Quantum operation and quantum entanglement
Conditions for optimal construction of two-qubit gate
If we can perform arbitrary single-qubit gates and CNOT gate, we can do universal quantum computation. In most cases, single-qubit gates are easy to implement, what we need to concern is the number of CNOT gate needed in implementing other gates. One progress in this direction is that it has been proved every two-qubit gate can be implemented at most by three applications of CNOT. Actually every nontrivial two-qubit gate plus single-qubit gates can do universal quantum computation. Quantum gates are usually generated by evolution of the Hamiltonian for some time. For general Hamiltonian it cannot generate CNOT directly, so we need to consider the gate construction by using the gates that are different from CNOT. We have obtained a necessary condition for two-qubit gate construction.
Nonlocal gate implementation with entanglement
In order to perform quantum computation it needs to have the ability of performing arbitrary single-qubit gates and a non-trivial two-qubit gate. In some cases, it is necessary to utilize entangled states to perform non-trivial two-qubit gates on two separate qubits. It has been proved that one Bell state can be used to implement arbitrary controlled-rotations on two separate qubits. If the used entangled state is not maximally entangled, the known protocols can only succeed with some probability. Though sometimes the protocols will fail, Duan and co-workers showed that effective quantum computation can still be achieved.
Faithful remote state preparation using finite classical bits and a nonmaximally entangled state
The question"What tasks may be accomplished using a given physical resource?"is of fundamental importance in many areas of physics. Remote state preparation (RSP) and quantum teleportation answer partly this question. Both protocols use classical communication and the previously shared entangled state to prepare a quantum state in a remote place. The differences between them are as follows. First, in RSP the sender (Alice) knows the state she wants Bob to prepare while in quantum teleportation Alice need not know the state she wants to send. Second, in RSP, the required resource can be traded off between classical communication cost and entanglement cost while in quantum teleportation, two bits of forward classical communication and one ebit of entanglement per teleported qubit are both necessary and sufficient, and neither resource can be traded off against the other. However, it is different in RSP. We proved that any pure quantum state can be remotely prepared by using finite classical bits and the previously shared nonmaximally entangled state.
Efficient measurement-based quantum computation with cluster states in quantum-bit fixed systems
we present a scheme to generate the 2D cluster net on a system in which the positions of all qubits are fixed, for example, quantum dot , which can realize scalable quantum computation.
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