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The Variational Quantum Eigensolver (VQE) is a method of choice to solve theelectronic structure problem for molecules on near-term gate-based quantumcomputers. However, the circuit depth is expected to grow significantly withproblem size. Increased depth can both degrade the accuracy of the results andreduce trainability. In this work, we propose a novel approach to reduce ansatzcircuit depth. Our approach, called PermVQE, adds an additional optimizationloop to VQE that permutes qubits in order to solve for the qubit Hamiltonianthat minimizes long-range correlations in the ground state. The choice ofpermutations is based on mutual information, which is a measure of interactionbetween electrons in spin-orbitals. Encoding strongly interacting spin-orbitalsinto proximal qubits on a quantum chip naturally reduces the circuit depthneeded to prepare the ground state. For representative molecular systems, LiH,H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubitconnectivity that placing entangled qubits in close proximity leads toshallower depth circuits required to reach a given eigenvalue-eigenvectoraccuracy. This approach can be extended to any qubit connectivity and cansignificantly reduce the depth required to reach a desired accuracy in VQE.Moreover, our approach can be applied to other variational quantum algorithmsbeyond VQE.

Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE