In this paper, we consider the control of two qubit systems in the presence of a weak measurement. In particular
we consider how Hamiltonian feedback can be applied to two qubit systems, both in the case where only one
qubit is measured, and in the case where a joint measurement is made of both qubits. We consider how the rate
of entanglement can be increased by using a joint measurement and feedback, and also how information can be
gathered about one qubit by measuring the other.
In this paper we consider feedback control algorithms for the deterministic purification of a bipartite state
consisting of two qubits, when the observer has access to only one of the qubits. We show that Hamiltonian
feedback control can be used to produce deterministic evolution of the purity of either qubit individually, or both
together.
This paper discusses the use of continuous weak measurement and quantum feedback for the rapid purification
of the quantum state of a model solid state qubit: a superconducting Cooper pair box. The feedback algorithm
uses Jacobs' rapid purification protocol, which starts with a completely mixed state and applies controls to rotate
the qubit Bloch vector onto the plane orthogonal to the measurement axis. This rotation maximises the rate
of increase of the average purity of the state but can require large changes in the control fields to produce the
required rotation. Since solid state qubits have finite controls and feedback channels have limited bandwidth,
such rotations may not be practical. This paper applies Jacobs' protocol to the Cooper pair box with realistic
control fields.
We propose a scheme for electron spin quantum computing based on
electron spin in semiconductors. This scheme shares many similarities
with the existing Kane nuclear spin proposal. We show how quantum
computation may be carried out in this proposal, including single
qubit rotations and CNOT gate. We show how this control can
potentially lead to gate speeds 100-1000 times faster than the
existing nuclear spin proposal, and up to 106 times faster than a typical electron spin dephasing time, T2(e).
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