3,994 research outputs found
Kerdock Codes Determine Unitary 2-Designs
The non-linear binary Kerdock codes are known to be Gray images of certain
extended cyclic codes of length over . We show that
exponentiating these -valued codewords by produces stabilizer states, that are quantum states obtained using
only Clifford unitaries. These states are also the common eigenvectors of
commuting Hermitian matrices forming maximal commutative subgroups (MCS) of the
Pauli group. We use this quantum description to simplify the derivation of the
classical weight distribution of Kerdock codes. Next, we organize the
stabilizer states to form mutually unbiased bases and prove that
automorphisms of the Kerdock code permute their corresponding MCS, thereby
forming a subgroup of the Clifford group. When represented as symplectic
matrices, this subgroup is isomorphic to the projective special linear group
PSL(). We show that this automorphism group acts transitively on the Pauli
matrices, which implies that the ensemble is Pauli mixing and hence forms a
unitary -design. The Kerdock design described here was originally discovered
by Cleve et al. (arXiv:1501.04592), but the connection to classical codes is
new which simplifies its description and translation to circuits significantly.
Sampling from the design is straightforward, the translation to circuits uses
only Clifford gates, and the process does not require ancillary qubits.
Finally, we also develop algorithms for optimizing the synthesis of unitary
-designs on encoded qubits, i.e., to construct logical unitary -designs.
Software implementations are available at
https://github.com/nrenga/symplectic-arxiv18a, which we use to provide
empirical gate complexities for up to qubits.Comment: 16 pages double-column, 4 figures, and some circuits. Accepted to
2019 Intl. Symp. Inf. Theory (ISIT), and PDF of the 5-page ISIT version is
included in the arXiv packag
Study of axial strain induced torsion of single wall carbon nanotubes by 2D continuum anharmonic anisotropic elastic model
Recent molecular dynamic simulations have found chiral single wall carbon
nanotubes (SWNTs) twist during stretching, which is similar to the motion of a
screw. Obviously this phenomenon, as a type of curvature-chirality effect, can
not be explained by usual isotropic elastic theory of SWNT. More interestingly,
with larger axial strains (before buckling), the axial strain induced torsion
(a-SIT) shows asymmetric behaviors for axial tensile and compressing strains,
which suggests anharmonic elasticity of SWNTs plays an important role in real
a-SIT responses. In order to study the a-SIT of chiral SWNTs with actual sizes,
and avoid possible deviations of computer simulation results due to the
finite-size effect, we propose a 2D analytical continuum model which can be
used to describe the the SWNTs of arbitrary chiralities, curvatures, and
lengths, with the concerning of anisotropic and anharmonic elasticity of SWNTs.
This elastic energy of present model comes from the continuum limit of lattice
energy based on Second Generation Reactive Empirical Bond Order potential
(REBO-II), a well-established empirical potential for solid carbons. Our model
has no adjustable parameters, except for those presented in REBO-II, and all
the coefficients in the model can be calculated analytically. Using our method,
we obtain a-SIT responses of chiral SWNTs with arbitrary radius, chiralities
and lengthes. Our results are in reasonable agreement with recent molecular
dynamic simulations. [Liang {\it et. al}, Phys. Rev. Lett, , 165501
(2006).] Our approach can also be used to calculate other curvature-chirality
dependent anharmonic mechanic responses of SWNTs.Comment: 14 pages, 2 figure
Experimental detection of quantum coherent evolution through the violation of Leggett-Garg-type inequalities
We discuss the use of inequalities of the Leggett-Garg type (LGtI) to witness
quantum coherence and present the first experimental violation of this type of
inequalities using a light-matter interfaced system. By separately benchmarking
the Markovian character of the evolution and the translational invariance of
the conditional probabilities, the observed violation of a LGtI is attributed
to the quantum coherent character of the process. These results provide a
general method to benchmark `quantumness' when the absence of memory effects
can be independently certified and confirm the persistence of quantum coherent
features within systems of increasing complexity.Comment: published version, including supplementary materia
Quantum computation with un-tunable couplings
Most quantum computer realizations require the ability to apply local fields
and tune the couplings between qubits, in order to realize single bit and two
bit gates which are necessary for universal quantum computation. We present a
scheme to remove the necessity of switching the couplings between qubits for
two bit gates, which are more costly in many cases. Our strategy is to compute
in and out of carefully designed interaction free subspaces analogous to
decoherence free subspaces, which allows us to effectively turn off and turn on
the interactions between the encoded qubits. We give two examples to show how
universal quantum computation is realized in our scheme with local
manipulations to physical qubits only, for both diagonal and off diagonal
interactions.Comment: 5 pages, 2 figure
Revisiting Bohr's principle of complementarity using a quantum device
Bohr's principle of complementarity lies at the central place of quantum
mechanics, according to which the light is chosen to behave as a wave or
particles, depending on some exclusive detecting devices. Later, intermediate
cases are found, but the total information of the wave-like and particle-like
behaviors are limited by some inequalities. One of them is Englert-Greenberger
(EG) duality relation. This relation has been demonstrated by many experiments
with the classical detecting devices. Here by introducing a quantum detecting
device into the experiment, we find the limit of the duality relation is
exceeded due to the interference between the photon's wave and particle
properties. However, our further results show that this experiment still obey a
generalized EG duality relation. The introducing of the quantum device causes
the new phenomenon, provides an generalization of the complementarity
principle, and opens new insights into our understanding of quantum mechanics.Comment: 5 pages, 4 figure
Linear optical quantum computation with imperfect entangled photon-pair sources and inefficient non-photon-number-resolving detectors
We propose a scheme for efficient cluster state quantum computation by using
imperfect polarization-entangled photon-pair sources, linear optical elements
and inefficient non-photon-number-resolving detectors. The efficiency threshold
for loss tolerance in our scheme requires the product of source and detector
efficiencies should be >1/2 - the best known figure. This figure applies to
uncorrelated loss. We further find that the loss threshold is unaffected by
correlated loss in the photon pair source. Our approach sheds new light on
efficient linear optical quantum computation with imperfect experimental
conditions.Comment: 5 pages, 2 figure
State estimation from pair of conjugate qudits
We show that, for parallel input states, an anti-linear map with respect
to a specific basis is essentially a classical operator. We also consider the
information contained in phase-conjugate pairs , and prove
that there is more information about a quantum state encoded in phase-conjugate
pairs than in parallel pairs.Comment: 4 pages, 1 tabl
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