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Peer-reviewedCC BY 4.0Quantum

A Symmetry-Enabled Direct Quantum Protocol for Many-Body Green's Functions

  • Changhao Yi1
  • Cunlu Zhou2,3,4
4 affiliations
  1. 1Department of Physics, Shanghai University, Shanghai, China
  2. 2Department of Computer Science, Université de Sherbrooke, QC, Canada
  3. 3Institut quantique, Université de Sherbrooke, QC, Canada
  4. 4Mila – Québec AI Institute, Montréal, QC, Canada
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Abstract

We present a symmetry-enabled direct quantum protocol for computing many-body Green's functions, a central tool for studying strongly correlated quantum systems. Our protocol relies only on native time evolution and straightforward measurements available on current hardware platforms. By exploiting parity symmetry—satisfied by a broad class of Hamiltonians in condensed matter physics and quantum chemistry, including the Fermi–Hubbard and Heisenberg models—we introduce a tailored quench spectroscopy scheme that recovers both the real and imaginary parts of two-point time correlators, from which Green's functions can be reconstructed via efficient classical signal processing. We further develop a tailored symmetric quantum Gibbs sampler that prepares parity-resolved (symmetric and antisymmetric) thermal states, enabling finite-temperature extensions within the same framework. Finally, we show that the same symmetry-based measurement primitive extends naturally to out-of-time-ordered correlators (OTOCs). Our results provide a practical route to estimating symmetry-resolved dynamical correlators on near-term and early fault-tolerant quantum hardware.

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Cite

BibTeXRIS
BibTeX
@article{yi2026symmetryenabled,
  title = {{A Symmetry-Enabled Direct Quantum Protocol for Many-Body Green's Functions}},
  author = {Changhao Yi and Cunlu Zhou},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-22-2245},
  url = {https://quantum-journal.org/papers/q-2026-10-22-2245/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Symmetry-Enabled Direct Quantum Protocol for Many-Body Green's Functions
AU  - Changhao Yi
AU  - Cunlu Zhou
PY  - 2026
DA  - 2026/10/22
JO  - Quantum
DO  - 10.22331/q-2026-10-22-2245
UR  - https://quantum-journal.org/papers/q-2026-10-22-2245/
AB  - We present a symmetry-enabled direct quantum protocol for computing many-body Green's functions, a central tool for studying strongly correlated quantum systems. Our protocol relies only on native time evolution and straightforward measurements available on current hardware platforms. By exploiting parity symmetry—satisfied by a broad class of Hamiltonians in condensed matter physics and quantum chemistry, including the Fermi–Hubbard and Heisenberg models—we introduce a tailored quench spectroscopy scheme that recovers both the real and imaginary parts of two-point time correlators, from which Green's functions can be reconstructed via efficient classical signal processing. We further develop a tailored symmetric quantum Gibbs sampler that prepares parity-resolved (symmetric and antisymmetric) thermal states, enabling finite-temperature extensions within the same framework. Finally, we show that the same symmetry-based measurement primitive extends naturally to out-of-time-ordered correlators (OTOCs). Our results provide a practical route to estimating symmetry-resolved dynamical correlators on near-term and early fault-tolerant quantum hardware.
SN  - 2521-327X
ER  -