TY - GEN

T1 - Learning quantum circuits of T -depth one

AU - Lai, Ching Yi

AU - Cheng, Hao Chung

N1 - Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - 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 algorithm to reconstruct its circuit representation by using O(n2) queries to it. It is unknown for decades how to handle circuits beyond the Clifford group for which the stabilizer formalism cannot be applied. Herein, we study quantum circuits of T -depth one on the computational basis. We show that their output states can be represented by a certain stabilizer pseudomixture. By analyzing the algebraic structure of the stabilizer pseudomixture, we can generate a hypothesis circuit that is equivalent to the unknown target T -depth one quantum circuit U on computational basis states, using Pauli and Bell measurements. If the number of T gates in U is of the order O(log n), our algorithm requires O(n2) queries to U to produce 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 U for arbitrary input states. Our results greatly extend the previously known facts that stabilizer states can be efficiently identified based on the stabilizer formalism.The full manuscript can be found at [1].

AB - 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 algorithm to reconstruct its circuit representation by using O(n2) queries to it. It is unknown for decades how to handle circuits beyond the Clifford group for which the stabilizer formalism cannot be applied. Herein, we study quantum circuits of T -depth one on the computational basis. We show that their output states can be represented by a certain stabilizer pseudomixture. By analyzing the algebraic structure of the stabilizer pseudomixture, we can generate a hypothesis circuit that is equivalent to the unknown target T -depth one quantum circuit U on computational basis states, using Pauli and Bell measurements. If the number of T gates in U is of the order O(log n), our algorithm requires O(n2) queries to U to produce 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 U for arbitrary input states. Our results greatly extend the previously known facts that stabilizer states can be efficiently identified based on the stabilizer formalism.The full manuscript can be found at [1].

UR - http://www.scopus.com/inward/record.url?scp=85136258469&partnerID=8YFLogxK

U2 - 10.1109/ISIT50566.2022.9834452

DO - 10.1109/ISIT50566.2022.9834452

M3 - Conference contribution

AN - SCOPUS:85136258469

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2213

EP - 2218

BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022

Y2 - 26 June 2022 through 1 July 2022

ER -