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Quantum Resource Comparison for Two Leading Surface Code Lattice Surgery Approaches

Tyler LeBlond and Ryan S. Bennink

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AbstractHamiltonian simulation is one of the most promising candidates for the demonstration of quantum advantage within the next ten years, and several studies have proposed end-to-end resource estimates for executing such algorithms on fault-tolerant quantum processors. Usually, these resource estimates are based upon the assumption that quantum error correction is implemented using the surface code, and that the best surface code compilation scheme involves serializing input circuits by eliminating all Clifford gates. This transformation is thought to make best use of the native multi-body measurement (lattice surgery) instruction set available to surface codes. Some work, however, has suggested that direct compilation from Clifford+T to lattice surgery operations may be beneficial for circuits that have high degrees of logical parallelism. In this study, we analyze the resource costs for implementing Hamiltonian simulation using example approaches from each of these leading surface code compilation families. The Hamiltonians whose dynamics we consider are those of the transverse-field Ising model in several geometries, the Kitaev honeycomb model, and the $\mathrm{\alpha-RuCl_3}$ complex under a time-varying magnetic field. We show, among other things, that the optimal scheme depends on whether Hamiltonian simulation is implemented using the quantum signal processing or Trotter-Suzuki algorithms, with Trotterization benefiting by orders of magnitude from direct Clifford+T compilation for these applications. Our results suggest that surface code quantum computers should not have a one-size-fits-all compilation scheme, but that smart compilers should predict the optimal scheme based upon high-level quantities from logical circuits such as average circuit density, numbers of logical qubits, and T fraction.► BibTeX data@article{LeBlond2026quantumresource, doi = {10.22331/q-2026-08-10-2187}, url = {https://doi.org/10.22331/q-2026-08-10-2187}, title = {Quantum {R}esource {C}omparison for {T}wo {L}eading {S}urface {C}ode {L}attice {S}urgery {A}pproaches}, author = {LeBlond, Tyler and Bennink, Ryan S.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2187}, month = aug, year = {2026} }► References [1] Barbara M Terhal. ``Quantum error correction for quantum memories''. Reviews of Modern Physics 87, 307–346 (2015). https://doi.org/10.1103/RevModPhys.87.307 [2] Rajeev Acharya, Dmitry A Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, et al. ``Quantum error correction below the surface code threshold''. Nature (2024). https://doi.org/10.1038/s41586-024-08449-y [3] Google Quantum AI. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676–681 (2023). https://doi.org/10.1038/s41586-022-05434-1 [4] Youwei Zhao, Yangsen Ye, He-Liang Huang, Yiming Zhang, Dachao Wu, Huijie Guan, Qingling Zhu, Zuolin Wei, Tan He, Sirui Cao, et al. ``Realization of an error-correcting surface code with superconducting qubits''.

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Physical Review Letters 127, 130505 (2021). https://doi.org/10.1103/PhysRevLett.127.130505Cited byCould not fetch Crossref cited-by data during last attempt 2026-08-10 06:40:17: Could not fetch cited-by data for 10.22331/q-2026-08-10-2187 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-08-10 06:40:17: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractHamiltonian simulation is one of the most promising candidates for the demonstration of quantum advantage within the next ten years, and several studies have proposed end-to-end resource estimates for executing such algorithms on fault-tolerant quantum processors. Usually, these resource estimates are based upon the assumption that quantum error correction is implemented using the surface code, and that the best surface code compilation scheme involves serializing input circuits by eliminating all Clifford gates. This transformation is thought to make best use of the native multi-body measurement (lattice surgery) instruction set available to surface codes. Some work, however, has suggested that direct compilation from Clifford+T to lattice surgery operations may be beneficial for circuits that have high degrees of logical parallelism. In this study, we analyze the resource costs for implementing Hamiltonian simulation using example approaches from each of these leading surface code compilation families. The Hamiltonians whose dynamics we consider are those of the transverse-field Ising model in several geometries, the Kitaev honeycomb model, and the $\mathrm{\alpha-RuCl_3}$ complex under a time-varying magnetic field. We show, among other things, that the optimal scheme depends on whether Hamiltonian simulation is implemented using the quantum signal processing or Trotter-Suzuki algorithms, with Trotterization benefiting by orders of magnitude from direct Clifford+T compilation for these applications. Our results suggest that surface code quantum computers should not have a one-size-fits-all compilation scheme, but that smart compilers should predict the optimal scheme based upon high-level quantities from logical circuits such as average circuit density, numbers of logical qubits, and T fraction.► BibTeX data@article{LeBlond2026quantumresource, doi = {10.22331/q-2026-08-10-2187}, url = {https://doi.org/10.22331/q-2026-08-10-2187}, title = {Quantum {R}esource {C}omparison for {T}wo {L}eading {S}urface {C}ode {L}attice {S}urgery {A}pproaches}, author = {LeBlond, Tyler and Bennink, Ryan S.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2187}, month = aug, year = {2026} }► References [1] Barbara M Terhal. ``Quantum error correction for quantum memories''. Reviews of Modern Physics 87, 307–346 (2015). https://doi.org/10.1103/RevModPhys.87.307 [2] Rajeev Acharya, Dmitry A Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, et al. ``Quantum error correction below the surface code threshold''. Nature (2024). https://doi.org/10.1038/s41586-024-08449-y [3] Google Quantum AI. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676–681 (2023). https://doi.org/10.1038/s41586-022-05434-1 [4] Youwei Zhao, Yangsen Ye, He-Liang Huang, Yiming Zhang, Dachao Wu, Huijie Guan, Qingling Zhu, Zuolin Wei, Tan He, Sirui Cao, et al. ``Realization of an error-correcting surface code with superconducting qubits''.

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Quantum Resource Comparison for Two Leading Surface Code Lattice Surgery Approaches

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