Implementing Translational Quantum Subspace Expansion with Fewer Qubits

Translational Quantum Subspace Expansion (TransQSE) is a hybrid quantum-classical algorithm for finding ground states of periodic systems by variationally exploring correlations within a finite sector of space, then mixing correlations across sectors via QSE. The original formulation requires 2N+1 qubits, where N is the number of orbitals within one sector. Applying our own ansatz and a qubit mapping developed for single-body band structure calculations, we implement a modified version of TransQSE requiring fewer qubits. We compare the performance of our implementation with the original formulation, subject to both ideal and noisy environments.