Evaluating Ground State Energies of Chemical Systems with Low-Depth
  Quantum Circuits and High Accuracy
Solving electronic structure problems is considered one of the most promising
applications of quantum computing. However, due to limitations imposed by the
coherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or
the capabilities of early fault-tolerant quantum devices, it is vital to design
algorithms with low-depth circuits. In this work, we develop an enhanced
Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster
(QCC) approach, which demands optimization over only $n$ parameters rather than
the usual $n+2m$ parameters, where $n$ represents the number of Pauli string
time evolution gates $e^{-itP}$, and $m$ is the number of qubits involved. We
evaluate the ground state energies of $\mathrm{O_3}$, $\mathrm{Li_4}$, and
$\mathrm{Cr_2}$, using CAS(2,2), (4,4) and (6,6) respectively in conjunction
with our enhanced QCC ansatz, UCCSD (Unitary Coupled Cluster Single Double)
ansatz, and canonical CCSD method as the active space solver, and compare with
CASCI results. Finally, we assess our enhanced QCC ansatz on two distinct
quantum hardware, IBM Kolkata and Quantinuum H1-1.
Shuo Sun Chandan Kumar Kevin Shen Elvira Shishenina Christian B. Mendl