8,629 research outputs found
Compression for quantum population coding
We study the compression of n quantum systems, each prepared in the same
state belonging to a given parametric family of quantum states. For a family of
states with f independent parameters, we devise an asymptotically faithful
protocol that requires a hybrid memory of size (f/2)log(n), including both
quantum and classical bits. Our construction uses a quantum version of local
asymptotic normality and, as an intermediate step, solves the problem of
compressing displaced thermal states of n identically prepared modes. In both
cases, we show that (f/2)log(n) is the minimum amount of memory needed to
achieve asymptotic faithfulness. In addition, we analyze how much of the memory
needs to be quantum. We find that the ratio between quantum and classical bits
can be made arbitrarily small, but cannot reach zero: unless all the quantum
states in the family commute, no protocol using only classical bits can be
faithful, even if it uses an arbitrarily large number of classical bits.Comment: 14 Pages, 4 Figures + Appendi
Numerical Analysis of Boosting Scheme for Scalable NMR Quantum Computation
Among initialization schemes for ensemble quantum computation beginning at
thermal equilibrium, the scheme proposed by Schulman and Vazirani [L. J.
Schulman and U. V. Vazirani, in Proceedings of the 31st ACM Symposium on Theory
of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322-329] is known for
the simple quantum circuit to redistribute the biases (polarizations) of qubits
and small time complexity. However, our numerical simulation shows that the
number of qubits initialized by the scheme is rather smaller than expected from
the von Neumann entropy because of an increase in the sum of the binary
entropies of individual qubits, which indicates a growth in the total classical
correlation. This result--namely, that there is such a significant growth in
the total binary entropy--disagrees with that of their analysis.Comment: 14 pages, 18 figures, RevTeX4, v2,v3: typos corrected, v4: minor
changes in PROGRAM 1, conforming it to the actual programs used in the
simulation, v5: correction of a typographical error in the inequality sign in
PROGRAM 1, v6: this version contains a new section on classical correlations,
v7: correction of a wrong use of terminology, v8: Appendix A has been added,
v9: published in PR
On compression rate of quantum autoencoders: Control design, numerical and experimental realization
Quantum autoencoders which aim at compressing quantum information in a
low-dimensional latent space lie in the heart of automatic data compression in
the field of quantum information. In this paper, we establish an upper bound of
the compression rate for a given quantum autoencoder and present a learning
control approach for training the autoencoder to achieve the maximal
compression rate. The upper bound of the compression rate is theoretically
proven using eigen-decomposition and matrix differentiation, which is
determined by the eigenvalues of the density matrix representation of the input
states. Numerical results on 2-qubit and 3-qubit systems are presented to
demonstrate how to train the quantum autoencoder to achieve the theoretically
maximal compression, and the training performance using different machine
learning algorithms is compared. Experimental results of a quantum autoencoder
using quantum optical systems are illustrated for compressing two 2-qubit
states into two 1-qubit states
Shortcuts to adiabaticity in a time-dependent box
A method is proposed to drive an ultrafast non-adiabatic dynamics of an
ultracold gas trapped in a box potential. The resulting state is free from
spurious excitations associated with the breakdown of adiabaticity, and
preserves the quantum correlations of the initial state up to a scaling factor.
The process relies on the existence of an adiabatic invariant and the inversion
of the dynamical self-similar scaling law dictated by it. Its physical
implementation generally requires the use of an auxiliary expulsive potential
analogous to those used in soliton control. The method is extended to a broad
family of many-body systems. As illustrative examples we consider the ultrafast
expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in
different dimensions, where the method exhibits an excellent robustness against
different regimes of interactions and the features of an experimentally
realizable box potential.Comment: 6 pp, 4 figures, typo in Eq. (6) fixe
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
Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system
Biology has taken strong steps towards becoming a computer science aiming at
reprogramming nature after the realisation that nature herself has reprogrammed
organisms by harnessing the power of natural selection and the digital
prescriptive nature of replicating DNA. Here we further unpack ideas related to
computability, algorithmic information theory and software engineering, in the
context of the extent to which biology can be (re)programmed, and with how we
may go about doing so in a more systematic way with all the tools and concepts
offered by theoretical computer science in a translation exercise from
computing to molecular biology and back. These concepts provide a means to a
hierarchical organization thereby blurring previously clear-cut lines between
concepts like matter and life, or between tumour types that are otherwise taken
as different and may not have however a different cause. This does not diminish
the properties of life or make its components and functions less interesting.
On the contrary, this approach makes for a more encompassing and integrated
view of nature, one that subsumes observer and observed within the same system,
and can generate new perspectives and tools with which to view complex diseases
like cancer, approaching them afresh from a software-engineering viewpoint that
casts evolution in the role of programmer, cells as computing machines, DNA and
genes as instructions and computer programs, viruses as hacking devices, the
immune system as a software debugging tool, and diseases as an
information-theoretic battlefield where all these forces deploy. We show how
information theory and algorithmic programming may explain fundamental
mechanisms of life and death.Comment: 30 pages, 8 figures. Invited chapter contribution to Information and
Causality: From Matter to Life. Sara I. Walker, Paul C.W. Davies and George
Ellis (eds.), Cambridge University Pres
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