479 research outputs found
Algorithmic Cooling and Scalable NMR Quantum Computers
We present here algorithmic cooling (via polarization-heat-bath)- a powerful
method for obtaining a large number of highly polarized spins in liquid
nuclear-spin systems at finite temperature. Given that spin-half states
represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the
Shannon's bound on data compression, by employing a set of rapidly
thermal-relaxing bits. Such auxiliary bits could be implemented using spins
that rapidly get into thermal equilibrium with the environment, e.g., electron
spins.
Cooling spins to a very low temperature without cooling the environment could
lead to a breakthrough in nuclear magnetic resonance experiments, and our
``spin-refrigerating'' method suggests that this is possible.
The scaling of NMR ensemble computers is probably the main obstacle to
building useful quantum computing devices, and our spin-refrigerating method
suggests that this problem can be resolved.Comment: 21 pages, 3 figure
Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization
An efficient technique to generate ensembles of spins that are highly
polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic
Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state
polarization biases that increase inversely with temperature, spins exhibiting
high polarization biases are considered cool, even when their environment is
warm. Existing spin-cooling techniques are highly limited in their efficiency
and usefulness. Algorithmic cooling is a promising new spin-cooling approach
that employs data compression methods in open systems. It reduces the entropy
of spins on long molecules to a point far beyond Shannon's bound on reversible
entropy manipulations (an information-theoretic version of the 2nd Law of
Thermodynamics), thus increasing their polarization. Here we present an
efficient and experimentally feasible algorithmic cooling technique that cools
spins to very low temperatures even on short molecules. This practicable
algorithmic cooling could lead to breakthroughs in high-sensitivity NMR
spectroscopy in the near future, and to the development of scalable NMR quantum
computers in the far future. Moreover, while the cooling algorithm itself is
classical, it uses quantum gates in its implementation, thus representing the
first short-term application of quantum computing devices.Comment: 24 pages (with annexes), 3 figures (PS). This version contains no
major content changes: fixed bibliography & figures, modified
acknowledgement
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
Algorithms on ensemble quantum computers.
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and Ï(z)(ÂŒ) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement
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
Demon-like Algorithmic Quantum Cooling and its Realization with Quantum Optics
The simulation of low-temperature properties of many-body systems remains one
of the major challenges in theoretical and experimental quantum information
science. We present, and demonstrate experimentally, a universal cooling method
which is applicable to any physical system that can be simulated by a quantum
computer. This method allows us to distill and eliminate hot components of
quantum states, i.e., a quantum Maxwell's demon. The experimental
implementation is realized with a quantum-optical network, and the results are
in full agreement with theoretical predictions (with fidelity higher than
0.978). These results open a new path for simulating low-temperature properties
of physical and chemical systems that are intractable with classical methods.Comment: 7 pages, 5 figures, plus supplementarity material
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
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