دسته بندی:
محاسبات کوانتومی - Quantum-Computing
سال انتشار:
2022
عنوان انگلیسی مقاله:
Learning Quantum Circuits of Some T Gates
ترجمه فارسی عنوان مقاله:
آموزش مدارهای کوانتومی برخی از T Gates
منبع:
ieee - ieee Transactions on Information Theory;2022;68;6;10:1109/TIT:2022:3151760
نویسنده:
Ching-Yi Lai; Hao-Chung Cheng
چکیده انگلیسی:
In this paper, we study the problem of learning
an unknown quantum circuit of a certain structure. If the
unknown target is an n-qubit Clifford circuit, we devise an
efficient algorithm to reconstruct its circuit representation by
using O(n2) queries to it. For decades, it has been unknown how
to handle circuits beyond the Clifford group since the stabilizer
formalism cannot be applied in this case. Herein, we study
quantum circuits of T -depth one on the computational basis.
We show that the output state of a T -depth one circuit can
be represented by a stabilizer pseudomixture with a specific
algebraic structure. Using Pauli and Bell measurements on copies
of the output states, we can generate a hypothesis circuit that is
equivalent to the unknown target circuit on computational basis
states as input. If the number of T gates of the target is of
the order O(log n), our algorithm requires O(n2) queries to it
and produces its equivalent circuit representation on the computational basis in time O(n3). Using further additional O(43n)
classical computations, we can derive an exact description of the
target for arbitrary input states. Our results greatly extend the
previously known facts that stabilizer states can be efficiently
identified based on the stabilizer formalism.
Index Terms: Stabilizer formalism | Clifford circuits | T -depth | stabilizer pseudomixture.
قیمت: رایگان
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