Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
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AbstractWe use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately $5\%$ without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.Featured image: A modified framework for variational quantum algorithms in which the quantum circuit calculations are performed via classical simulation.Popular summaryOne of the most promising applications of quantum computers is quantum simulation, where preparing the lowest-energy, or ground-state, quantum wavefunctions on quantum hardware is a key task. A common approach is to design a parameterized circuit to prepare such a ground state, with the parameters optimized by minimizing the energy within a variational framework. Typically, the energy and its gradient are evaluated using quantum hardware. However, limited access to quantum devices makes this procedure very costly in practice. In this work, we show that the training process for a variational quantum algorithm can be carried out in some cases on a classical computer using a powerful simulation technique known as the Pauli Path method, or sparse Pauli dynamics. This approach approximates quantum operators evolved in the Heisenberg picture, allowing us to emulate large quantum circuits without an actual quantum processor. Using this method, we successfully optimized circuits capable of preparing ground states for systems with over one hundred qubits, including the one- and two-dimensional quantum Ising models and the Kitaev honeycomb model—a cornerstone of topological quantum matter. We then deployed these classically trained circuits on Quantinuum’s quantum hardware, where we prepared a 48-qubit ground state of the Kitaev honeycomb model. We further demonstrated the braiding of Abelian anyons, a hallmark of topological order. Our results establish a scalable route for quantum state preparation, bridging the gap between classical simulation and quantum execution. This hybrid strategy offers a practical path toward large-scale quantum simulations and future explorations of exotic quantum phenomena on real devices.► BibTeX data@article{Lin2026utilityscalequantum, doi = {10.22331/q-2026-03-09-2014}, url = {https://doi.org/10.22331/q-2026-03-09-2014}, title = {Utility-{S}cale {Q}uantum {S}tate {P}reparation: {C}lassical {T}raining using {P}auli {P}ath {S}imulation}, author = {Lin, Cheng-Ju and Gharibyan, Hrant and Su, Vincent P.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2014}, month = mar, year = {2026} }► References [1] J. 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Pollmann, Probing non-equilibrium topological order on a quantum processor, Nature 645, 348 (2025). https://doi.org/10.1038/s41586-025-09456-3Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-09 09:42:01: Could not fetch cited-by data for 10.22331/q-2026-03-09-2014 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-09 09:42:01: No response from ADS or unable to decode the received json data when getting the list of citing works.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. AbstractWe use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately $5\%$ without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.Featured image: A modified framework for variational quantum algorithms in which the quantum circuit calculations are performed via classical simulation.Popular summaryOne of the most promising applications of quantum computers is quantum simulation, where preparing the lowest-energy, or ground-state, quantum wavefunctions on quantum hardware is a key task. A common approach is to design a parameterized circuit to prepare such a ground state, with the parameters optimized by minimizing the energy within a variational framework. Typically, the energy and its gradient are evaluated using quantum hardware. However, limited access to quantum devices makes this procedure very costly in practice. In this work, we show that the training process for a variational quantum algorithm can be carried out in some cases on a classical computer using a powerful simulation technique known as the Pauli Path method, or sparse Pauli dynamics. This approach approximates quantum operators evolved in the Heisenberg picture, allowing us to emulate large quantum circuits without an actual quantum processor. Using this method, we successfully optimized circuits capable of preparing ground states for systems with over one hundred qubits, including the one- and two-dimensional quantum Ising models and the Kitaev honeycomb model—a cornerstone of topological quantum matter. We then deployed these classically trained circuits on Quantinuum’s quantum hardware, where we prepared a 48-qubit ground state of the Kitaev honeycomb model. We further demonstrated the braiding of Abelian anyons, a hallmark of topological order. Our results establish a scalable route for quantum state preparation, bridging the gap between classical simulation and quantum execution. This hybrid strategy offers a practical path toward large-scale quantum simulations and future explorations of exotic quantum phenomena on real devices.► BibTeX data@article{Lin2026utilityscalequantum, doi = {10.22331/q-2026-03-09-2014}, url = {https://doi.org/10.22331/q-2026-03-09-2014}, title = {Utility-{S}cale {Q}uantum {S}tate {P}reparation: {C}lassical {T}raining using {P}auli {P}ath {S}imulation}, author = {Lin, Cheng-Ju and Gharibyan, Hrant and Su, Vincent P.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2014}, month = mar, year = {2026} }► References [1] J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79 [2] Y. Kim, A. Eddins, S. Anand, K. X. 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Pollmann, Probing non-equilibrium topological order on a quantum processor, Nature 645, 348 (2025). https://doi.org/10.1038/s41586-025-09456-3Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-09 09:42:01: Could not fetch cited-by data for 10.22331/q-2026-03-09-2014 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-09 09:42:01: No response from ADS or unable to decode the received json data when getting the list of citing works.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.