We present a procedure to reduce
the depth of quantum circuits
and improve the accuracy of results in computing post-Hartree–Fock
electronic structure energies in large molecular systems. The method
is based on molecular fragmentation where a molecular system is divided
into overlapping fragments through a graph-theoretic procedure. This
allows us to create a set of projection operators that decompose the
unitary evolution of the full system into separate sets of processes,
some of which can be treated on quantum hardware and others on classical
hardware. Thus, we develop a procedure for an electronic structure
that can be asynchronously spawned onto a potentially large ensemble
of classical and quantum hardware systems. We demonstrate this method
by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies
for a set of [H2]
n
clusters,
with n ranging from 4 to 128. We implement our methodology
using quantum circuits, and when these quantum circuits are processed
on a quantum simulator, we obtain energies in agreement with the UCCSD
energies in the milli-hartree energy range. We also show that our
circuit decomposition approach yields up to 9 orders of magnitude
reduction in the number of CNOT gates and quantum circuit
depth for the large-sized clusters when compared to a standard quantum
circuit implementation available on IBM’s Quantum Information
Science kit, known as Qiskit.