VQE for excited states

VQE for excited states

by Eyuel Elala · View the channel on PSI

Formal & Physical Sciences Computing & Cybersecurity UYComputer scienceUYXNatural computing
🎙 Eyuel Elala 👥 106 📅 February 22, 2024 ⏱ 52 min 👁 190 📄 tutorial 🧭 2026-10-09
Available in: English (current) Français

Keywords

VQEexcited statesvariational quantum deflationsubspace search VQEquantum chemistry

Summary

This seminar by Eyuel Elala at KAIST introduces methods for calculating excited state energies using variational quantum algorithms. It begins with a review of the Variational Quantum Eigensolver (VQE) for ground states, highlighting its suitability for near-term devices. The core of the talk presents two algorithms for excited states: Variational Quantum Deflation (VQD) and Subspace Search VQE. VQD extends VQE by adding an overlap penalty term to the cost function to enforce orthogonality with already-found eigenstates, while Subspace Search VQE finds a unitary that maps a set of orthogonal initial states to the eigenstates of the Hamiltonian in a single optimization. The speaker discusses practical considerations such as choosing the penalty parameter, measuring state overlaps using swap tests or inverse preparation, and the trade-offs in circuit depth and qubit overhead. Additionally, symmetry constraints can be incorporated to target specific excited states by adding penalty terms for operators like spin. Numerical results for the H2 molecule are shown from the referenced papers. The talk concludes with a Q&A session clarifying how the algorithms relate to each other and the difficulty of implementing them on current hardware.

185 words

Critical Evaluation

Value of the Information & Strength of the Argument

The video offers a valuable educational walkthrough of two key quantum algorithms for excited states, explaining their motivation and operational principles. The argumentation is logical and well-structured, clearly contrasting the iterative nature of VQD with the single-optimization approach of Subspace Search. However, the treatment is introductory and lacks mathematical depth, with several derivations only sketched or omitted. The speaker effectively communicates the trade-offs (e.g., hyperparameter tuning in VQD vs. circuit depth and ansatz expressibility in Subspace Search) but does not critically evaluate performance relative to classical methods or other quantum approaches. Overall, the information is useful for a learner seeking an overview, but the scientific argumentation is not exhaustive.

Scientific Rigor, Source Quality, Title Accuracy

The presentation is based on two papers (likely Higgott et al. for VQD and Nakanishi et al. for Subspace Search), though full citations are not provided in the video or description. The speaker does not present original results; instead, he explains published algorithms with illustrative numerical examples. The title matches the content precisely. The scientific rigor is moderate: the speaker avoids overclaiming but does not include detailed error analysis or comparisons. The description contains no links to sources, limiting verification. The lack of explicit references weakens the ability to fact-check, but the content aligns with known literature. The Q&A adds clarifying details, suggesting good grasp of the subject.

232 words

Title / Content Match

The title accurately reflects the content, which focuses on extending VQE to compute excited state energies.

Quality & Reliability

6/10

The presentation offers a clear technical overview of algorithms for excited states in quantum computing, but relies on unpublished claims and lacks detailed citations or peer-reviewed references. The speaker appears knowledgeable, yet the content is not fully rigorous.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Contribution & Novelties

The video predominantly serves as a pedagogical summary of existing algorithms for excited states in VQE, providing a clear comparison between VQD and Subspace Search. Its original contribution lies in the concise explanation of the algorithms and the practical considerations (e.g., overlap measurement techniques, hyperparameter selection) that are often scattered across research papers. The speaker emphasizes the trade-offs and implementation challenges, which is helpful for researchers entering the field. However, no new theoretical results are presented.

Pour aller plus loin :

124 words

Radar Profile

The profile indicates a talk with solid technical depth (niveau_technique=8) and good information quantity (quantite_information=8), but moderate quality and reliability scores (6) suggest that while the content is coherent and based on known algorithms, it lacks rigorous citations and in-depth analysis. The fiabilite_globale at 6 reflects the seminar nature and absence of external verification.

Reliability 6/10