6 research outputs found
Programming Quantum Computers Using Design Automation
Recent developments in quantum hardware indicate that systems featuring more
than 50 physical qubits are within reach. At this scale, classical simulation
will no longer be feasible and there is a possibility that such quantum devices
may outperform even classical supercomputers at certain tasks. With the rapid
growth of qubit numbers and coherence times comes the increasingly difficult
challenge of quantum program compilation. This entails the translation of a
high-level description of a quantum algorithm to hardware-specific low-level
operations which can be carried out by the quantum device. Some parts of the
calculation may still be performed manually due to the lack of efficient
methods. This, in turn, may lead to a design gap, which will prevent the
programming of a quantum computer. In this paper, we discuss the challenges in
fully-automatic quantum compilation. We motivate directions for future research
to tackle these challenges. Yet, with the algorithms and approaches that exist
today, we demonstrate how to automatically perform the quantum programming flow
from algorithm to a physical quantum computer for a simple algorithmic
benchmark, namely the hidden shift problem. We present and use two tool flows
which invoke RevKit. One which is based on ProjectQ and which targets the IBM
Quantum Experience or a local simulator, and one which is based on Microsoft's
quantum programming language Q.Comment: 10 pages, 10 figures. To appear in: Proceedings of Design, Automation
and Test in Europe (DATE 2018
Scalar Field Theories with Polynomial Shift Symmetries
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz
type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG)
modes associated with spontaneous symmetry breaking. Such systems allow for an
extension of the constant shift symmetry to a shift by a polynomial of degree
in spatial coordinates. These "polynomial shift symmetries" in turn protect
the technical naturalness of modes with a higher-order dispersion relation, and
lead to a refinement of the proposed classification of infrared Gaussian fixed
points available to describe NG modes in nonrelativistic theories. Generic
interactions in such theories break the polynomial shift symmetry explicitly to
the constant shift. It is thus natural to ask: Given a Gaussian fixed point
with polynomial shift symmetry of degree , what are the lowest-dimension
operators that preserve this symmetry, and deform the theory into a
self-interacting scalar field theory with the shift symmetry of degree ? To
answer this (essentially cohomological) question, we develop a new
graph-theoretical technique, and use it to prove several classification
theorems. First, in the special case of (essentially equivalent to
Galileons), we reproduce the known Galileon -point invariants, and find
their novel interpretation in terms of graph theory, as an equal-weight sum
over all labeled trees with vertices. Then we extend the classification to
and find a whole host of new invariants, including those that represent
the most relevant (or least irrelevant) deformations of the corresponding
Gaussian fixed points, and we study their uniqueness.Comment: 70 pages. v2: minor clarifications, typos corrected, a reference
adde
Time series causality analysis and EEG data analysis on music improvisation
This thesis describes a PhD project on time series causality analysis and applications. The project is motivated by two EEG measurements of music improvisation experiments, where we aim to use causality measures to construct neural networks to identify the neural differences
between improvisation and non-improvisation. The research is based on mathematical backgrounds of time series analysis, information theory and network theory. We first studied a series of popular causality measures, namely, the Granger causality, partial directed coherence (PDC) and directed transfer function (DTF), transfer entropy (TE), conditional mutual information from mixed embedding (MIME) and partial MIME (PMIME), from which we proposed our new measures: the direct transfer entropy (DTE) and the wavelet-based extensions of MIME and PMIME. The new measures improved the properties and applications of their father measures, which were verified by simulations and examples. By comparing the measures we studied, MIME was found to be the most useful causality measure for our EEG analysis. Thus, we used MIME to construct both the intra-brain and cross-brain neural networks for musicians and listeners during the music performances. Neural differences were identified in terms of direction and distribution of
neural information flows and activity of the large brain regions. Furthermore, we applied MIME on other EEG and financial data applications, where reasonable causality results were obtained.Open Acces