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Circuit Complexity through phase transitions: consequences in quantum state preparation
by Sebastián Roca-Jerat, Teresa Sancho-Lorente, Juan Román-Roche, David Zueco
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Submission summary
| Authors (as registered SciPost users): | Sebastián Roca-Jerat · Juan Román-Roche · David Zueco |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202307_00035v1 (pdf) |
| Date submitted: | 2023-07-28 12:56 |
| Submitted by: | Roca-Jerat, Sebastián |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.
Author comments upon resubmission
We thank the referees for their time and dedication in reviewing our work and providing comments and suggestions for improvement. We agree with all the requested changes proposed by both referees and have updated our work accordingly.
Regarding the first referee, the typos and inconsistencies have been corrected, as well as the consideration and integration in the text of the suggested reference.
On the second referee’s report, we have added theoretical and numerical results and their corresponding discussions (including a new appendix and updated figures), addressing the lack of quantitative statements in section IV. In addition, comments and discussions have been added in sections I A 3 and II A/B, providing clarity according to the referee’s suggestions.
Detailed responses to each referee report are provided separately via the “Reply to the above Report” functionality on the website.
An overview of all the changes in the updated manuscript is provided below.
List of changes
Minor changes in abstract, introduction and discussion commenting new results
Text rewritten to improve clarity in section IA3
Text added in section IB commenting on new quantitative results on Nielsen complexity
Minor changes in the text of sections IIA and IIB
Minor changes in figures 1 and 2: added ticks on the axes of panels 1c, 1f, 2c, 2d.
Minor changes in figures 3,5,6,7,10,11,12: labels updated for consistency with the main text
Major changes in section IV: Theoretical and numerical results added regarding the quantitative aspects of Nielsen complexity. In-depth exploration of the complexity's different scalings with system parameters, updating the figures presented in the section.
Appendix added. Appendix C included to support the discussion in section IVA: dependence of Nielsen complexity on the energy gap in the adiabatic preparation.
Anonymous on 2023-08-30 [id 3938]
A comment on the references. The authors mentioned Krylov complexity but did not cite the main paper arXiv: 1812.08657. Instead they cited Ref. [71-72] which are erroneous.
Author: David Zueco on 2023-10-04 [id 4026]
(in reply to Anonymous Comment on 2023-08-30 [id 3938])We appreciate your comment. You are right, we missed the reference you mentioned, and we will add it in the final version of the paper. As you can see, we have addressed the referees' comments satisfactorily, but we have not heard from the editorial board yet. When this happens, we will update the paper with the suggested reference.
Anonymous on 2023-08-04 [id 3875]
The authors improved the manuscript according to the requested changes. I believe the manuscript is ready for publication.
Author: David Zueco on 2023-10-04 [id 4025]
(in reply to Anonymous Comment on 2023-08-04 [id 3875])We appreciate your comment. We also believe that we have addressed the referees' comments and are waiting for news from the editorial board.