# Exact solution of qubit decoherence models by a transfer matrix method

## Abstract

We present a method for the solution of the behavior of an ensemble of qubits in a random time-dependent external field. The forward evolution in time is governed by a transfer matrix. The elements of this matrix determine the various decoherence times. The method provides an exact solution in cases where the noise is piecewise constant in time. We show that it applies, for example, to a realistic model of decoherence of electron spins in semiconductors. Results are obtained for the nonperturbative regimes of the models, and we see a transition from weak relaxation to overdamped behavior as a function of noise anisotropy.

- Authors:

- Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706 (United States)

- Publication Date:

- OSTI Identifier:
- 20786882

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.032333; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ALGEBRA; ANISOTROPY; ELECTRONS; EXACT SOLUTIONS; NOISE; QUANTUM COMPUTERS; QUBITS; RANDOMNESS; RELAXATION; SEMICONDUCTOR MATERIALS; SPIN; TIME DEPENDENCE; TRANSFER MATRIX METHOD

### Citation Formats

```
Nghiem, Diu, and Joynt, Robert.
```*Exact solution of qubit decoherence models by a transfer matrix method*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Nghiem, Diu, & Joynt, Robert.
```*Exact solution of qubit decoherence models by a transfer matrix method*. United States. doi:10.1103/PHYSREVA.73.0.

```
Nghiem, Diu, and Joynt, Robert. Wed .
"Exact solution of qubit decoherence models by a transfer matrix method". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786882,
```

title = {Exact solution of qubit decoherence models by a transfer matrix method},

author = {Nghiem, Diu and Joynt, Robert},

abstractNote = {We present a method for the solution of the behavior of an ensemble of qubits in a random time-dependent external field. The forward evolution in time is governed by a transfer matrix. The elements of this matrix determine the various decoherence times. The method provides an exact solution in cases where the noise is piecewise constant in time. We show that it applies, for example, to a realistic model of decoherence of electron spins in semiconductors. Results are obtained for the nonperturbative regimes of the models, and we see a transition from weak relaxation to overdamped behavior as a function of noise anisotropy.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}

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