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Phase-Sensitive Measurements on a Fermi–Hubbard Quantum Processor

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Researchers led by Alberto R. Cavallar developed a hardware-efficient protocol to measure complex Loschmidt echoes in fermionic quantum processors, enabling spectral analysis of correlated electron systems. The method uses optical superlattices with cold fermionic atoms to simulate the Fermi–Hubbard model at half-filling and finite doping, avoiding fully programmable quantum circuits. Short imaginary-time evolution via optimized pulse sequences and global quench dynamics extracts spectral properties like local density of states from large many-body states. Numerical results confirm efficiency across broad spectral ranges, paving the way for finite-temperature studies in current quantum simulators. This approach combines plaquette state preparation, analog dynamics, and phase-sensitive measurements to overcome classical computational limits in strongly interacting systems.

Phase-Sensitive Measurements on a Fermi–Hubbard Quantum Processor

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AbstractFermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi–Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi–Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.Popular summaryQuantum simulators can reproduce models of strongly interacting particles that are challenging to analyze with classical computers. The Fermi–Hubbard model is a paradigmatic model for correlated electron systems. Cold fermionic atoms in optical lattices can naturally realize this model, but extracting spectral information from the many-body system remains difficult. In this work, we propose a hardware-efficient protocol to access such spectral information on a fermionic quantum processor. Our approach avoids fully programmable quantum circuits that implement controlled global time-evolution operators. Instead, it combines optical-superlattice preparation of small plaquette states, optimized pulses implementing short imaginary-time evolution, and analog Fermi–Hubbard dynamics. This allows one to measure the complex-valued Loschmidt echo, a quantity that encodes spectral information about the Fermi-Hubbard model both at half-filling and for doped systems.► BibTeX data@article{Cavallar2026phasesensitive, doi = {10.22331/q-2026-05-12-2103}, url = {https://doi.org/10.22331/q-2026-05-12-2103}, title = {Phase-{S}ensitive {M}easurements on a {F}ermi–{H}ubbard {Q}uantum {P}rocessor}, author = {Cavallar, Alberto R. and Escalera-Moreno, Luis and Franz, Titus and Hilker, Timon and Cirac, J. Ignacio and Preiss, Philipp M. and Schiffer, Benjamin F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2103}, month = may, year = {2026} }► References [1] P. A. Lee, N. Nagaosa, and X.-G. Wen. ``Doping a Mott insulator: Physics of high-temperature superconductivity''. Rev. Mod. Phys. 78, 17–85 (2006). https://doi.org/10.1103/RevModPhys.78.17 [2] M. Qin, T. Schäfer, S. Andergassen, P. Corboz, and E. Gull. ``The Hubbard Model: A Computational Perspective''. Annual Review of Condensed Matter Physics 13, 275–302 (2022). https://doi.org/10.1146/annurev-conmatphys-090921-033948 [3] W. S. Bakr, Z. Ba, and M. L. Prichard. ``Microscopy of Ultracold Fermions in Optical Lattices'' (2025). arXiv:2507.04042 [cond-mat.quant-gas]. https://doi.org/10.48550/arXiv.2507.04042 arXiv:2507.04042 [4] L. Tarruell and L. Sanchez-Palencia. ``Quantum simulation of the Hubbard model with ultracold fermions in optical lattices''. Comptes Rendus. Physique 19, 365–393 (2018). https://doi.org/10.1016/j.crhy.2018.10.013 [5] V. Havlíček, M. Troyer, and J. D. Whitfield. ``Operator locality in the quantum simulation of fermionic models''. Physical Review A 95, 032332 (2017). https://doi.org/10.1103/PhysRevA.95.032332 [6] A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu. ``Theory of Trotter Error with Commutator Scaling''. Physical Review X 11, 011020 (2021). https://doi.org/10.1103/PhysRevX.11.011020 [7] A. Y. Kitaev. ``Quantum measurements and the Abelian Stabilizer Problem''. Electron. Colloquium Comput. Complex. TR96 (1995). https://doi.org/10.48550/arXiv.quant-ph/9511026 arXiv:quant-ph/9511026 [8] M. A. Nielsen and I. L. Chuang. ``Quantum Computation and Quantum Information''.

