Ground State Energy via Adiabatic Evolution and Phase Measurement for a Molecular Hamiltonian on an Ion-Trap Quantum Computer

TL;DR

This paper demonstrates a quantum algorithm on an ion-trap computer to estimate the ground state energy of a molecule, highlighting leakage errors as the main obstacle to achieving chemical accuracy.

Contribution

It presents a practical implementation of adiabatic state preparation and phase measurement on ion-trap hardware, identifying leakage errors as critical to address for accuracy.

Findings

Leakage errors are the main obstacle to chemical accuracy.

Hardware noise has minimal impact from coherent and incoherent sources.

Simulations suggest near-chemical accuracy is achievable without leakage errors.

Abstract

Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.