33 research outputs found
Physical Limits of Heat-Bath Algorithmic Cooling
Simultaneous near-certain preparation of qubits (quantum bits) in their ground states is a key hurdle in quantum computing proposals as varied as liquid-state NMR and ion traps. "Closed-system" cooling mechanisms are of limited applicability due to the need for a continual supply of ancillas for fault tolerance, and to the high initial temperatures of some systems. "Open-system" mechanisms are therefore required. We describe a new, efficient initialization procedure for such open systems. With this procedure, an n-qubit device that is originally maximally mixed, but is in contact with a heat bath of bias epsilon>>2-n, can be almost perfectly initialized. This performance is optimal due to a newly discovered threshold effect: for bias epsilon<<2-n no cooling procedure can, even in principle (running indefinitely without any decoherence), significantly initialize even a single qubit
Paramagnetic Materials and Practical Algorithmic Cooling for NMR Quantum Computing
Algorithmic Cooling is a method that uses novel data compression techniques
and simplecquantum computing devices to improve NMR spectroscopy, and to offer
scalable NMR quantum computers. The algorithm recursively employs two steps. A
reversible entropy compression of the computation quantum-bits (qubits) of the
system and an irreversible heat transfer from the system to the environment
through a set of reset qubits that reach thermal relaxation rapidly.
Is it possible to experimentally demonstrate algorithmic cooling using
existing technology? To allow experimental algorithmic cooling, the
thermalization time of the reset qubits must be much shorter than the
thermalization time of the computation qubits. However such
thermalization-times ratios have yet to be reported.
We investigate here the effect of a paramagnetic salt on the
thermalization-times ratio of computation qubits (carbons) and a reset qubit
(hydrogen). We show that the thermalization-times ratio is improved by
approximately three-fold. Based on this result, an experimental demonstration
of algorithmic cooling by thermalization and magnetic ions is currently
performed by our group and collaborators.Comment: 5 pages, A conference version of this paper appeared in SPIE, volume
5105, pages 185-194 (2003
Physical Limits of Heat-Bath Algorithmic Cooling
Simultaneous near-certain preparation of qubits (quantum bits) in their ground states is a key hurdle in quantum computing proposals as varied as liquid-state NMR and ion traps. âClosed-systemâ cooling mechanisms are of limited applicability due to the need for a continual supply of ancillas for fault tolerance and to the high initial temperatures of some systems. âOpen-systemâ mechanisms are therefore required. We describe a new, efficient initialization procedure for such open systems. With this procedure, an -qubit device that is originally maximally mixed, but is in contact with a heat bath of bias , can be almost perfectly initialized. This performance is optimal due to a newly discovered threshold effect: For bias no cooling procedure can, even in principle (running indefinitely without any decoherence), significantly initialize even a single qubit
Prospects and Limitations of Algorithmic Cooling
Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful
effective cooling approach, that (ideally) cools spins with low polarization
exponentially better than cooling by reversible entropy manipulations alone.
Here, we investigate the limitations and prospects of AC. For non-ideal and
semioptimal AC, we study the impact of finite relaxation times of reset and
computation spins on the achievable effective cooling. We derive, via
simulations, the attainable cooling levels for given ratios of relaxation times
using two semioptimal practicable algorithms. We expect this analysis to be
valuable for the planning of future experiments. For ideal and optimal AC, we
make use of lower bounds on the number of required reset steps, based on
entropy considerations, to present important consequences of using AC as a tool
for improving signal-to-noise ratio in liquid-state magnetic resonance
spectroscopy. We discuss the potential use of AC for noninvasive clinical
diagnosis and drug monitoring, where it may have significantly lower specific
absorption rate (SAR) with respect to currently used methods.Comment: 12 pages, 5 figure
Semi-optimal Practicable Algorithmic Cooling
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.Comment: 13 pages, 5 figure
Experimental Heat-Bath Cooling of Spins
Algorithmic cooling (AC) is a method to purify quantum systems, such as
ensembles of nuclear spins, or cold atoms in an optical lattice. When applied
to spins, AC produces ensembles of highly polarized spins, which enhance the
signal strength in nuclear magnetic resonance (NMR). According to this cooling
approach, spin-half nuclei in a constant magnetic field are considered as bits,
or more precisely, quantum bits, in a known probability distribution.
Algorithmic steps on these bits are then translated into specially designed NMR
pulse sequences using common NMR quantum computation tools. The
cooling of spins is achieved by alternately combining reversible,
entropy-preserving manipulations (borrowed from data compression algorithms)
with , the transfer of entropy from selected spins to the
environment. In theory, applying algorithmic cooling to sufficiently large spin
systems may produce polarizations far beyond the limits due to conservation of
Shannon entropy.
Here, only selective reset steps are performed, hence we prefer to call this
process "heat-bath" cooling, rather than algorithmic cooling. We experimentally
implement here two consecutive steps of selective reset that transfer entropy
from two selected spins to the environment. We performed such cooling
experiments with commercially-available labeled molecules, on standard
liquid-state NMR spectrometers. Our experiments yielded polarizations that
- , so that the entire
spin-system was cooled. This paper was initially submitted in 2005, first to
Science and then to PNAS, and includes additional results from subsequent years
(e.g. for resubmission in 2007). The Postscriptum includes more details.Comment: 20 pages, 8 figures, replaces quant-ph/051115