Objective and Background

In a recent manuscript titled “The Bonsai algorithm: grow your own fermion-to-qubit mapping” [1], which follows from my master’s thesis, we introduce a tree-based formalism for mapping electrons to qubits. This formalism includes many traditional fermion-to-qubit mappings as specific instances which conventionally are mathematically dense but now can be understood as symmetric cases of an underlying tree structure, offering an easy and intuitive way to conceptualise them. Our methodology introduces substantial flexibility to design mappings, making it possible to create efficient, problem- and device-specific custom mappings outside the set of rigid orthodox mappings.

To exemplify these theoretical findings, we propose the Bonsai algorithm as a method of “growing” fermion-to-qubit mappings from subtrees of quantum devices, ensuring that the mappings are hardware-efficient and boosting the feasibility of near-term quantum chemistry simulation. As a practical example, we apply the algorithm to IBM quantum devices to find a favourable mapping of the device with a square root advantage over the best traditional mapping of the device. Part of my doctoral research will be focused on applying this framework to reduce the cost of quantum chemical simulation, and further developing theoretical understanding of this graph based approach