טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentYossi Weinstein
SubjectAlgorithmic Cooling of Spins
DepartmentDepartment of Physics
Supervisors Professor Mor Tal
Full Professor Mann Ady
Full Thesis textFull thesis text - English Version


Abstract

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.