Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
Published: | 2023-12-04, volume 7, page 1195 |
Eprint: | arXiv:2208.04427v2 |
Doi: | https://doi.org/10.22331/q-2023-12-04-1195 |
Citation: | Quantum 7, 1195 (2023). |
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Abstract
The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the $apriori$ knowledge of the environment noise parameters to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates using a "spectator" system, which estimates the noise parameter in real-time, then feed-forwards the outcome to the recovery protocol as a classical side-information. The memory qubits and the spectator system hence comprise the building blocks for a real-time (i.e. drift-adapting) quantum memory. In this article, I consider spectator-based (incomplete knowledge) recovery protocols as a real-time parameter estimation problem (generally with nuisance parameters present), followed by the application of the "best-guess" recovery map to the memory qubits, as informed by the estimation outcome. I present information-theoretic and metrological bounds on the performance of this protocol, quantified by the diamond distance between the "best-guess" recovery and optimal recovery outcomes, thereby identifying the cost of adaptation in real-time quantum memories. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge of the noise could be an advantage, as errors from various cycles can cohere. These results are illustrated for the approximate [4,1] code of the amplitude-damping channel and relations to various fields are discussed.
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Featured image: Performance of noise-adaptive [4,1] amplitude damping code
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Cited by
[1] Samudra Dasgupta, Travis S. Humble, and Arshag Danageozian, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 99 (2023) ISBN:979-8-3503-4323-6.
[2] Samudra Dasgupta and Travis S. Humble, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 223 (2023) ISBN:979-8-3503-4323-6.
[3] Samudra Dasgupta, Arshag Danageozian, and Travis S. Humble, "Adaptive mitigation of time-varying quantum noise", arXiv:2308.14756, (2023).
[4] Samudra Dasgupta and Travis S. Humble, "Reliable Devices Yield Stable Quantum Computations", arXiv:2307.05381, (2023).
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