98,191 research outputs found
Linear-algebraic lambda-calculus
With a view towards models of quantum computation and/or the interpretation
of linear logic, we define a functional language where all functions are linear
operators by construction. A small step operational semantic (and hence an
interpreter/simulator) is provided for this language in the form of a term
rewrite system. The linear-algebraic lambda-calculus hereby constructed is
linear in a different (yet related) sense to that, say, of the linear
lambda-calculus. These various notions of linearity are discussed in the
context of quantum programming languages. KEYWORDS: quantum lambda-calculus,
linear lambda-calculus, -calculus, quantum logics.Comment: LaTeX, 23 pages, 10 figures and the LINEAL language
interpreter/simulator file (see "other formats"). See the more recent
arXiv:quant-ph/061219
Quantum field theory on affine bundles
We develop a general framework for the quantization of bosonic and fermionic
field theories on affine bundles over arbitrary globally hyperbolic spacetimes.
All concepts and results are formulated using the language of category theory,
which allows us to prove that these models satisfy the principle of general
local covariance. Our analysis is a preparatory step towards a full-fledged
quantization scheme for the Maxwell field, which emphasises the affine bundle
structure of the bundle of principal U(1)-connections. As a by-product, our
construction provides a new class of exactly tractable locally covariant
quantum field theories, which are a mild generalization of the linear ones. We
also show the existence of a functorial assignment of linear quantum field
theories to affine ones. The identification of suitable algebra homomorphisms
enables us to induce whole families of physical states (satisfying the
microlocal spectrum condition) for affine quantum field theories by pulling
back quasi-free Hadamard states of the underlying linear theories.Comment: 34 pages, no figures; v2: 35 pages, compatible with version to be
published in Annales Henri Poincar
A Class of -Invariant Topological Phases of Interacting Electrons
We describe a class of parity- and time-reversal-invariant topological states
of matter which can arise in correlated electron systems in 2+1-dimensions.
These states are characterized by particle-like excitations exhibiting exotic
braiding statistics. and invariance are maintained by a `doubling' of
the low-energy degrees of freedom which occurs naturally without doubling the
underlying microscopic degrees of freedom. The simplest examples have been the
subject of considerable interest as proposed mechanisms for high-
superconductivity. One is the `doubled' version (i.e. two opposite-chirality
copies) of the U(1) chiral spin liquid. The second example corresponds to
gauge theory, which describes a scenario for spin-charge separation. Our main
concern, with an eye towards applications to quantum computation, are richer
models which support non-Abelian statistics. All of these models, richer or
poorer, lie in a tightly-organized discrete family. The physical inference is
that a material manifesting the gauge theory or a doubled chiral spin
liquid might be easily altered to one capable of universal quantum computation.
These phases of matter have a field-theoretic description in terms of gauge
theories which, in their infrared limits, are topological field theories. We
motivate these gauge theories using a parton model or slave-fermion
construction and show how they can be solved exactly. The structure of the
resulting Hilbert spaces can be understood in purely combinatorial terms. The
highly-constrained nature of this combinatorial construction, phrased in the
language of the topology of curves on surfaces, lays the groundwork for a
strategy for constructing microscopic lattice models which give rise to these
phases.Comment: Typos fixed, references adde
Grammar-Aware Question-Answering on Quantum Computers
Natural language processing (NLP) is at the forefront of great advances in
contemporary AI, and it is arguably one of the most challenging areas of the
field. At the same time, with the steady growth of quantum hardware and notable
improvements towards implementations of quantum algorithms, we are approaching
an era when quantum computers perform tasks that cannot be done on classical
computers with a reasonable amount of resources. This provides a new range of
opportunities for AI, and for NLP specifically. Earlier work has already
demonstrated a potential quantum advantage for NLP in a number of manners: (i)
algorithmic speedups for search-related or classification tasks, which are the
most dominant tasks within NLP, (ii) exponentially large quantum state spaces
allow for accommodating complex linguistic structures, (iii) novel models of
meaning employing density matrices naturally model linguistic phenomena such as
hyponymy and linguistic ambiguity, among others. In this work, we perform the
first implementation of an NLP task on noisy intermediate-scale quantum (NISQ)
hardware. Sentences are instantiated as parameterised quantum circuits. We
encode word-meanings in quantum states and we explicitly account for
grammatical structure, which even in mainstream NLP is not commonplace, by
faithfully hard-wiring it as entangling operations. This makes our approach to
quantum natural language processing (QNLP) particularly NISQ-friendly. Our
novel QNLP model shows concrete promise for scalability as the quality of the
quantum hardware improves in the near future
A Quantum Many-body Wave Function Inspired Language Modeling Approach
The recently proposed quantum language model (QLM) aimed at a principled
approach to modeling term dependency by applying the quantum probability
theory. The latest development for a more effective QLM has adopted word
embeddings as a kind of global dependency information and integrated the
quantum-inspired idea in a neural network architecture. While these
quantum-inspired LMs are theoretically more general and also practically
effective, they have two major limitations. First, they have not taken into
account the interaction among words with multiple meanings, which is common and
important in understanding natural language text. Second, the integration of
the quantum-inspired LM with the neural network was mainly for effective
training of parameters, yet lacking a theoretical foundation accounting for
such integration. To address these two issues, in this paper, we propose a
Quantum Many-body Wave Function (QMWF) inspired language modeling approach. The
QMWF inspired LM can adopt the tensor product to model the aforesaid
interaction among words. It also enables us to reveal the inherent necessity of
using Convolutional Neural Network (CNN) in QMWF language modeling.
Furthermore, our approach delivers a simple algorithm to represent and match
text/sentence pairs. Systematic evaluation shows the effectiveness of the
proposed QMWF-LM algorithm, in comparison with the state of the art
quantum-inspired LMs and a couple of CNN-based methods, on three typical
Question Answering (QA) datasets.Comment: 10 pages,4 figures,CIK
A Potentiality and Conceptuality Interpretation of Quantum Physics
We elaborate on a new interpretation of quantum mechanics which we introduced
recently. The main hypothesis of this new interpretation is that quantum
particles are entities interacting with matter conceptually, which means that
pieces of matter function as interfaces for the conceptual content carried by
the quantum particles. We explain how our interpretation was inspired by our
earlier analysis of non-locality as non-spatiality and a specific
interpretation of quantum potentiality, which we illustrate by means of the
example of two interconnected vessels of water. We show by means of this
example that philosophical realism is not in contradiction with the recent
findings with respect to Leggett's inequalities and their violations. We
explain our recent work on using the quantum formalism to model human concepts
and their combinations and how this has given rise to the foundational ideas of
our new quantum interpretation. We analyze the equivalence of meaning in the
realm of human concepts and coherence in the realm of quantum particles, and
how the duality of abstract and concrete leads naturally to a Heisenberg
uncertainty relation. We illustrate the role played by interference and
entanglement and show how the new interpretation explains the problems related
to identity and individuality in quantum mechanics. We put forward a possible
scenario for the emergence of the reality of macroscopic objects.Comment: 20 pages, 1 figur
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