Shallowcircuit variational quantum eigensolver based on symmetryinspired Hilbert space partitioning for quantum chemical calculations
Abstract
Development of resourcefriendly quantum algorithms remains highly desirable for noisy intermediatescale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupledcluster Ansatz, we demonstrate that partitioning of the Hilbert space made possible by the pointgroup symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a singleterm representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit by a factor of 48. With these strategies, VQE calculations on a noisefree quantum simulator achieve energies within a few meVs of those obtained with the full unitary coupledcluster Ansatz with single and double excitations for the H_{4}square, H_{4}chain, and H_{6}hexagon molecules, while the number of CNOT gates, a measure of the quantumcircuit 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 the H_{4} square and H_{4} chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational Ansatz.
 Publication:

Physical Review Research
 Pub Date:
 January 2021
 DOI:
 10.1103/PhysRevResearch.3.013039
 arXiv:
 arXiv:2006.11213
 Bibcode:
 2021PhRvR...3a3039Z
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 Phys. Rev. Research 3, 013039 (2021)