Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale computing. Based on the variational eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that partitioning Hilbert space made possible by point group symmetry molecular systems greatly reduces number operators confining search within a subspace. In addition, found instead including all subterms each excitation operator, single-term representation suffices to reach required accuracy various molecules tested, resulting in an additional shortening circuit. With these strategies, VQE calculations noiseless simulator achieve energies few meVs those obtained full UCCSD ansatz $\mathrm{H}_4$ square, chain and $\mathrm{H}_6$ hexagon molecules; while controlled-NOT (CNOT) gates, measure quantum-circuit depth, is reduced factor as large 35. Furthermore, introduced efficient "score" parameter rank operators, so causing larger energy reduction can be applied first. Using square examples, We demonstrated simulators first bring chemical accuracy, do not improve since accumulative noise outweighs gain from expansion ansatz.