12,178 research outputs found
Efficiently Realizing Interval Sequences
We consider the problem of realizable interval-sequences. An interval
sequence comprises of integer intervals such that , and is said to be graphic/realizable if there exists a
graph with degree sequence, say, satisfying the condition
, for each . There is a characterisation
(also implying an verifying algorithm) known for realizability of
interval-sequences, which is a generalization of the Erdos-Gallai
characterisation for graphic sequences. However, given any realizable
interval-sequence, there is no known algorithm for computing a corresponding
graphic certificate in time.
In this paper, we provide an time algorithm for computing a
graphic sequence for any realizable interval sequence. In addition, when the
interval sequence is non-realizable, we show how to find a graphic sequence
having minimum deviation with respect to the given interval sequence, in the
same time. Finally, we consider variants of the problem such as computing the
most regular graphic sequence, and computing a minimum extension of a length
non-graphic sequence to a graphic one.Comment: 19 pages, 1 figur
Protecting dissipative quantum state preparation via dynamical decoupling
We show that dissipative quantum state preparation processes can be protected
against qubit dephasing by interlacing the state preparation control with
dynamical decoupling (DD) control consisting of a sequence of short
-pulses. The inhomogeneous broadening can be suppressed to second order of
the pulse interval, and the protection efficiency is nearly independent of the
pulse sequence but determined by the average interval between pulses. The DD
protection is numerically tested and found to be efficient against
inhomogeneous dephasing on two exemplary dissipative state preparation schemes
that use collective pumping to realize many-body singlets and linear cluster
states respectively. Numerical simulation also shows that the state preparation
can be efficiently protected by -pulses with completely random arrival
time. Our results make possible the application of these state preparation
schemes in inhomogeneously broadened systems. DD protection of state
preparation against dynamical noises is also discussed using the example of
Gaussian noise with a semiclasscial description.Comment: 9 pages, 8 figure
Protecting unknown two-qubit entangled states by nesting Uhrig's dynamical decoupling sequences
Future quantum technologies rely heavily on good protection of quantum
entanglement against environment-induced decoherence. A recent study showed
that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in
theory) lock an arbitrary but known two-qubit entangled state to the th
order using a sequence of control pulses [Mukhtar et al., Phys. Rev. A 81,
012331 (2010)]. By nesting three layers of explicitly constructed UDD
sequences, here we first consider the protection of unknown two-qubit states as
superposition of two known basis states, without making assumptions of the
system-environment coupling. It is found that the obtained decoherence
suppression can be highly sensitive to the ordering of the three UDD layers and
can be remarkably effective with the correct ordering. The detailed theoretical
results are useful for general understanding of the nature of controlled
quantum dynamics under nested UDD. As an extension of our three-layer UDD, it
is finally pointed out that a completely unknown two-qubit state can be
protected by nesting four layers of UDD sequences. This work indicates that
when UDD is applicable (e.g., when environment has a sharp frequency cut-off
and when control pulses can be taken as instantaneous pulses), dynamical
decoupling using nested UDD sequences is a powerful approach for entanglement
protection.Comment: 11 pages, 3 figures, published versio
Keeping a Quantum Bit Alive by Optimized -Pulse Sequences
A general strategy to maintain the coherence of a quantum bit is proposed.
The analytical result is derived rigorously including all memory and
back-action effects. It is based on an optimized -pulse sequence for
dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The
optimized sequence is very efficient, in particular for strong couplings to the
environment.Comment: 4 pages, 2 figures; revised version with additional references for
better context, more stringent discussio
Simultaneous Representation of Proper and Unit Interval Graphs
In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary
Quantum error correction of coherent errors by randomization
A general error correction method is presented which is capable of correcting
coherent errors originating from static residual inter-qubit couplings in a
quantum computer. It is based on a randomization of static imperfections in a
many-qubit system by the repeated application of Pauli operators which change
the computational basis. This Pauli-Random-Error-Correction (PAREC)-method
eliminates coherent errors produced by static imperfections and increases
significantly the maximum time over which realistic quantum computations can be
performed reliably. Furthermore, it does not require redundancy so that all
physical qubits involved can be used for logical purposes.Comment: revtex 4 pages, 3 fig
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