Leveraging small scale quantum computers with unitarily downfolded
  Hamiltonians
In this work, we propose a quantum unitary downfolding formalism based on the
driven similarity renormalization group (QDSRG) that may be combined with
quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a
classical polynomially-scaling downfolding method that avoids the evaluation of
costly three- and higher-body reduced density matrices while retaining the
accuracy of classical multireference many-body theories. We calibrate and test
the QDSRG on several challenging chemical problems and propose a strategy for
avoiding classical exponential-scaling steps in the QDSRG scheme. We report
QDSRG computations of two chemical systems using the variational quantum
eigensolver on IBM quantum devices: i) the dissociation curve of H$_2$ using a
quintuple-$\zeta$ basis and ii) the bicyclobutane isomerization reaction to
$trans$-butadiene, demonstrating the reduction of problems that require several
hundred qubits to a single qubit. Our work shows that the QDSRG is a viable
approach to leverage near-term quantum devices for the accurate estimation of
molecular properties.
Renke Huang Chenyang Li Francesco A. Evangelista