Chemistry beyond the Hartree–Fock energy via quantum computed moments

Abstract

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H$$_6$$ 6 . On a superconducting quantum processor, Hamiltonian moments, $$\langle H^p\rangle$$ ⟨ H p ⟩ are computed with respect to the Hartree–Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree–Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H$$_6$$ 6 . Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H$$_2$$ 2 , over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree–Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

A Qubit-Efficient Variational Selected Configuration-Interaction Method

“…In the work of [39] the H 2 molecule was computed on real quantum devices for the larger 6-31 basis set using 4 qubits, reaching an energy deviation of roughly 0.01 Ha from the corresponding FCI solution. In the work of [66] the H 2 groundstate was computed through the variational quantum computed moments (QCM) method (introduced in [67]) using 2 qubits. The obtained groundstate energy deviated by ∆E = 0.001 Ha from the FCI solution, thereby reaching chemical accuracy.…”

Quantum chemistry simulations in an undergraduate project: tellurophenes as narrow bandgap semiconductor materials

“…Ideally, the length of the polymer chain would very large, to ensure the band gap converges as closely as possible on the true value of the band gap at the large-N limit. However, it is expected that the length of time of the simulations will increase as a strong (approximately exponential) function of increasing chain length [45,46]. On a similar note, the sidechains and moiety structures associated with organic molecules and polymers may add a significant computational cost, whilst not contributing directly to the πorbital structure.…”

The basics of quantum computing for chemists

“…In a similar vein, quantum computers can be employed to prepare entangled states with sizable overlap with the true ground state and carry out the subsequent measurements in an efficient fashion. This can pave the way for widespread adoption of methodologies which estimate the ground state energy based on moments of the Hamiltonian [113][114][115][116][117], which share some commonalities with ITE [118], and real-time evolution on the grounds of Krylov basis ideas [66].…”

“…While some of the earlier instances of quantum chemistry revolved around variational approaches, some recent examples feature implementations of ITE and some of its variants, which were initially applied to the H 2 molecule and alkali-metal hydrides with a variety of different IBM chips [157,158]. In the same category can also be added algorithms derived from moments expansions, which have been experimentally realized for small hydrogen chains (up to H 6 ) on IBM's hardware [159]. Huggins et al have showcased ITE in the context of quantum Monte Carlo, enabling a simulation of N 2 with the cc-pVTZ basis set, amounting to 120 spin-orbitals, with only 16 qubits on Google Sycamore chip [160].…”