Ph.D Thesis | |

Ph.D Student | Weinstein Yossi |
---|---|

Subject | Algorithmic Cooling of Spins |

Department | Department of Physics |

Supervisors | ASSOCIATE PROF. Tal Mor |

PROF. Ady Mann | |

Full Thesis text |

*Algorithmic Cooling (AC) of spins *applies entropy manipulation
algorithms in open spin-systems in order to cool spins far beyond Shannon’s entropy bound. AC of nuclear spins was demonstrated experimentally, and may
contribute to nuclear magnetic resonance (NMR) spectroscopy. Several cooling
algorithms were suggested in recent years, including practicable algorithmic
cooling (PAC). *Practicable *algorithms have simple implementations, yet
their level of cooling is far from optimal. We introduce *Exhaustive* algorithms,
which cool much better, and some even reach (asymptotically) an optimal level
of cooling, but they are not practicable.

We also introduce *semi-optimal *practicable
AC (SOPAC), wherein few cycles (typically 2-6) are performed at each recursive
level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain
cooling levels significantly better than PAC, and are much more efficient than
the exhaustive algorithms. The new algorithms are shown to bridge the gap
between PAC and exhaustive AC. In addition, we calculated the number of spins
required by SOPAC in order to purify qubits for quantum computation. As few as
12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60%
polarized) from initial polarizations of 1% and 10%, respectively. In the
latter case, about five more spins are sufficient to produce a highly pure spin
(99.99% polarized), which could be relevant for fault-tolerant quantum
computing.

For the sake of future experimental AC and quantum computing (QC) research, we supply tools to bridge the gap between the languages of theoretical QC and AC, and experimental NMR.