arXiv subjects
Publications and source records attributed to Ming-Yong Ye.
A simple proof of quantum adiabatic theorem is provided. Quantum adiabatic approximation is divided into two kinds. For Hamiltonian H(t/T), a relation between the size of the error caused by quantum adiabatic approximation and the parameter T is given.
Implementation of controlled-rotations using entanglement is considered. We show that the successful probability is closely related to the entanglement and the rotation angle. The successful probability will increase if we increase the entanglement we use or decrease the controlled-rotation angle and the probability will trend to unit when the entangled state trends to a Bell state or the controlled-rotation angle trends to zero.
We give a sufficient condition for the quantum adiabatic approximation, which is quantitative and can be used to estimate error caused by this approximation. We also discuss when the traditional condition is sufficient.
Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the B gate is the unique gate that can construct a two-qubit universal circuit with only two applications, i.e. this condition is also sufficient in the case of two applications of the elementary two-qubit gate. It is also shown that one half of perfect entanglers can not simulate an arbitrary two-qubit gate with only 3 applications.
In two-qubit gate simulations an entangling gate is used several times together with single qubit gates to simulate another two-qubit gate. We show how a two-qubit gate's simulation power is related to the simulation power of its mirror gate. And we show that an arbitrary two-qubit gate can be simulated by three applications of a super controlled gate together with single qubit gates. We also give the gates set that can be simulated by n applications of a controlled gate in a constructive way. In addition we give some gates which can be used four times to simulate an arbitrary two-qubit gate.