Preparing and readout of the qubit on the particle in the potential well

Background and Objectives: There are known Rabi oscillations between the basic states of a two-level system, and the preparation of any qubit states is possible using these oscillations. There are several ways to readout qubits. It can be the strong random projective measurement, the weak continuous selective measurement, even the non-demolition readout of the qubit by a measurement of the ancillary qubit. Another qubit readout scheme is proposed in this article. Methods: The non-stationary Schrodinger equation is solved numerically by the finite element method to simulate the preparation and the readout of the qubit. Two levels near the bottom of the one-dimensional rectangle potential well are considered as a qubit. The Rabi oscillations and time-averaging Fourier-type integrals are calculated. Results and Conclusion: It is shown that there is also another way to read out the state of a qubit. After preparing the superposition state by the Rabi oscillations the external field must be turned off so that the prepared state can be measured. The first step of measurement is a random choice of the basic state to which the reduction leads. Then there is an instant projective reduction or continuous selective reduction. The presence of only two levels in a qubit system makes it possible to propose a scheme for effective control over continuous reduction. The measurement scheme is proposed in which continuous reduction to the basis wave function occurs over a period at the Bohr transition frequency and for a multiple of this period.