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 polynomial-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 reducing the measurement cost. We report QDSRG compu-tations of two chemical systems using the variational quantum eigensolver on IBM quantum devices: (i) the dissociation curve of H2 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 estimating molecular properties with chemical accuracy, using only up to the diagonal elements of the two-body reduced density matrix of the reference state.