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arXiv:quant-ph/0301006 · Journal of Physics A Mathematical and General

Targeting qubit states using open-loop control

C D Helon, V. Protopopescu, R Perez

Published Jun 11, 2003• 2 citations
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Abstract

We present an open-loop (bang–bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman and Milburn (2001 Phys. Rev. A 64 063810) for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favourably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.

DOI
10.1088/0305-4470/36/25/315

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We present an open-loop (bang–bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman and Milburn (2001 Phys. Rev. A 64 063810) for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favourably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.
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This letter considers target state preparation for Markovian open quantum systems subject to continuous measurement. Conditions on invariant and attractive subspaces are investigated, which ensure the stabilization of the target state/subspace. For a class of open quantum systems with time delay in the feedback loop, a bang-bang-like control law is proposed, and the stability of the feedback control strategy is proved. An example of four-level Markovian open quantum systems is presented to demonstrate the effectiveness of the proposed control strategy.
How to Transfer between Arbitrary nnn-Qubit Quantum States by Coherent Control and Simplest Switchable Noise on a Single Qubit
We explore reachable sets of open nnn-qubit quantum systems, the coherent parts of which are under full unitary control and that have just one qubit whose Markovian noise amplitude can be modulated in time such as to provide an additional degree of incoherent control. In particular, adding bang-bang control of amplitude damping noise (non-unital) allows the dynamic system to act transitively on the entire set of density operators. This means one can transform any initial quantum state into any desired target state. Adding switchable bit-flip noise (unital), on the other hand, suffices to explore all states majorised by the initial state. We have extended our open-loop optimal control algorithm (DYNAMO package) by such degrees of incoherent control so that these unprecedented reachable sets can systematically be exploited in experiments. As illustrated for an ion trap experimental setting, open-loop control with noise switching can accomplish all state transfers one can get by the more complicated measurement-based closed-loop feedback schemes.
We describe two recent techniques, along with related experiments, to control and reduce the noise affecting a photon polarization qubit. The first is based on the open-loop 'bang–bang' method, where suitably tailored pulses are implemented on the system to prevent polarization decoherence. This requires only passive elements when the physical system is a photon and the operation is performed in space rather than in time. The second technique is based on closed-loop 'asymmetric feedback', where some quantities are measured and used for a real-time correction of the system dynamics. This technique necessarily requires active electronics to work.
We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.