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Efficient qudit based scheme for photonic quantum computing
by Márton Karácsony, László Oroszlány, Zoltan Zimboras
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Submission summary
| Authors (as registered SciPost users): | Zoltan Zimboras |
| Submission information | |
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| Preprint Link: | scipost_202304_00012v1 (pdf) |
| Date submitted: | 2023-04-12 22:58 |
| Submitted by: | Zimboras, Zoltan |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context, usually qubit based quantum circuits are considered, however, photonic systems naturally allow also for d-ary, i.e., qudit based, algorithms. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities. We illustrate the benefit of our qudit scheme by applying it to the k-coloring problem.
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Report
In this paper the authors present a high-dimensional generalisation of the KLM scheme for universal quantum computation that rests on passive linear optics and post-processing of a continuously monitored system. They use this scheme to implement non-deterministic many-qudit gates, numerically optimizing the parameters of the unitary implementing the gate to obtain the maximal success rate. The authors then move to discuss cluster states in high-dimensional qudits and their application in solving the k-coloring problem.
The work is well written, clear and pedagogical enough to introduce a reader from a related field to the discussion at hand. The presented results increments on ideas and techniques well known in the field of photonic quantum computing by generalising them to higher dimensions. The work advances research in the field and for this reason I do recommend the paper be accepted for publication in SciPost Physics.
Requested changes
1 - A main motivation for realising cluster states seems to be that they require less optical modes and less entangling states than qubit cluster states with analogous computational capabilities. Although it is clear how this can be advantageous, it seems it could come at the expense of experimental realisability. The authors may want to cite the relevant experimental literature comparing the feasibility of the two.
2 - In the beginning of Section 2.2 the authors present the multi-rail qudit encoding as the simplest way to encode a qudit in an optical system. I would suggest including references supporting this statement and a brief discussion stating the disadvantages of the alternatives.
3 - In the optimisation protocol the authors dynamically modify the optimal point by modulating the different parameters of the cost function. I wonder if they could explain in detail the reasoning behind this choice and what made them prefer the trust-region method to all other alternatives that could be implemented in a more direct manner. Moreover, is the optimum found by the authors guaranteed to be the global optimum?
4 - The optimisation performed by the authors is justified in light of the acceptance probability of the CZ gate scaling ad 1/16^{d-1} which it unusable for practical applications. The authors then proceed to provide their alternative scheme but do not provide a lower bound above which the gate could be considered “feasable” or “practically useful”. This would help benchmark the actual impact provided by the optimisation procedure.
5 - From Table I, where the authors report the naive and optimised acceptance probabilities for the two-qutrit gates, it is clear that there is an advantage provided by the optimisation procedure. The authors should however show how this advantage scales with d, to make sure it is not only a different prerefactor in and analogous unfavourable scaling.