one in nine people over the age of sixty-five worldwide. Despite the previous belief that IDPs lack defined functions due to their structural flexibility, we now recognize they play significant roles in biological pathways and disease mechanisms, serving as both markers and potential modulators in neurodegenerative disorders. We propose to harness the potential of quantum computing for analyzing biological processes to improve human health, focusing on two key proteins closely associated with the pathology of AD and PD: amyloid-$\beta$ and $\alpha$-synuclein, respectively. The multi-faceted nature of proteins like amyloid-$\beta$ and $\alpha$-synuclein, their crucial role in the progression of neurodegenerative diseases like Alzheimer's and Parkinson's, and their complex interactions with metals, present considerable challenges to both experimental and computational study. Metals, key influencers in disease pathogenesis, interact with these proteins and even affect their aggregation. They also extend their influence to metal chaperones, which are pivotal for transporting metals throughout the body and maintaining distinct metal concentrations in various organ systems, tissues, and subcellular organelles. These connections hint at possible therapeutic intervention pathways, yet the challenges they pose render conventional methods of analysis inadequate. Our project explores pioneering new computational techniques, integrating quantum chemistry with quantum computing to shed light on these intricate interactions, aiming to provide insights that could have far-reaching implications for human health. We believe this to be well-aligned with the objectives of Wellcome Leap's Quantum for Bio program, representing a promising early adoption of emerging quantum computing hardware for healthcare.