14 research outputs found
The power of quantum systems on a line
We study the computational strength of quantum particles (each of finite
dimensionality) arranged on a line. First, we prove that it is possible to
perform universal adiabatic quantum computation using a one-dimensional quantum
system (with 9 states per particle). This might have practical implications for
experimentalists interested in constructing an adiabatic quantum computer.
Building on the same construction, but with some additional technical effort
and 12 states per particle, we show that the problem of approximating the
ground state energy of a system composed of a line of quantum particles is
QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to
the fact that the analogous classical problem, namely, one-dimensional
MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the
QMA-completeness result requires an additional idea beyond the usual techniques
in the area: Not all illegal configurations can be ruled out by local checks,
so instead we rule out such illegal configurations because they would, in the
future, evolve into a state which can be seen locally to be illegal. Our
construction implies (assuming the quantum Church-Turing thesis and that
quantum computers cannot efficiently solve QMA-complete problems) that there
are one-dimensional systems which take an exponential time to relax to their
ground states at any temperature, making them candidates for being
one-dimensional spin glasses.Comment: 21 pages. v2 has numerous corrections and clarifications, and most
importantly a new author, merged from arXiv:0705.4067. v3 is the published
version, with additional clarifications, publisher's version available at
http://www.springerlink.co
Efficient Algorithms for Universal Quantum Simulation
A universal quantum simulator would enable efficient simulation of quantum
dynamics by implementing quantum-simulation algorithms on a quantum computer.
Specifically the quantum simulator would efficiently generate qubit-string
states that closely approximate physical states obtained from a broad class of
dynamical evolutions. I provide an overview of theoretical research into
universal quantum simulators and the strategies for minimizing computational
space and time costs. Applications to simulating many-body quantum simulation
and solving linear equations are discussed
Large expert-curated database for benchmarking document similarity detection in biomedical literature search
Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe
Exponential Separations for One-Way Quantum Communication Complexity, with Applications to Cryptography
We give an exponential separation between one-way quantum and classical communication protocols for two
partial Boolean functions, both of which are variants of the Boolean Hidden Matching Problem of Bar-Yossef et
al. Earlier such an exponential separation was known only for a relational version of the Hidden Matching
Problem. Our proofs use the Fourier coefficients inequality of Kahn, Kalai, and Linial. We give a number
of applications of this separation. In particular, in the bounded-storage model of cryptography we exhibit
a scheme that is secure against adversaries with a certain amount of classical storage,
but insecure against adversaries with a similar (or even much smaller) amount of \emph{quantum}
storage; in the setting of privacy amplification, we show that there are strong extractors that yield a
classically secure key, but are insecure against a quantum adversary