دسته بندی:
محاسبات کوانتومی - Quantum-Computing
سال انتشار:
2022
عنوان انگلیسی مقاله:
Limitations on Transversal Gates for Hypergraph Product Codes
ترجمه فارسی عنوان مقاله:
محدودیت در دروازه های عرضی برای کدهای محصول Hypergraph
منبع:
ieee - ieee Transactions on Information Theory;2022;68;3;10:1109/TIT:2021:3131043
نویسنده:
Simon Burton and Dan Browne
چکیده انگلیسی:
In a fault tolerant quantum computer, quantum
codes are expected to serve the conflicting purposes of protecting
quantum information while also allowing that information to
be manipulated by fault-tolerant gates. We introduce a new
technique for placing limitations on such gates, and apply this
technique to a class of quantum codes known as hypergraph
product codes contained within the vertical sector. These codes
are constructed from input which is a pair of classical linear
codes, and generalize the Kitaev surface code which is the
hypergraph product of classical repetition codes. We provide
a necessary condition on these input codes, under which the
resulting hypergraph product code has transversal gates limited
to the Clifford group. We conjecture that this condition is satisfied
by all [n, k, d] Gallagher codes with d ≥ 3 and k ≤ n/2. This
work is a generalization of an argument due to Bravyi and König,
and we also conjecture this is a refinement of the recent notion
of disjointness due to Jochym-O’Connor et al.
Index Terms: Computers and information processing | quantum computing.
قیمت: رایگان
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