M.Sc Thesis

M.Sc StudentAtia Yosi
SubjectAlgorithmic Cooling of Spins by Optimal Control
DepartmentDepartment of Computer Science
Supervisor ASSOCIATE PROF. Tal Mor
Full Thesis textFull thesis text - English Version


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 13C- 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).