Minimizing State Preparations in Variational Quantum Eigensolver by
  Partitioning into Commuting Families
Variational quantum eigensolver (VQE) is a promising algorithm suitable for
near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an
exponentially sized matrix in polynomial time. It minimizes quantum resource
requirements both by co-processing with a classical processor and by
structuring computation into many subproblems. Each quantum subproblem involves
a separate state preparation terminated by the measurement of one Pauli string.
However, the number of such Pauli strings scales as $N^4$ for typical problems
of interest--a daunting growth rate that poses a serious limitation for
emerging applications such as quantum computational chemistry. We introduce a
systematic technique for minimizing requisite state preparations by exploiting
the simultaneous measurability of partitions of commuting Pauli strings. Our
work encompasses algorithms for efficiently approximating a
MIN-COMMUTING-PARTITION, as well as a synthesis tool for compiling simultaneous
measurement circuits. For representative problems, we achieve 8-30x reductions
in state preparations, with minimal overhead in measurement circuit cost. We
demonstrate experimental validation of our techniques by estimating the ground
state energy of deuteron on an IBM Q 20-qubit machine. We also investigate the
underlying statistics of simultaneous measurement and devise an adaptive
strategy for mitigating harmful covariance terms.
Pranav Gokhale Olivia Angiuli Yongshan Ding Kaiwen Gui Teague Tomesh Martin Suchara Margaret Martonosi Frederic T. Chong