4,657 research outputs found
Fast optimization algorithms and the cosmological constant
Denef and Douglas have observed that in certain landscape models the problem
of finding small values of the cosmological constant is a large instance of an
NP-hard problem. The number of elementary operations (quantum gates) needed to
solve this problem by brute force search exceeds the estimated computational
capacity of the observable universe. Here we describe a way out of this
puzzling circumstance: despite being NP-hard, the problem of finding a small
cosmological constant can be attacked by more sophisticated algorithms whose
performance vastly exceeds brute force search. In fact, in some parameter
regimes the average-case complexity is polynomial. We demonstrate this by
explicitly finding a cosmological constant of order in a randomly
generated -dimensional ADK landscape.Comment: 19 pages, 5 figure
What is the Computational Value of Finite Range Tunneling?
Quantum annealing (QA) has been proposed as a quantum enhanced optimization
heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling
can provide considerable computational advantage. For a crafted problem
designed to have tall and narrow energy barriers separating local minima, the
D-Wave 2X quantum annealer achieves significant runtime advantages relative to
Simulated Annealing (SA). For instances with 945 variables, this results in a
time-to-99%-success-probability that is times faster than SA
running on a single processor core. We also compared physical QA with Quantum
Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical
processors. We observe a substantial constant overhead against physical QA:
D-Wave 2X again runs up to times faster than an optimized
implementation of QMC on a single core. We note that there exist heuristic
classical algorithms that can solve most instances of Chimera structured
problems in a timescale comparable to the D-Wave 2X. However, we believe that
such solvers will become ineffective for the next generation of annealers
currently being designed. To investigate whether finite range tunneling will
also confer an advantage for problems of practical interest, we conduct
numerical studies on binary optimization problems that cannot yet be
represented on quantum hardware. For random instances of the number
partitioning problem, we find numerically that QMC, as well as other algorithms
designed to simulate QA, scale better than SA. We discuss the implications of
these findings for the design of next generation quantum annealers.Comment: 17 pages, 13 figures. Edited for clarity, in part in response to
comments. Added link to benchmark instance
Survivable algorithms and redundancy management in NASA's distributed computing systems
The design of survivable algorithms requires a solid foundation for executing them. While hardware techniques for fault-tolerant computing are relatively well understood, fault-tolerant operating systems, as well as fault-tolerant applications (survivable algorithms), are, by contrast, little understood, and much more work in this field is required. We outline some of our work that contributes to the foundation of ultrareliable operating systems and fault-tolerant algorithm design. We introduce our consensus-based framework for fault-tolerant system design. This is followed by a description of a hierarchical partitioning method for efficient consensus. A scheduler for redundancy management is introduced, and application-specific fault tolerance is described. We give an overview of our hybrid algorithm technique, which is an alternative to the formal approach given
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