Quantum EigenGame for excited state calculation

David A. Quiroga, Jason Han, Anastasios Kyrillidis
Conference on Parsimony and Learning, PMLR 280:837-864, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v280-quiroga25a, title = {Quantum EigenGame for excited state calculation}, author = {Quiroga, David A. and Han, Jason and Kyrillidis, Anastasios}, booktitle = {Conference on Parsimony and Learning}, pages = {837--864}, year = {2025}, editor = {Chen, Beidi and Liu, Shijia and Pilanci, Mert and Su, Weijie and Sulam, Jeremias and Wang, Yuxiang and Zhu, Zhihui}, volume = {280}, series = {Proceedings of Machine Learning Research}, month = {24--27 Mar}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v280/main/assets/quiroga25a/quiroga25a.pdf}, url = {https://proceedings.mlr.press/v280/quiroga25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Quantum EigenGame for excited state calculation %A David A. Quiroga %A Jason Han %A Anastasios Kyrillidis %B Conference on Parsimony and Learning %C Proceedings of Machine Learning Research %D 2025 %E Beidi Chen %E Shijia Liu %E Mert Pilanci %E Weijie Su %E Jeremias Sulam %E Yuxiang Wang %E Zhihui Zhu %F pmlr-v280-quiroga25a %I PMLR %P 837--864 %U https://proceedings.mlr.press/v280/quiroga25a.html %V 280 %X 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.
APA
Quiroga, D.A., Han, J. & Kyrillidis, A.. (2025). Quantum EigenGame for excited state calculation. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 280:837-864 Available from https://proceedings.mlr.press/v280/quiroga25a.html.

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