21 research outputs found
Cellular Automata as a Model of Physical Systems
Cellular Automata (CA), as they are presented in the literature, are abstract
mathematical models of computation. In this pa- per we present an alternate
approach: using the CA as a model or theory of physical systems and devices.
While this approach abstracts away all details of the underlying physical
system, it remains faithful to the fact that there is an underlying physical
reality which it describes. This imposes certain restrictions on the types of
computations a CA can physically carry out, and the resources it needs to do
so. In this paper we explore these and other consequences of our
reformalization.Comment: To appear in the Proceedings of AUTOMATA 200
Models of Quantum Cellular Automata
In this paper we present a systematic view of Quantum Cellular Automata
(QCA), a mathematical formalism of quantum computation. First we give a general
mathematical framework with which to study QCA models. Then we present four
different QCA models, and compare them. One model we discuss is the traditional
QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam.
We discuss also Margolus QCA, also discussed by Schumacher and Werner. We
introduce two new models, Coloured QCA, and Continuous-Time QCA. We also
compare our models with the established models. We give proofs of computational
equivalence for several of these models. We show the strengths of each model,
and provide examples of how our models can be useful to come up with
algorithms, and implement them in real-world physical devices
On Algorithms, Separability and Cellular Automata in Quantum Computing
In Part I of this thesis, we present a new model of quantum cellular automata
(QCA) based on local unitary operations. We will describe a set of desirable
properties for any QCA model, and show that all of these properties are
satisfied by the new model, while previous models of QCA do not. We will also
show that the computation model based on Local Unitary QCA is equivalent to
the Quantum Circuit model of computation, and give a number of applications of
this new model of QCA. We also present a physical model of classical CA, on
which the Local Unitary QCA model is based, and Coloured QCA, which is an
alternative to the Local Unitary QCA model that can be used as the basis for
implementing QCA in actual physical systems.
In Part II, we explore the quantum separability problem, where we are given a
density matrix for a state over two quantum systems, and we are to determine
whether the state is separable with respect to these systems. We also look at
the converse problem of finding an entanglement witness, which is an
observable operator which can give a verification that a particular quantum
state is indeed entangled. Although the combined problem is known to be
NP-hard in general, it reduces to a convex optimization problem, and by
exploiting specific properties of the set of separable states, we introduce a
classical algorithm for solving this problem based on an Interior Point
Algorithm introduced by Atkinson and Vaidya in 1995.
In Part III, we explore the use of a low-depth AQFT (approximate quantum
Fourier transform) in quantum phase estimation. It has been shown previously
that the logarithmic-depth AQFT is as effective as the full QFT for the
purposes of phase estimation. However, with sub-logarithmic depth, the phase
estimation algorithm no longer works directly. In this case, results of the
phase estimation algorithm need classical post-processing in order to retrieve
the desired phase information. A generic technique such as the method of
maximum likelihood can be used in order to recover the original phase.
Unfortunately, working with the likelihood function analytically is
intractable for the phase estimation algorithm. We develop some computational
techniques to handle likelihood functions that occur in phase estimation
algorithms. These computational techniques may potentially aid in the analysis
of certain likelihood functions
Local Unitary Quantum Cellular Automata
In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review
BERT for Long Documents: A Case Study of Automated ICD Coding
Transformer models have achieved great success across many NLP problems.
However, previous studies in automated ICD coding concluded that these models
fail to outperform some of the earlier solutions such as CNN-based models. In
this paper we challenge this conclusion. We present a simple and scalable
method to process long text with the existing transformer models such as BERT.
We show that this method significantly improves the previous results reported
for transformer models in ICD coding, and is able to outperform one of the
prominent CNN-based methods
Luncheon Speaker about Day in the Life of a MN Bureau of Criminal Apprehension Computer Forensics Officer
Luncheon Speaker on a Day in the Life of a MN Bureau of Criminal Apprehension Computer Forensics Officer by Donny Cheun
Cellular automata as a model of physical systems
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While this approach abstracts away all details of the underlying physical system, it remains faithful to the fact that there is an underlying physical reality which it describes. This imposes certain restrictions on the types of computations a CA can physically carry out, and the resources it needs to do so. In this paper we explore these and other consequences of our reformalization
Models of quantum cellular automata
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different QCA models, and compare them. One model we discuss is the traditional QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam. We discuss also Margolus QCA, also discussed by Schumacher and Werner. We introduce two new models, Coloured QCA, and Continuous-Time QCA. We also compare our models with the established models. We give proofs of computational equivalence for several of these models. We show the strengths of each model, and provide examples of how our models can be useful to come up with algorithms, and implement them in real-world physical devices