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GitLab repository, version v1.0-paper, https://gitlab.physik.uni-muenchen.de/A.Cavallar/ite-ramp-optimization.git. https://gitlab.physik.uni-muenchen.de/A.Cavallar/ite-ramp-optimization.git [46] U. Schollwöck. ``The density-matrix renormalization group in the age of matrix product states''. Annals of Physics 326, 96–192 (2011). https://doi.org/10.1016/j.aop.2010.09.012 [47] M. Fishman, S. White, and E. Stoudenmire. ``The ITensor Software Library for Tensor Network Calculations''. SciPost Physics Codebases (2022). https://doi.org/10.21468/SciPostPhysCodeb.4 [48] B. F. Schiffer, D. v. Vreumingen, J. Tura, and S. Polla. ``Virtual mitigation of coherent non-adiabatic transitions by echo verification''. Quantum 8, 1346 (2024). https://doi.org/10.22331/q-2024-05-14-1346 [49] R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu. ``A Limited Memory Algorithm for Bound Constrained Optimization''. SIAM Journal on Scientific Computing 16, 1190–1208 (1995). https://doi.org/10.1137/0916069 [50] C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal. ``Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization''. ACM Trans. Math. Softw. 23, 550–560 (1997). https://doi.org/10.1145/279232.279236 [51] P. Weinberg and M. Bukov. ``QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. part I: spin chains''. SciPost Phys. 2, 003 (2017). https://doi.org/10.21468/SciPostPhys.2.1.003 [52] P. Weinberg and M. Bukov. ``QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. part II: bosons, fermions and higher spins''. SciPost Phys. 7, 020 (2019). https://doi.org/10.21468/SciPostPhys.7.2.020Cited by[1] Cristian Tabares, Dominik S. Wild, J. Ignacio Cirac, Peter Zoller, Alejandro González-Tudela, and Daniel González-Cuadra, "Estimating ground-state properties in quantum simulators with global control", arXiv:2511.04434, (2025). [2] Alexander Roth, Liyang Qiu, Timon Hilker, Titus Franz, and Philipp M. Preiss, "Constructing Arbitrary Coherent Rearrangements in Optical Lattices", arXiv:2603.04210, (2026). [3] Cristian Tabares, Alberto Muñoz de las Heras, Jan T. Schneider, and Alejandro González-Tudela, "Programming long-range interactions in analog quantum simulators", arXiv:2604.22483, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-05-12 14:02:17). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-05-12 14:02:16: Could not fetch cited-by data for 10.22331/q-2026-05-12-2103 from Crossref. This is normal if the DOI was registered recently.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. AbstractFermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi–Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi–Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.Popular summaryQuantum simulators can reproduce models of strongly interacting particles that are challenging to analyze with classical computers. The Fermi–Hubbard model is a paradigmatic model for correlated electron systems. Cold fermionic atoms in optical lattices can naturally realize this model, but extracting spectral information from the many-body system remains difficult. In this work, we propose a hardware-efficient protocol to access such spectral information on a fermionic quantum processor. Our approach avoids fully programmable quantum circuits that implement controlled global time-evolution operators. Instead, it combines optical-superlattice preparation of small plaquette states, optimized pulses implementing short imaginary-time evolution, and analog Fermi–Hubbard dynamics. This allows one to measure the complex-valued Loschmidt echo, a quantity that encodes spectral information about the Fermi-Hubbard model both at half-filling and for doped systems.► BibTeX data@article{Cavallar2026phasesensitive, doi = {10.22331/q-2026-05-12-2103}, url = {https://doi.org/10.22331/q-2026-05-12-2103}, title = {Phase-{S}ensitive {M}easurements on a {F}ermi–{H}ubbard {Q}uantum {P}rocessor}, author = {Cavallar, Alberto R. and Escalera-Moreno, Luis and Franz, Titus and Hilker, Timon and Cirac, J. Ignacio and Preiss, Philipp M. and Schiffer, Benjamin F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2103}, month = may, year = {2026} }► References [1] P. A. Lee, N. Nagaosa, and X.-G. Wen. ``Doping a Mott insulator: Physics of high-temperature superconductivity''. Rev. Mod. Phys. 78, 17–85 (2006). https://doi.org/10.1103/RevModPhys.78.17 [2] M. Qin, T. Schäfer, S. Andergassen, P. Corboz, and E. Gull. ``The Hubbard Model: A Computational Perspective''. Annual Review of Condensed Matter Physics 13, 275–302 (2022). https://doi.org/10.1146/annurev-conmatphys-090921-033948 [3] W. S. Bakr, Z. Ba, and M. L. Prichard. ``Microscopy of Ultracold Fermions in Optical Lattices'' (2025). arXiv:2507.04042 [cond-mat.quant-gas]. https://doi.org/10.48550/arXiv.2507.04042 arXiv:2507.04042 [4] L. Tarruell and L. Sanchez-Palencia. ``Quantum simulation of the Hubbard model with ultracold fermions in optical lattices''. Comptes Rendus. Physique 19, 365–393 (2018). https://doi.org/10.1016/j.crhy.2018.10.013 [5] V. Havlíček, M. Troyer, and J. D. Whitfield. ``Operator locality in the quantum simulation of fermionic models''. Physical Review A 95, 032332 (2017). https://doi.org/10.1103/PhysRevA.95.032332 [6] A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu. ``Theory of Trotter Error with Commutator Scaling''. Physical Review X 11, 011020 (2021). https://doi.org/10.1103/PhysRevX.11.011020 [7] A. Y. Kitaev. ``Quantum measurements and the Abelian Stabilizer Problem''. Electron. Colloquium Comput. Complex. TR96 (1995). https://doi.org/10.48550/arXiv.quant-ph/9511026 arXiv:quant-ph/9511026 [8] M. A. Nielsen and I. L. Chuang. ``Quantum Computation and Quantum Information''.

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Phase-Sensitive Measurements on a Fermi–Hubbard Quantum Processor

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