Benchmarking the performance of variational quantum eigensolvers (VQE) applied to the HCN molecule.

We compute the ground state energy of HCN within several representations of VQE/UCCSD using Qiskit [1,2] and EUMEN [3] to find the minimum number of qubits, variational parameters, and gates needed to perform chemically accurate simulation in a STO-6G basis. We compare several different avenues for optimization: fermion-to-qubit transformations (JW, BK, parity, para-particle [4]); imposing existing symmetries (no symmetries; Z2 symmetries with and without explicit molecular orbital symmetrisation); qubit tapering; level of compilation. Using tapering without symmetrised orbitals needs 15 qubits, and 284 variational parameters. Imposing symmetry in PySCF on the initial state results in 14 qubits, and 166 parameters. Finally, applying high-level tket-optimisation [3] results in a CNOT gate count of about 3300 (total gate count about 4700). The lowest gate count was obtained with EUMEN and tket using a para-particle approach [4]: 14 qubits, 166 parameters, 2589 CNOT gates, total gate count 3897 for Ansatz preparation, potentially within reach of near-future NISQ processors.

[1] P. Lolur, et al, AIP Conf. Proc. 2362, 030005 (2021); [2] Qiskit: https://qiskit.org/; [3] EUMEN; https://cqcl.github.io/eumen/build/html/index.html; [4] D. A. Mazziotti, et al.; arXiv:2101.11607