QUANTUM INFORMATION SCIENCE
QUANTUM CONTROL
Current Research - Robust control of decoherence in one qubit quantum gates
 Fig. 1: The unitary, adiabatically decohered, and controlled evolution of the Im{r12} element of the density matrix for the initial state i/÷2|0> + 1/÷2|1>. There are three parameters characterizing these plots: the time between control pulses, T (scaled in terms of the Rabi frequency), the decoherence rate, g (dimensionless), and the standard deviation, DI, of the control pulses after adding normally-distributed noise. (a) T=0.5, g=1, D I=0; (b) T=0.5, g=1, DI=0.1; (c) T=5, g=0.1, DI=0; (d) T=5, g=0.1, DI=0.1. (Click on image for larger view ) |
The realization of any quantum computer relies on maintaining quantum coherence in the system, for a period of time spanning at least the duration of the desired computation. Unfortunately, due to coupling to the environment, the evolution within the quantum computer loses its unitary character; in other words, the system decoheres. Several approaches have been proposed to eliminate or mitigate the undesirable effects of decoherence, including open loop (quantum bang-bang) control, decoherence free subspaces (DFS), error-correction codes, and quantum feedback. To date, open loop schemes seem to realize an optimal combination of efficiency and scalability.
We have implemented an open-loop control for a one qubit quantum gate realized as a two level system in contact with a boson bath. The external control is included from the beginning in the Hamiltonian as an independent interaction term. Adiabatic and thermal decoherence arise from various couplings of the system to the outside world. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. By comparing the evolution of the reduced density matrix in the presence of decoherence and (unknown) control with the ideal (unitary) evolution, we determine explicitly the control that cancels out the effect of the decoherence and momentarily restores unitarity. The control scheme advances through a cycle of eight time steps, to handle in turn the real and imaginary parts of the matrix elements of the two-level system. The values of the control pulses stabilize rapidly after the first cycle of eight time steps, as shown in Figure 1, in the case of adiabatic decoherence. For thermal decoherence, similar results are obtained.
Our implementation has several new aspects: (i) decoherence and control are taken to act simultaneously within a realistic model, which allows one to deal with thermal decoherence; (ii) the required control is directly related to and calculated from the decoherence effects, which presents the practical advantage of maintaining the frequency and amplitude of the required controls at manageable levels; (iii) the knowledge of the decoherence function is needed only for a finite period of time since after initial transients, controls will stabilize and the whole cycle will repeat; finally, (iv) the effect of imperfect controls is easily assessed and show the robustness of the scheme.
Research done by: V. Protopopescu, C. d'Helon, and R. Perez; M3AS 9, 305 (1999); Phys. Rev. A, submitted; various conference papers.
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