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  • Featured in Physics
  • Open Access

Quantum Error-Corrected Computation of Molecular Energies

Kentaro Yamamoto1,*, Yuta Kikuchi1,2, David Amaro3, Ben Criger3, Silas Dilkes3, Ciarán Ryan-Anderson4, Andrew Tranter3, Joan M. Dreiling4, Dan Gresh4 et al.

Cameron Foltz4, Michael Mills4, Steven A. Moses4,†, Peter E. Siegfried4, Maxwell D. Urmey4, Justin J. Burau4, Aaron Hankin4, Dominic Lucchetti4, John P. Gaebler4, Natalie C. Brown4, Brian Neyenhuis4, and David Muñoz Ramo3

  • *Contact author: kentaro.yamamoto@quantinuum.com
  • †Present address: AWS Center for Quantum Computing, Pasadena, CA 91125.
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PRX Quantum 7, 020319 – Published 30 April, 2026

DOI: https://doi.org/10.1103/m7j3-5sk6

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 techniques for the Clifford+RZ (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 (midcircuit measurements), and ∼3900 (∼760) total operations are applied on average. The energy E is experimentally estimated to within E−EFCI=0.001(13) hartree, where EFCI 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 toward higher memory noise protection is the most promising avenue to improve our experimental results.

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synopsis

Reliable Quantum Computation of Molecular Energies

Published 30 April, 2026

By combining quantum error correction with fault-tolerant techniques, researchers have improved how accurately a quantum computer estimates a molecule’s energy.

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Quantum computers could transform computational chemistry by predicting molecular energies that challenge powerful classical computers. The obstacle is noise: small errors creep in while the computation runs. In this work, we develop an end-to-end pipeline to run a quantum-chemistry algorithm with quantum error correction (QEC) and demonstrate the workflow on a real quantum device.

Despite the rapid progress, the capabilities of quantum hardware to be realized in the near future are yet to be powerful enough to be completely tolerant against hardware noise, i.e., fully fault-tolerant, due to a significant amount of computational overhead. To overcome the difficulties, we adopt a partially fault-tolerant design principle, which saves the overhead cost while allowing some influence of noise to remain. With the partially fault-tolerant quantum circuits, we successfully estimate the ground state energy of a hydrogen molecule on a programmable trapped-ion quantum computer.

Looking ahead, our results offer a practical blueprint: codesign the algorithm, the compiler, and the errorcorrection and validate the whole stack on hardware. This approach is portable to other platforms and algorithms. The next steps are to scale up QEC codes for stronger protection against noise and combine these tools with larger chemistry problems moving closer to reliable, highprecision quantum simulation.

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PRX Quantum 7, 020319– Published 30 April, 2026
  • Received 25 September 2025
  • Accepted 3 March 2026
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