283 research outputs found
ASAM : Automatic Architecture Synthesis and Application Mapping; dl. 3.2: Instruction set synthesis
No abstract
Clifford Orbits from Cayley Graph Quotients
We describe the structure of the -qubit Clifford group via
Cayley graphs, whose vertices represent group elements and edges represent
generators. In order to obtain the action of Clifford gates on a given quantum
state, we introduce a quotient procedure. Quotienting the Cayley graph by the
stabilizer subgroup of a state gives a reduced graph which depicts the state's
Clifford orbit. Using this protocol for , we reproduce and
generalize the reachability graphs introduced in arXiv:2204.07593. Since the
procedure is state-independent, we extend our study to non-stabilizer states,
including the W and Dicke states. Our new construction provides a more precise
understanding of state evolution under Clifford circuit action.Comment: 42 pages, 22 figures, 1 Mathematica packag
Mining and analysis of real-world graphs
Networked systems are everywhere - such as the Internet, social networks, biological networks, transportation networks, power grid networks, etc. They can be very large yet enormously complex. They can contain a lot of information, either open and transparent or under the cover and coded. Such real-world systems can be modeled using graphs and be mined and analyzed through the lens of network analysis. Network analysis can be applied in recognition of frequent patterns among the connected components in a large graph, such as social networks, where visual analysis is almost impossible. Frequent patterns illuminate statistically important subgraphs that are usually small enough to analyze visually. Graph mining has different practical applications in fraud detection, outliers detection, chemical molecules, etc., based on the necessity of extracting and understanding the information yielded. Network analysis can also be used to quantitatively evaluate and improve the resilience of infrastructure networks such as the Internet or power grids. Infrastructure networks directly affect the quality of people\u27s lives. However, a disastrous incident in these networks may lead to a cascading breakdown of the whole network and serious economic consequences. In essence, network analysis can help us gain actionable insights and make better data-driven decisions based on the networks. On that note, the objective of this dissertation is to improve upon existing tools for more accurate mining and analysis of real-world networks --Abstract, page iv
Automated detection of symmetry-protected subspaces in quantum simulations
The analysis of symmetry in quantum systems is of utmost theoretical
importance, useful in a variety of applications and experimental settings, and
is difficult to accomplish in general. Symmetries imply conservation laws,
which partition Hilbert space into invariant subspaces of the time-evolution
operator, each of which is demarcated according to its conserved quantity. We
show that, starting from a chosen basis, any invariant, symmetry-protected
subspaces which are diagonal in that basis are discoverable using transitive
closure on graphs representing state-to-state transitions under -local
unitary operations. Importantly, the discovery of these subspaces relies
neither upon the explicit identification of a symmetry operator or its
eigenvalues nor upon the construction of matrices of the full Hilbert space
dimension. We introduce two classical algorithms, which efficiently compute and
elucidate features of these subspaces. The first algorithm explores the entire
symmetry-protected subspace of an initial state in time complexity linear to
the size of the subspace by closing local basis state-to-basis state
transitions. The second algorithm determines, with bounded error, if a given
measurement outcome of a dynamically-generated state is within the
symmetry-protected subspace of the state in which the dynamical system is
initialized. We demonstrate the applicability of these algorithms by performing
post-selection on data generated from emulated noisy quantum simulations of
three different dynamical systems: the Heisenberg-XXX model and the and
quantum cellular automata. Due to their efficient computability and
indifference to identifying the underlying symmetry, these algorithms lend
themselves to the post-selection of quantum computer data, optimized classical
simulation of quantum systems, and the discovery of previously hidden
symmetries in quantum mechanical systems.Comment: 23 pages, 7 figures, 4 appendice
Functional completeness of planar Rydberg blockade structures
The construction of Hilbert spaces that are characterized by local
constraints as the low-energy sectors of microscopic models is an important
step towards the realization of a wide range of quantum phases with long-range
entanglement and emergent gauge fields. Here we show that planar structures of
trapped atoms in the Rydberg blockade regime are functionally complete: Their
ground state manifold can realize any Hilbert space that can be characterized
by local constraints in the product basis. We introduce a versatile framework,
together with a set of provably minimal logic primitives as building blocks, to
implement these constraints. As examples, we present lattice realizations of
the string-net Hilbert spaces that underlie the surface code and the Fibonacci
anyon model. We discuss possible optimizations of planar Rydberg structures to
increase their geometrical robustness.Comment: 33 pages, 14 figures, v2: fixed typos, added additional references
and comment
Hypertiling -- a high performance Python library for the generation and visualization of hyperbolic lattices
Hypertiling is a high-performance Python library for the generation and
visualization of regular hyperbolic lattices embedded in the Poincar\'e disk
model. Using highly optimized, efficient algorithms, hyperbolic tilings with
millions of vertices can be created in a matter of minutes on a single
workstation computer. Facilities including computation of adjacent vertices,
dynamic lattice manipulation, refinements, as well as powerful plotting and
animation capabilities are provided to support advanced uses of hyperbolic
graphs. In this manuscript, we present a comprehensive exploration of the
package, encompassing its mathematical foundations, usage examples,
applications, and a detailed description of its implementation.Comment: 52 pages, 20 figure
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