دسته بندی:

محاسبات کوانتومی - Quantum-Computing

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سال انتشار:

2022

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عنوان انگلیسی مقاله:

Linear Programming Bounds for Approximate Quantum Error Correction Over Arbitrary Quantum Channels

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ترجمه فارسی عنوان مقاله:

مرزهای برنامه ریزی خطی برای تصحیح تقریبی خطای کوانتومی در کانال های کوانتومی دلخواه

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منبع:

ieee - ieee Transactions on Information Theory;2022;68;8;10:1109/TIT:2022:3162264

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نویسنده:

Yingkai Ouyang; Ching-Yi Lai

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چکیده انگلیسی:

While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary quantum channels that describe bespoke noise models. Herein, for any Kraus decomposition of any given quantum channel, we introduce corresponding quantum weight enumerators that naturally generalize the Shor-Laflamme quantum weight enumerators. We establish an indirect linear relationship between these generalized quantum weight enumerators by introducing an auxiliary exact weight enumerator that completely quantifies the quantum code’s projector, and is independent of the underlying noise process. By additionally working within the framework of approximate quantum error correction, we establish a general framework for constructing a linear program that is infeasible whenever approximate quantum error correcting codes with corresponding parameters do not exist. Our linear programming framework allows us to establish the non-existence of certain quantum codes that approximately correct amplitude damping errors, and obtain non-trivial upper bounds on the maximum dimension of a broad family of permutation-invariant quantum codes.
Index Terms: Quantum information science | error correction codes | linear programming.

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قیمت: رایگان

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توضیحات اضافی:

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