M.Sc Thesis | |

M.Sc Student | Atia Yosi |
---|---|

Subject | Algorithmic Cooling of Spins by Optimal Control |

Department | Department of Computer Science |

Supervisor | ASSOCIATE PROF. Tal Mor |

Full Thesis text |

Nuclear magnetic resonance (NMR) has proven to be a leading implementation of quantum information processors where each molecule in the sample constitutes a register of quantum bits (qubits) realized by spin half nuclei (hereinafter spins). The quantum logic gates are implemented by radio frequency (RF) waves transmitted on an ensemble of indistinguishable molecules, and by using the scalar coupling between the spins. The large number of molecules of the sample generates a detectable signal corresponding to the average state of the spin system.

At room temperature and under a constant and homogeneous magnetic field typical for NMR, the nuclear spins are in a highly mixed state; in terms of information theory, the Shannon entropy of the spin state is close to 1. Using data compression tools, the entropy of the spin system can be manipulated, effectively cooling some spins while heating others. However this closed-system technique is limited by Shannon’s entropy conservation on reversible operations .

Algorithmic cooling (AC) of spins
utilizes opening the system to the heat bath as a method for cooling spins beyond Shannon's bound. AC requires a spin system where some spins , called *reset spins*,
thermalize significantly faster than other spins, called *computation spins*. Polarization compression or polarization exchange is applied to
the spin system, manipulating some of the computation spins' entropy to
the reset spins, which quickly lose most of it to the environment. The process
is similar to a heat engine and can be
repeated until reaching a stable trajectory in the density-matrix space. The
efficiency of AC is limited by the relaxation time ratios between the
computation spins and the reset spins.

In this work, multiple rounds of AC were applied on ^{13}C- trichloroethylene
(TCE), a three-spin system, at the Technion NMR lab, following the
heat-bath cooling experiments conducted on TCE by my collaborators Mor, Elias,
and Weinstein in 2002-2007. We applied the
first AC in liquid state NMR, in continuation of
the pioneering AC experiments
conducted in solid state NMR (2005, 2008) by Laflamme's group. The parameters of the Hamiltonian were measured from the spectrum
and fed to GRAPE, an optimal control algorithm utilized to design efficient and robust RF pulses
required for AC .

Our main results are cooling a single spin by a factor of 4.61 to 65K bypassing the Shannon bound (4.22), and reaching an information content of 28.0 on the three spins far beyond Shannon's bound (18).