Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in the Variational Quantum Eigensolver

The variational quantum eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based computers. However, circuit depth expected grow significantly with size. Increased can both degrade accuracy results and reduce trainability. In this work, we propose an approach ansatz depth. Our approach, called “PermVQE,” adds additional optimization loop VQE that permutes qubits in order qubit Hamiltonian maximally localizes correlations ground state. permutations based mutual information, which measure interaction between electrons and/or holes spin-orbitals. Encoding strongly entangled spin-orbitals into proximal chip naturally reduces needed prepare For representative molecular systems, LiH, H2, (H2)2, H4≠, H3+, N2, demonstrate placing close proximity leads shallower circuits required reach given eigenvalue-eigenvector accuracy. designed hardware-efficient any connectivity, examples are demonstrated linear two-dimensional grid architectures. main ideas also be applied simulate other as well algorithms beyond VQE. particular, beneficial effect build fermionic–adaptive derivative assembled pseudo-Trotter connectivity architecture nearly twofold reduction number controlled not gates.4 MoreReceived 14 September 2020Revised 22 January 2021Accepted 19 April 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020337Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum computationQuantum Information