Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories

Arshag Danageozian

Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA

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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.

Noise drift in quantum hardware is an important obstacle for scalable quantum computation and communication, e.g. when building a long-time quantum memory that protects encoded information from decoherence. For better protection of quantum information under time-varying noise, this work proposes the inclusion of spectator qubits that are co-located with their memory counterparts. These qubits monitor the change in the noise parameters in real-time by performing quantum multi-parameter estimation, thereby providing the most up-to-date information on the optimal correction parameters for errors (i.e. decoherence) in the quantum memory. The author derives a fundamental bound on the performance of such a noise-adaptive quantum memory as a function of the physical properties of the spectator qubits used, thereby providing a quantitative formula for selecting better versus worse spectators for a given quantum hardware. The article provides a consistent framework for combining quantum information theory, quantum error correction, and quantum parameter estimation, in the pursuit of quantum memories with longer coherence times.

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Cited by

[1] Samudra Dasgupta, Arshag Danageozian, and Travis S. Humble, "Adaptive mitigation of time-varying quantum noise", arXiv:2308.14756, (2023).

[2] Samudra Dasgupta and Travis S. Humble, "Reliable Devices Yield Stable Quantum Computations", arXiv:2307.05381, (2023).

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