Abstract
The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the molecular energy. Due to finite coherence times and gate errors, the number of gates that can be implemented remains limited. In this work, we propose an alternative algorithm where device-level pulse shapes are variationally optimized for the state preparation rather than using an abstract-level quantum circuit. In doing so, the coherence time required for the state preparation is drastically reduced. We numerically demonstrate this by directly optimizing pulse shapes which accurately model the dissociation of H2 and HeH+, and we compute the ground state energy for LiH with four transmons where we see reductions in state preparation times of roughly three orders of magnitude compared to gate-based strategies.
Highlights
Molecular modeling stands in the juncture of key advances in many important fields including and not limited to energy storage, material designs, and drug discovery
We find that our results below do not qualitatively depend on the frequency difference between the qubits, and in the SI we provide a comparison of this current device to one with a larger detuning between the transmons
We present an alternative to the gate-based VQE algorithm, replacing the parameterized state-preparation circuit with a parameterized laboratory-frame pulse representation, which is optimized in an analogous manner, but with the benefit of a much faster state preparation, opening up the possibility of more accurate simulations on NISQ devices
Summary
Molecular modeling stands in the juncture of key advances in many important fields including and not limited to energy storage, material designs, and drug discovery. Approximate numerical methods which are built on a single Slater determinant reference state, such as density functional theory (DFT), perturbation theory, or coupled cluster, perform well when the amount of electron correlation, ranges from minimal to moderate. For systems which are qualitatively governed by electron correlation effects (strongly correlated systems), such approximate methods fail to be sufficiently accurate. While alternative strategies exist, such as density matrix renormalization group (DMRG)[1,2,3] or selected configurational interaction (SCI) methods[4,5,6,7,8,9,10,11,12,13], which can handle strong correlation, these approaches assume that the correlations are either low-dimensional, or limited in scale. No polynomially scaling classical algorithm exists which can solve for arbitrary molecular ground states
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