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Unconventional complexity measures for unconventional computers
Published 2011“…One particular motivation behind unconventional computation is the desire efficiently to solve classically difficult problems—we recall chemical-computer attempts at solving NP-complete problems such as the Travelling Salesperson Problem—, with computational complexity theory offering the criteria for judging this efficiency. …”
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R-prime numbers of degree k
Published 2018-02-01“…Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. …”
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Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering
Published 2024-06-01“…Thus, our findings provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA.…”
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Using Stochastic Spiking Neural Networks on SpiNNaker to Solve Constraint Satisfaction Problems
Published 2017-12-01“…However, CSPs belong to the NP-complete complexity class, for which the existence (or not) of efficient algorithms remains a major unsolved question in computational complexity theory. In the face of this fundamental difficulty heuristics and approximation methods are used to approach instances of NP (e.g., decision and hard optimization problems). …”
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Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems
Published 2017-06-01“…The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. …”
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The Complexity of Bipartite Gaussian Boson Sampling
Published 2022-11-01“…There is therefore significant interest, from the perspective of computational complexity theory, in solidifying the mathematical foundation for the hardness of simulating these devices. …”
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Importance of the Spectral gap in Estimating Ground-State Energies
Published 2022-12-01“…The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. …”
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Real-Time Trading System Based on Selections of Potentially Profitable, Uncorrelated, and Balanced Stocks by NP-Hard Combinatorial Optimization
Published 2023-01-01“…Financial portfolio construction problems are often formulated as quadratic and discrete (combinatorial) optimization that belong to the nondeterministic polynomial time (NP)-hard class in computational complexity theory. Ising machines are hardware devices that work in quantum-mechanical/quantum-inspired principles for quickly solving NP-hard optimization problems, which potentially enable making trading decisions based on NP-hard optimization in the time constraints for high-speed trading strategies. …”
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Classical simulation complexity of restricted models of quantum computation
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DISCRETE MATHEMATICS FOR COMPUTER SCIENTIST /
Published 2012“…As the book serves as an introductory level to computer science students, it is expected that once the students are already familiar with the presented contents, it will enable them to understand the advanced topics in computer science such as advanced theory of computer science and computational complexity theories. The chapters in this book have been organized for the students to learn and understand the main concepts of discrete mathematics for developing computer applications during the period of their studies. …”
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