aiqbench analysis
This research bridges theoretical quantum error correction with experimental physics by demonstrating that Rains' quantum shadow enumerators can be directly measured via Bell sampling on trapped-ion hardware. By establishing rigorous sample complexity bounds and robustness guarantees against experimental imperfections, the work provides a practical framework for characterizing the entanglement structure of quantum codes. This cross-fertilization between entanglement theory and error correction offers a tangible method for validating code performance without relying solely on theoretical simulations.
Experimental measurement and a physical interpretation of quantum shadow enumerators
arXiv:2408.16914v2 Announce Type: replace Abstract: Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.
Authors:Daniel Miller, Kyano Levi, Lukas Postler, Alex Steiner, Lennart Bittel, Gregory A. L. White, Yifan Tang, Eric J. Kuehnke, Antonio A. Mele, Sumeet Khatri, Lorenzo Leone, Jose Carrasco, Christian D. Marciniak, Ivan Pogorelov, Milena Guevara-Bertsch, Robert Freund, Rainer Blatt, Philipp Schindler, Thomas Monz, Martin Ringbauer, Jens Eisert
Abstract:Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.
arXiv:2408.16914 [quant-ph]
(or arXiv:2408.16914v2 [quant-ph] for this version)
Full text under the publisher's open licence · 263 words
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