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Variational Quantum Gate Optimization at the Pulse Level
by Sean Greenaway, Francesco Petiziol, Hongzheng Zhao, Florian Mintert
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Submission summary
| Authors (as registered SciPost users): | Sean Greenaway |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2211.16322v2 (pdf) |
| Date submitted: | 2023-03-27 13:05 |
| Submitted by: | Greenaway, Sean |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Experimental |
Abstract
We experimentally investigate the viability of a variational quantum gate optimization protocol informed by the underlying physical Hamiltonian of fixed-frequency transmon qubits. The utility of the scheme is demonstrated through the successful experimental optimization of two and three qubit quantum gates tailored on the native cross-resonance interaction. The limits of such a strategy are investigated through the optimization of a gate based on Floquet-engineered three-qubit interactions, however parameter drift is identified as a key limiting factor preventing the implementation of such a scheme which the variational optimization protocol is unable to overcome.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023-6-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2211.16322v2, delivered 2023-06-06, doi: 10.21468/SciPost.Report.7312
Report
Please find here enclosed my review of the manuscript entitled "Variational quantum gate optimization at the pulse level", submitted for publication in SciPost in Physics.
The authors investigate a variational quantum gate optimization protocol. Experimental optimization of two and three qubit gates is performed with the IBM quantum experience. The limits of the strategy are discussed and shown on a specific example.
The description and the understanding of fundamental limits in quantum control is a subject of fundamental interest and a basic prerequisite for applications in quantum computing and more generally in quantum technologies. In a closed-loop framework, the authors are able to optimize gate parameters that maximize the fidelity and are robust against noise effect, unwanted interactions or experimental imperfections. The proposed method and the results are interesting. The results of the paper seem sound and the paper is well-written. I support the publication of this paper. Optimization procedure is a very active area in quantum technologies with many different applications. In order to complete the bibliography of the paper, I suggest the authors to cite at least a recent review paper on the subject (1).
(1)- C. P. Koch et al., "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", EPJ Quantum Technology volume 9, 19 (2022) [DOI: https://doi.org/10.1140/epjqt/s40507-022-00138-x]
Anonymous Report 1 on 2023-5-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2211.16322v2, delivered 2023-05-02, doi: 10.21468/SciPost.Report.7117
Strengths
1) Straightforward application of pulse optimization on a quantum computer
2) Explore the possibility to create 2 and 3 qubit gates without complicated decomposition into small quantum gates.
3) Discuss the limit of the protocol
4) Use interesting figure of merit/cost functions that are adapted to quantum computers constraints.
Weaknesses
1) Poor comparison with the state-of-the-art quantum gates
2) The robustness of the pulses is not discussed
Report
The paper investigates the generation of quantum gates by optimizing the pulse shape directly on a quantum computer, which is ultimately an interesting thing, since we are not limited by the idealized model system, which can deviate more or less from the real experimental setup.
The paper focuses on quite complicated quantum gates, 2-qubit and 3-qubit gates, which are obviously typical systems where the method can reveal its full potential.
A critical point of view is applied, and an example where the optimization procedure fails is detailed, showing that the optimization problem is not trivial, and further work seems necessary to arrive at a general optimization scheme.
The paper globally well written and with a good reading flow. The first part is pedagogical, and the subtleties concerning the choice of cost function are well presented.
However, I think that the analysis of the optimized pulses is quite limited, in the sense that they are only partially compared to the existing pulse sequence. This is particularly true at the end of Sec. IV where the performance gain of performance remains only a hypothesis. Would it be possible to provide a quantitative comparison in this case? Moreover, at the end Sec. III, the direct comparison with a CNOT gate is not very fair since $U_{ZX}(\pi/4)$ is not exactly a CNOT gate.
In addition, the comparison is limited, in all cases, to a study of the fidelity, but the duration of the control fields, and their robustness are also important data. Obviously, the robustness of the optimized pulses are not easily determined, but it may be possible to estimate by simulating the system (like the simulation described in Appendix A) for a wide range of system parameters , and to compute the loss of fidelity with from the initial parameters. Maybe the optimized pulses are in average more robust than the state-of-the-art ones (for instance, the optimized CNOT gates may have a fidelity of >=93% on a larger area than the CNOT gate with a fidelity of 95%). Such a robustness analysis requires quite an important additional work, but I encourage the author to consider the inclusion of this kind of analysis in the paper (following the proposed idea or any other smarter comparison method).
I suspect that improving the elements of comparison with existing control fields would not be necessarily bad for the optimized pulses, in fact, the results may be slightly better than expected.
In addition to these remarks, I have a side question: How complicated are the optimized control field? Are they very different from the state-of-the-art ones? It could be nice to have a graph showing the difference between optimized and non-optimized control fields.
Concerning the validity of the work, I'm not able to reproduce the results in a reasonable amount of time, but the results look good. Sharing parts of the code used for the optimization (e.g., as a supplementary material) could be interesting for the community.
Requested changes
1) Provide a fair and quantitative comparison between state-of-the-art solution(s) for the optimized pulse discussed in Sec. III and IV.
2)Provide an additional element of comparisons for the pulses. The pulse duration seems an important and interesting quantity, and (optionally) the robustness of the pulses.