5,901 research outputs found
Fault-Tolerant Quantum Dynamical Decoupling
Dynamical decoupling pulse sequences have been used to extend coherence times
in quantum systems ever since the discovery of the spin-echo effect. Here we
introduce a method of recursively concatenated dynamical decoupling pulses,
designed to overcome both decoherence and operational errors. This is important
for coherent control of quantum systems such as quantum computers. For
bounded-strength, non-Markovian environments, such as for the spin-bath that
arises in electron- and nuclear-spin based solid-state quantum computer
proposals, we show that it is strictly advantageous to use concatenated, as
opposed to standard periodic dynamical decoupling pulse sequences. Namely, the
concatenated scheme is both fault-tolerant and super-polynomially more
efficient, at equal cost. We derive a condition on the pulse noise level below
which concatenated is guaranteed to reduce decoherence.Comment: 5 pages, 4 color eps figures. v3: Minor changes. To appear in Phys.
Rev. Let
Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays
The task of decoupling, i.e., removing unwanted interactions in a system
Hamiltonian and/or couplings with an environment (decoherence), plays an
important role in controlling quantum systems. There are many efficient
decoupling schemes based on combinatorial concepts like orthogonal arrays,
difference schemes and Hadamard matrices. So far these (combinatorial)
decoupling schemes have relied on the ability to effect sequences of
instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To
overcome the shortcomings of bang-bang control Viola and Knill proposed a
method called Eulerian decoupling that allows the use of bounded-strength
controls for decoupling. However, their method was not directly designed to
take advantage of the composite structure of multipartite quantum systems. In
this paper we define a combinatorial structure called an Eulerian orthogonal
array. It merges the desirable properties of orthogonal arrays and Eulerian
cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show
that this structure gives rise to decoupling schemes with bounded-strength
control Hamiltonians that can be applied to composite quantum systems with few
body Hamiltonians and special couplings with the environment. Furthermore, we
show how to construct Eulerian orthogonal arrays having good parameters in
order to obtain efficient decoupling schemes.Comment: 8 pages, revte
Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
We demonstrate the advantages of randomization in coherent quantum dynamical
control. For systems which are either time-varying or require decoupling cycles
involving a large number of operations, we find that simple randomized
protocols offer superior convergence and stability as compared to deterministic
counterparts. In addition, we show how randomization always allows to
outperform purely deterministic schemes at long times, including combinatorial
and concatenated methods. General criteria for optimally interpolating between
deterministic and stochastic design are proposed and illustrated in explicit
decoupling scenarios relevant to quantum information storage.Comment: 4 pages, 3 figures, replaced with final versio
Introduction to Quantum Error Correction
In this introduction we motivate and explain the ``decoding'' and
``subsystems'' view of quantum error correction. We explain how quantum noise
in QIP can be described and classified, and summarize the requirements that
need to be satisfied for fault tolerance. Considering the capabilities of
currently available quantum technology, the requirements appear daunting. But
the idea of ``subsystems'' shows that these requirements can be met in many
different, and often unexpected ways.Comment: 44 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/ecprhtm
Dynamical Decoupling Using Slow Pulses: Efficient Suppression of 1/f Noise
The application of dynamical decoupling pulses to a single qubit interacting
with a linear harmonic oscillator bath with spectral density is studied,
and compared to the Ohmic case. Decoupling pulses that are slower than the
fastest bath time-scale are shown to drastically reduce the decoherence rate in
the case. Contrary to conclusions drawn from previous studies, this shows
that dynamical decoupling pulses do not always have to be ultra-fast. Our
results explain a recent experiment in which dephasing due to charge
noise affecting a charge qubit in a small superconducting electrode was
successfully suppressed using spin-echo-type gate-voltage pulses.Comment: 5 pages, 3 figures. v2: Many changes and update
Advances in decoherence control
I address the current status of dynamical decoupling techniques in terms of
required control resources and feasibility. Based on recent advances in both
improving the theoretical design and assessing the control performance for
specific noise models, I argue that significant progress may still be possible
on the road of implementing decoupling under realistic constraints.Comment: 14 pages, 3 encapsulated eps figures. To appear in Journal of Modern
Optics, Special Proceedings Volume of the XXXIV Winter Colloquium on the
Physics of Quantum Electronics, Snowbird, Jan 200
Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos
We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev.
A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum
chaotic behavior. Since generalized entanglement depends directly on a choice
of preferred observables, exploring how generalized entanglement increases
under dynamical evolution is possible without invoking an auxiliary coupled
system or decomposing the system into arbitrary subsystems. We find that, in
the chaotic regime, the long-time saturation value of generalized entanglement
agrees with random matrix theory predictions. For our system, we provide
physical intuition into generalized entanglement within a single system by
invoking the notion of extent of a state. The latter, in turn, is related to
other signatures of quantum chaos.Comment: clarified and expanded version accepted by Europhys. Let
Single-bit Feedback and Quantum Dynamical Decoupling
Synthesizing an effective identity evolution in a target system subjected to
unwanted unitary or non-unitary dynamics is a fundamental task for both quantum
control and quantum information processing applications. Here, we investigate
how single-bit, discrete-time feedback capabilities may be exploited to enact
or to enhance quantum procedures for effectively suppressing unwanted dynamics
in a finite-dimensional open quantum system. An explicit characterization of
the joint unitary propagators correctable by a single-bit feedback strategy for
arbitrary evolution time is obtained. For a two-dimensional target system, we
show how by appropriately combining quantum feedback with dynamical decoupling
methods, concatenated feedback-decoupling schemes may be built, which can
operate under relaxed control assumptions and can outperform purely closed-loop
and open-loop protocols.Comment: 12 pages, 2 figure
Chiral Partition Functions of Quantum Hall Droplets
Chiral partition functions of conformal field theory describe the edge
excitations of isolated Hall droplets. They are characterized by an index
specifying the quasiparticle sector and transform among themselves by a
finite-dimensional representation of the modular group. The partition functions
are derived and used to describe electron transitions leading to Coulomb
blockade conductance peaks. We find the peak patterns for Abelian hierarchical
states and non-Abelian Read-Rezayi states, and compare them. Experimental
observation of these features can check the qualitative properties of the
conformal field theory description, such as the decomposition of the Hilbert
space into sectors, involving charged and neutral parts, and the fusion rules.Comment: 37 pages, 8 figure
Experimental Implementation of a Concatenated Quantum Error-Correcting Code
Concatenated coding provides a general strategy to achieve the desired level
of noise protection in quantum information storage and transmission. We report
the implementation of a concatenated quantum error-correcting code able to
correct against phase errors with a strong correlated component. The experiment
was performed using liquid-state nuclear magnetic resonance techniques on a
four spin subsystem of labeled crotonic acid. Our results show that
concatenation between active and passive quantum error-correcting codes offers
a practical tool to handle realistic noise contributed by both independent and
correlated errors.Comment: 4 pages, 2 encapsulated eps figures. REVTeX4 styl
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