Quantum Error-Corrected Computation of Molecular Energies

TL;DR

This paper demonstrates a quantum error correction pipeline for molecular energy calculations, achieving high fidelity and precise energy estimates using fault-tolerant techniques and real-time error correction.

Contribution

First end-to-end quantum error correction implementation for molecular electronic structure calculation with improved fidelity and real-time error correction techniques.

Findings

Achieved energy estimation within 0.001(13) hartree of exact value.

Implemented partially fault-tolerant techniques for Clifford+$R_{Z}$ gates.

Identified memory noise protection as key to improving results.

Abstract

We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2-2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.