Improving operator averaging in hybrid algorithms with approximate N-representability constraints

Presenting Author: Nicholas Rubin, Rigetti Computing
Contributing Author(s): Jarrod R. McClean Ryan Babbush

The two most well known hybrid classical/quantum algorithms require calculating expected values of Pauli operators by repeated state preparation and measurement. Accelerating the operator averaging step correlates directly with minimizing the total runtime of the algorithms. We derive an optimal bound on the number of measurements required to calculate the expected value of a sum of non-commuting Pauli operators to fixed precision that improves upon the bound derived from central limit theorem. To further reduce the required measurements, we propose the use of approximate N-representability constraints as a set of conditions for reconstructing marginals. These techniques take the form of projections onto the set of N-representable two-electron reduced density matrices (2-RDMs) enforcing non-negativity of the marginal, particle number conservation, and the appropriate magnetization of the targeted Fermionic state prepared on the quantum resource. Most importantly, the projection techniques restore physicality of the measured states corrupted by an error channel. We present the performance of the N-representability inspired 2-RDM reconstruction procedures on marginals mimicking real measured data. For small systems, the projection techniques give a significant reduction in the number of samples required for operator averaging to a given precision.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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