Quantum EigenGame for excited state calculation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916655247917056 |
|---|---|
| author | Quiroga, David Han, Jason Kyrillidis, Anastasios |
| author_facet | Quiroga, David Han, Jason Kyrillidis, Anastasios |
| contents | Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in decomposing a matrix into a collection of principal components. Classically, PCA is a well-studied problem setting, for which both centralized and distributed approaches have been developed. On the distributed side, one recent approach is that of EigenGame, a game-theoretic approach to finding eigenvectors where each eigenvector reaches a Nash equilibrium either sequentially or in parallel. With this work, we extend the EigenGame algorithm for both a $0^\text{th}$-order approach and for quantum computers, and harness the framework that quantum computing provides in computing excited states. Results show that using the Quantum EigenGame allows us to converge to excited states of a given Hamiltonian without the need of a deflation step. We also develop theory on error accumulation for finite-differences and parameterized approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum EigenGame for excited state calculation Quiroga, David Han, Jason Kyrillidis, Anastasios Quantum Physics Data Structures and Algorithms Machine Learning Optimization and Control Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in decomposing a matrix into a collection of principal components. Classically, PCA is a well-studied problem setting, for which both centralized and distributed approaches have been developed. On the distributed side, one recent approach is that of EigenGame, a game-theoretic approach to finding eigenvectors where each eigenvector reaches a Nash equilibrium either sequentially or in parallel. With this work, we extend the EigenGame algorithm for both a $0^\text{th}$-order approach and for quantum computers, and harness the framework that quantum computing provides in computing excited states. Results show that using the Quantum EigenGame allows us to converge to excited states of a given Hamiltonian without the need of a deflation step. We also develop theory on error accumulation for finite-differences and parameterized approaches. |
| title | Quantum EigenGame for excited state calculation |
| topic | Quantum Physics Data Structures and Algorithms Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2503.13644 |