混合态量子克隆、连续量子克隆及远程量子 CNOT 门

Li-Ping Deng, Haibo Wang, Kaige Wang

We propose a polarization-controlled-NOT (P-CNOT) gate and an orbital-angular-momentum-controlled-NOT (OAM-CNOT) gate for single-photon two-qubit quantum logic. Both of the controlled-NOT (CNOT) gates are simple and deterministic. Moreover the entanglement swap between polarization and orbital angular momentum (OAM) can be realized using the P-CNOT gate and the OAM-CNOT gate.

毕慧聪 BI Huicong, 刘涛 LIU Tao, 张荣香 ZHANG Rongxiang +2 more

勇介 井出, 尭 小松, 紀雄 今野 +2 more

Matthew Amy, Parsiad Azimzadeh, Michele Mosca

Abstract We study the problem of CNOT -optimal quantum circuit synthesis over gate sets consisting of CNOT and Z -basis rotations of arbitrary angles. We show that the circuit-polynomial correspondence relates such circuits to Fourier expansions of pseudo-Boolean functions, and that for certain classes of functions this expansion uniquely determines the minimum CNOT cost of an implementation. As a corollary we prove that CNOT minimization over CNOT and phase gates is at least as hard as synthesizing a CNOT -optimal circuit computing a set of parities of its inputs. We then show that this problem is NP-complete for two restricted cases where all CNOT gates are required to have the same target, and where the circuit inputs are encoded in a larger state space. The latter case has applications to CNOT optimization over more general Clifford+ T circuits. We further present an efficient heuristic algorithm for synthesizing circuits over CNOT and Z -basis rotations with small CNOT cost. Our experiments show a 23% reduction of CNOT gates on average across a suite of Clifford+ T benchmark circuits, with a maximum reduction of 43%.

周英 Zhou Ying, 朱成杰 Zhu Chengjie

Gui-Fang Dang, Heng Fan

Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.