The Bonsai Algorithm: Mitigate Hardware Limitations By Growing Your Own Fermion-to-Qubit Mapping

In recent years, quantum computers have shown promising potential for solving the electronic structure problem in chemical systems. However, the limited connectivity of current quantum hardware still poses a major challenge for tackling complex chemical systems of actual relevance, as circuit overheads incurred by these constraints can quickly become unmanageable.

To address this challenge, we present the tree-based Bonsai algorithm [1], a formalism that takes into account connectivity constraints from the outset by ”growing” a fermion-to-qubit mapping tailored to architecture, reducing SWAP overhead. Applied to the heavy-hexagon topology used in IBM quantum computers, it produces mappings with a favourable Pauli weight scaling while avoiding the need for SWAP gates for single excitation operations. Furthermore, we relate the distribution of mode occupancy over qubits to the graph structure of the underlying mapping tree and formalize it by introducing the concept of the ”delocalization” of a fermion-to-qubit mapping. With this understanding, we can directly control how we associate mode occupancy over qubits. Moreover, we show that paradigmatic mappings, such as the Jordan-Wigner, Parity, Brayvi-Kiteav, and ternary tree, are easily understood within this formalism.

[1] Miller, A., Zimborás, Z., Knecht, S., Maniscalco, S. & García-Peréz, G. The Bonsai algorithm: grow your own fermion-to-
qubit mapping. (2022)