27,294 research outputs found
Efficient computation of middle levels Gray codes
For any integer a middle levels Gray code is a cyclic listing of
all bitstrings of length that have either or entries equal to
1 such that any two consecutive bitstrings in the list differ in exactly one
bit. The question whether such a Gray code exists for every has been
the subject of intensive research during the last 30 years, and has been
answered affirmatively only recently [T. M\"utze. Proof of the middle levels
conjecture. Proc. London Math. Soc., 112(4):677--713, 2016]. In this work we
provide the first efficient algorithm to compute a middle levels Gray code. For
a given bitstring, our algorithm computes the next bitstrings in the
Gray code in time , which is
on average per bitstring provided that
A constant-time algorithm for middle levels Gray codes
For any integer a middle levels Gray code is a cyclic listing of
all -element and -element subsets of such that
any two consecutive subsets differ in adding or removing a single element. The
question whether such a Gray code exists for any has been the subject
of intensive research during the last 30 years, and has been answered
affirmatively only recently [T. M\"utze. Proof of the middle levels conjecture.
Proc. London Math. Soc., 112(4):677--713, 2016]. In a follow-up paper [T.
M\"utze and J. Nummenpalo. An efficient algorithm for computing a middle levels
Gray code. To appear in ACM Transactions on Algorithms, 2018] this existence
proof was turned into an algorithm that computes each new set in the Gray code
in time on average. In this work we present an algorithm for
computing a middle levels Gray code in optimal time and space: each new set is
generated in time on average, and the required space is
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
On connectivity-dependent resource requirements for digital quantum simulation of -level particles
A primary objective of quantum computation is to efficiently simulate quantum
physics. Scientifically and technologically important quantum Hamiltonians
include those with spin-, vibrational, photonic, and other bosonic degrees
of freedom, i.e. problems composed of or approximated by -level particles
(qudits). Recently, several methods for encoding these systems into a set of
qubits have been introduced, where each encoding's efficiency was studied in
terms of qubit and gate counts. Here, we build on previous results by including
effects of hardware connectivity. To study the number of SWAP gates required to
Trotterize commonly used quantum operators, we use both analytical arguments
and automatic tools that optimize the schedule in multiple stages. We study the
unary (or one-hot), Gray, standard binary, and block unary encodings, with
three connectivities: linear array, ladder array, and square grid. Among other
trends, we find that while the ladder array leads to substantial efficiencies
over the linear array, the advantage of the square over the ladder array is
less pronounced. These results are applicable in hardware co-design and in
choosing efficient qudit encodings for a given set of near-term quantum
hardware. Additionally, this work may be relevant to the scheduling of other
quantum algorithms for which matrix exponentiation is a subroutine.Comment: Accepted to QCE20 (IEEE Quantum Week). Corrected erroneous circuits
in Figure
Random access quantum information processors
Qubit connectivity is an important property of a quantum processor, with an
ideal processor having random access -- the ability of arbitrary qubit pairs to
interact directly. Here, we implement a random access superconducting quantum
information processor, demonstrating universal operations on a nine-bit quantum
memory, with a single transmon serving as the central processor. The quantum
memory uses the eigenmodes of a linear array of coupled superconducting
resonators. The memory bits are superpositions of vacuum and single-photon
states, controlled by a single superconducting transmon coupled to the edge of
the array. We selectively stimulate single-photon vacuum Rabi oscillations
between the transmon and individual eigenmodes through parametric flux
modulation of the transmon frequency, producing sidebands resonant with the
modes. Utilizing these oscillations for state transfer, we perform a universal
set of single- and two-qubit gates between arbitrary pairs of modes, using only
the charge and flux bias of the transmon. Further, we prepare multimode
entangled Bell and GHZ states of arbitrary modes. The fast and flexible
control, achieved with efficient use of cryogenic resources and control
electronics, in a scalable architecture compatible with state-of-the-art
quantum memories is promising for quantum computation and simulation.Comment: 7 pages, 5 figures, supplementary information ancillary file, 21
page
Generalized Gray Codes for Local Rank Modulation
We consider the local rank-modulation scheme in which a sliding window going
over a sequence of real-valued variables induces a sequence of permutations.
Local rank-modulation is a generalization of the rank-modulation scheme, which
has been recently suggested as a way of storing information in flash memory. We
study Gray codes for the local rank-modulation scheme in order to simulate
conventional multi-level flash cells while retaining the benefits of rank
modulation. Unlike the limited scope of previous works, we consider code
constructions for the entire range of parameters including the code length,
sliding window size, and overlap between adjacent windows. We show our
constructed codes have asymptotically-optimal rate. We also provide efficient
encoding, decoding, and next-state algorithms.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201
Autoencoding the Retrieval Relevance of Medical Images
Content-based image retrieval (CBIR) of medical images is a crucial task that
can contribute to a more reliable diagnosis if applied to big data. Recent
advances in feature extraction and classification have enormously improved CBIR
results for digital images. However, considering the increasing accessibility
of big data in medical imaging, we are still in need of reducing both memory
requirements and computational expenses of image retrieval systems. This work
proposes to exclude the features of image blocks that exhibit a low encoding
error when learned by a autoencoder (). We examine the
histogram of autoendcoding errors of image blocks for each image class to
facilitate the decision which image regions, or roughly what percentage of an
image perhaps, shall be declared relevant for the retrieval task. This leads to
reduction of feature dimensionality and speeds up the retrieval process. To
validate the proposed scheme, we employ local binary patterns (LBP) and support
vector machines (SVM) which are both well-established approaches in CBIR
research community. As well, we use IRMA dataset with 14,410 x-ray images as
test data. The results show that the dimensionality of annotated feature
vectors can be reduced by up to 50% resulting in speedups greater than 27% at
expense of less than 1% decrease in the accuracy of retrieval when validating
the precision and recall of the top 20 hits.Comment: To appear in proceedings of The 5th International Conference on Image
Processing Theory, Tools and Applications (IPTA'15), Nov 10-13, 2015,
Orleans, Franc
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