Semi-optimal Practicable Algorithmic Cooling

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) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; Exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here 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.

13 pages, 5 figures

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• Achievable polarization for Heat-Bath Algorithmic Cooling
• Correlation-Enhanced Algorithmic Cooling
• Heat-Bath Cooling of Spins in Two Amino Acids
• Algorithmic Cooling in Liquid State NMR
• Strong Algorithmic Cooling in Large Star-Topology Quantum Registers
• Dynamic Cooling on Contemporary Quantum Computers
• Few-qubit quantum refrigerator for cooling a multi-qubit system
• Designing refrigerators in higher dimensions using quantum spin models
• Quantum Computing Gates via Optimal Control
• State-independent robust heat-bath algorithmic cooling of nuclear spins
• Expressivity of deterministic quantum computation with one qubit
• Prospects and Limitations of Algorithmic Cooling
• Post-selection-free preparation of high-quality physical qubits
• Algorithmic cooling for resolving state preparation and measurement errors in quantum computing