2,177 research outputs found
On Statistical Query Sampling and NMR Quantum Computing
We introduce a ``Statistical Query Sampling'' model, in which the goal of an
algorithm is to produce an element in a hidden set with
reasonable probability. The algorithm gains information about through
oracle calls (statistical queries), where the algorithm submits a query
function and receives an approximation to . We
show how this model is related to NMR quantum computing, in which only
statistical properties of an ensemble of quantum systems can be measured, and
in particular to the question of whether one can translate standard quantum
algorithms to the NMR setting without putting all of their classical
post-processing into the quantum system. Using Fourier analysis techniques
developed in the related context of {em statistical query learning}, we prove a
number of lower bounds (both information-theoretic and cryptographic) on the
ability of algorithms to produces an , even when the set is fairly
simple. These lower bounds point out a difficulty in efficiently applying NMR
quantum computing to algorithms such as Shor's and Simon's algorithm that
involve significant classical post-processing. We also explicitly relate the
notion of statistical query sampling to that of statistical query learning.
An extended abstract appeared in the 18th Aunnual IEEE Conference of
Computational Complexity (CCC 2003), 2003.
Keywords: statistical query, NMR quantum computing, lower boundComment: 17 pages, no figures. Appeared in 18th Aunnual IEEE Conference of
Computational Complexity (CCC 2003
Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm
We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which
attempts to provide a "scalable" implementation on an expectation-value NMR
quantum computer. We show that this ensemble implementation of the DJ algorithm
is at best as efficient as the classical random algorithm. As soon as any
attempt is made to classify all possible functions with certainty, the
implementation requires an exponentially large number of molecules. The
discrepancies arise out of the interpretation of mixed state density matrices.Comment: Minor changes, reference added, replaced with publised versio
Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
We introduce machine learning models of quantum mechanical observables of
atoms in molecules. Instant out-of-sample predictions for proton and carbon
nuclear chemical shifts, atomic core level excitations, and forces on atoms
reach accuracies on par with density functional theory reference. Locality is
exploited within non-linear regression via local atom-centered coordinate
systems. The approach is validated on a diverse set of 9k small organic
molecules. Linear scaling of computational cost in system size is demonstrated
for saturated polymers with up to sub-mesoscale lengths
Machine Learning, Quantum Mechanics, and Chemical Compound Space
We review recent studies dealing with the generation of machine learning
models of molecular and solid properties. The models are trained and validated
using standard quantum chemistry results obtained for organic molecules and
materials selected from chemical space at random
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Mixed state Pauli channel parameter estimation
The accuracy of any physical scheme used to estimate the parameter describing
the strength of a single qubit Pauli channel can be quantified using standard
techniques from quantum estimation theory. It is known that the optimal
estimation scheme, with m channel invocations, uses initial states for the
systems which are pure and unentangled and provides an uncertainty of
O[1/m^(1/2)]. This protocol is analogous to a classical repetition and
averaging scheme. We consider estimation schemes where the initial states
available are not pure and compare a protocol involving quantum correlated
states to independent state protocols analogous to classical repetition
schemes. We show, that unlike the pure state case, the quantum correlated state
protocol can yield greater estimation accuracy than any independent state
protocol. We show that these gains persist even when the system states are
separable and, in some cases, when quantum discord is absent after channel
invocation. We describe the relevance of these protocols to nuclear magnetic
resonance measurements
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
Trends in template/fragment-free protein structure prediction
Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward
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