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

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