# Decoherence control in open quantum systems via classical feedback

## Abstract

In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum systemmore »

- Authors:

- Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130 (United States)

- Publication Date:

- OSTI Identifier:
- 20982269

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032323; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL SYSTEMS; CONTROL THEORY; DECOUPLING; DISTURBANCES; EQUATIONS; EXTRACTION; FEEDBACK; INTERACTIONS; MODIFICATIONS; QUANTUM COMPUTERS; QUANTUM DECOHERENCE; QUANTUM MECHANICS; QUBITS

### Citation Formats

```
Ganesan, Narayan, and Tarn, Tzyh-Jong.
```*Decoherence control in open quantum systems via classical feedback*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032323.

```
Ganesan, Narayan, & Tarn, Tzyh-Jong.
```*Decoherence control in open quantum systems via classical feedback*. United States. doi:10.1103/PHYSREVA.75.032323.

```
Ganesan, Narayan, and Tarn, Tzyh-Jong. Thu .
"Decoherence control in open quantum systems via classical feedback". United States.
doi:10.1103/PHYSREVA.75.032323.
```

```
@article{osti_20982269,
```

title = {Decoherence control in open quantum systems via classical feedback},

author = {Ganesan, Narayan and Tarn, Tzyh-Jong},

abstractNote = {In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations.},

doi = {10.1103/PHYSREVA.75.032323},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}