  The extension of quantum trajectory theory to incorporate realistic
imperfections in the measurement of solid-state qubits is important for quantum
computation, particularly for the purposes of state preparation and
error-correction as well as for readout of computations. Previously this has
been achieved for low-frequency (dc) weak measurements. In this paper we extend
realistic quantum trajectory theory to include radio frequency (rf) weak
measurements where a low-transparency quantum point contact (QPC), coupled to a
charge qubit, is used to damp a classical oscillator circuit. The resulting
realistic quantum trajectory equation must be solved numerically. We present an
analytical result for the limit of large dissipation within the oscillator
(relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode
of operation is considered. Here the QPC is biased (dc) as well as subjected to
a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be
a low-efficiency charge-qubit detector, that may nevertheless be higher than
the dc-QPC (which is subject to 1/f noise).

Mesoscale and Nanoscale Physics;Quantum Physics