Quantum algorithm for one quasi-particle excitations in the thermodynamic limit via cluster-additive block-diagonalization
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911257355878400 |
|---|---|
| author | Sumeet Hörmann, M. Schmidt, K. P. |
| author_facet | Sumeet Hörmann, M. Schmidt, K. P. |
| contents | We propose a quantum algorithm for computing one quasi-particle excitation energies in the thermodynamic limit by combining numerical linked-cluster expansions (NLCEs) and the variational quantum eigensolver (VQE). Our approach uses VQE to block-diagonalize the cluster Hamiltonian through a single-unitary transformation. This unitary is then post-processed using the projective cluster-additive transformation (PCAT) to ensure cluster additivity, a key requirement for NLCE convergence. We benchmark our method on the transverse-field Ising model (TFIM) in one and two dimensions, and with longitudinal field, computing one quasi-particle dispersions in the high-field polarized phase. We compare two cost function classes, trace minimization and variance-based, demonstrating their effectiveness with the Hamiltonian variational ansatz (HVA). For pure TFIM, $\lceil N/2 \rceil$ layers suffice: NLCE+VQE matches exact diagonalization. For TFIM with longitudinal field, where parity symmetry breaks and PCAT becomes essential, both $\lceil N/2 \rceil$ and $N$ layers converge with increasing cluster size, with $N$ layers providing improved accuracy. Our results establish PCAT as a cluster-additive framework that extends variational quantum algorithms to excited-state calculations in the thermodynamic limit via NLCE. While demonstrated with VQE, the PCAT post-processing approach, which requires only low-energy eigenspace information, applies to any quantum eigenstate preparation method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum algorithm for one quasi-particle excitations in the thermodynamic limit via cluster-additive block-diagonalization Sumeet Hörmann, M. Schmidt, K. P. Quantum Physics Strongly Correlated Electrons We propose a quantum algorithm for computing one quasi-particle excitation energies in the thermodynamic limit by combining numerical linked-cluster expansions (NLCEs) and the variational quantum eigensolver (VQE). Our approach uses VQE to block-diagonalize the cluster Hamiltonian through a single-unitary transformation. This unitary is then post-processed using the projective cluster-additive transformation (PCAT) to ensure cluster additivity, a key requirement for NLCE convergence. We benchmark our method on the transverse-field Ising model (TFIM) in one and two dimensions, and with longitudinal field, computing one quasi-particle dispersions in the high-field polarized phase. We compare two cost function classes, trace minimization and variance-based, demonstrating their effectiveness with the Hamiltonian variational ansatz (HVA). For pure TFIM, $\lceil N/2 \rceil$ layers suffice: NLCE+VQE matches exact diagonalization. For TFIM with longitudinal field, where parity symmetry breaks and PCAT becomes essential, both $\lceil N/2 \rceil$ and $N$ layers converge with increasing cluster size, with $N$ layers providing improved accuracy. Our results establish PCAT as a cluster-additive framework that extends variational quantum algorithms to excited-state calculations in the thermodynamic limit via NLCE. While demonstrated with VQE, the PCAT post-processing approach, which requires only low-energy eigenspace information, applies to any quantum eigenstate preparation method. |
| title | Quantum algorithm for one quasi-particle excitations in the thermodynamic limit via cluster-additive block-diagonalization |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.06623 |