119,035 research outputs found
Guided Unfoldings for Finding Loops in Standard Term Rewriting
In this paper, we reconsider the unfolding-based technique that we have
introduced previously for detecting loops in standard term rewriting. We
improve it by guiding the unfolding process, using distinguished positions in
the rewrite rules. This results in a depth-first computation of the unfoldings,
whereas the original technique was breadth-first. We have implemented this new
approach in our tool NTI and compared it to the previous one on a bunch of
rewrite systems. The results we get are promising (better times, more
successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt
am Main, Germany, 4-6 September 2018 (arXiv:1808.03326
Priority-Independent Rewrite Systems for Pointer-based Data-Structures
20 pagesWe define a syntactic class of graphs and graph rewrite systems for which the normal forms are independent from the order in which the nodes are reduced. This result, that is not covered by existing approaches in graph rewriting, allows us to devise simple confluence criteria and efficient normalization algorithms. It is based on a static analysis of the rewrite system, including a thorough analysis of the shape of the graphs generated during the rewriting process. The considered graphs naturally encode pointer-based data structures that are commonly used in practical programming and the rewrite rules can simulate any elementary transformation on these data structures (edge redirection, node relabeling etc.)
Efficient measurement of quantum dynamics via compressive sensing
The resources required to characterise the dynamics of engineered quantum
systems-such as quantum computers and quantum sensors-grow exponentially with
system size. Here we adapt techniques from compressive sensing to exponentially
reduce the experimental configurations required for quantum process tomography.
Our method is applicable to dynamical processes that are known to be
nearly-sparse in a certain basis and it can be implemented using only
single-body preparations and measurements. We perform efficient, high-fidelity
estimation of process matrices on an experiment attempting to implement a
photonic two-qubit logic-gate. The data base is obtained under various
decoherence strengths. We find that our technique is both accurate and noise
robust, thus removing a key roadblock to the development and scaling of quantum
technologies.Comment: New title and authors. A new experimental section. Significant
rewrite of the theor
Convergence condition of simulated quantum annealing for closed and open systems
We derive a generic condition for simulated quantum annealing to converge to
thermal equilibrium at a given, typically low, temperature. Both closed and
open systems are treated. We rewrite the classical master equation for
simulated quantum annealing into an imaginary-time Schr\"odinger equation, to
which we apply the imaginary-time variant of asymptotic adiabatic condition to
deduce the convergence condition. The result agrees qualitatively with a
rigorous convergence condition of simulated quantum annealing for closed
systems, which was derived from the theory of inhomogeneous Markov process.
Also observed is qualitative agreement with a rigorous convergence condition of
quantum annealing for closed systems under the real-time Schr\"odinger
dynamics. This coincidence of convergence conditions for classical stochastic
processes for simulated quantum annealing and the real-time quantum dynamics
for quantum annealing is highly non-trivial and calls for further scrutiny.Comment: 9 page
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