Qronecker: A Certifiable Kronecker Compression Primitive for Quantum-Chemistry Hamiltonians
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918378024730624 |
|---|---|
| author | Zhang, Yuqi Chen, Sixu Cheng, Feixiong Guan, Qiang |
| author_facet | Zhang, Yuqi Chen, Sixu Cheng, Feixiong Guan, Qiang |
| contents | Processing qubit Hamiltonians derived from electronic-structure problems can become classically prohibitive because many downstream manipulations still rely on dense operator constructions whose cost grows exponentially with qubit number. We introduce Qronecker, a cut-aware low-rank Kronecker decomposition algorithm that turns Hamiltonian compression into a certifiable, resource-aware decision primitive. Operating entirely in Pauli coefficient space, Qronecker avoids forming dense 2^n x 2^n matrices, constructs low-rank Kronecker approximations under a chosen bipartition, and returns both an instance-specific compressibility curve and a state-independent worst-case energy certificate that links rank and cut choices to conservative energy-deviation bounds. Across molecular benchmarks comprising hundreds of systems up to 30 qubits, we find that traceless low-rank structure is common but heterogeneous: many screened systems reach high coefficient-space fidelity at low rank, yielding large savings in classical preprocessing and conditional reductions in downstream circuit-resource proxies, while the certificate remains valid but conservative on the auditable subset. The same analysis shows that fixed global fidelity targets are not generally sufficient for chemistry-level guarantees, motivating adaptive rank and cut selection. These results position Qronecker as a certifiable compression primitive for rank and cut selection in quantum-chemistry Hamiltonian processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Qronecker: A Certifiable Kronecker Compression Primitive for Quantum-Chemistry Hamiltonians Zhang, Yuqi Chen, Sixu Cheng, Feixiong Guan, Qiang Quantum Physics Processing qubit Hamiltonians derived from electronic-structure problems can become classically prohibitive because many downstream manipulations still rely on dense operator constructions whose cost grows exponentially with qubit number. We introduce Qronecker, a cut-aware low-rank Kronecker decomposition algorithm that turns Hamiltonian compression into a certifiable, resource-aware decision primitive. Operating entirely in Pauli coefficient space, Qronecker avoids forming dense 2^n x 2^n matrices, constructs low-rank Kronecker approximations under a chosen bipartition, and returns both an instance-specific compressibility curve and a state-independent worst-case energy certificate that links rank and cut choices to conservative energy-deviation bounds. Across molecular benchmarks comprising hundreds of systems up to 30 qubits, we find that traceless low-rank structure is common but heterogeneous: many screened systems reach high coefficient-space fidelity at low rank, yielding large savings in classical preprocessing and conditional reductions in downstream circuit-resource proxies, while the certificate remains valid but conservative on the auditable subset. The same analysis shows that fixed global fidelity targets are not generally sufficient for chemistry-level guarantees, motivating adaptive rank and cut selection. These results position Qronecker as a certifiable compression primitive for rank and cut selection in quantum-chemistry Hamiltonian processing. |
| title | Qronecker: A Certifiable Kronecker Compression Primitive for Quantum-Chemistry Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.06963 |