CHSH mod 3 reaches its exact maximal quantum value only with maximally entangled qutrit pairs (unique up to symmetry) and any strategy within ε of the optimum is O(√ε)-close to a direct sum of those optimal strategies.
Tool reference
Julia: AFreshApproach to Numerical Computing.arXiv:1411.1607 [cs], July 2015
Tool reference. 100% of classified Pith citations use this work as a method, library, or software dependency, not as a substantive claim.
8
Pith papers citing it
Method reference
100% of classified citations
abstract
Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as "laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment, and 3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts. We introduce the Julia programming language and its design --- a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can have machine performance without sacrificing human convenience.
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use method 5representative citing papers
A general conic optimization solver computes finite-size QKD rates from Rényi entropies more reliably than prior Frank-Wolfe methods.
Finite-size general security for DPSK QKD is achieved with positive key rates for 10^5 signals beyond 12 dB loss via variable-length entropy accumulation and conic optimization.
Intensity interferometry offers a way to measure micro-image swarm sizes in lensed quasars, revealing stellar and compact dark matter mass functions beyond collective intensity fluctuations.
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.
Design guidelines and a Go library (Infergo) for deploying probabilistic programming in production systems, with benchmark comparisons.
PySR delivers a distributed evolutionary symbolic regression tool with a new EmpiricalBench for recovering historical scientific equations from data.
citing papers explorer
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Robust self-testing with CHSH mod 3
CHSH mod 3 reaches its exact maximal quantum value only with maximally entangled qutrit pairs (unique up to symmetry) and any strategy within ε of the optimum is O(√ε)-close to a direct sum of those optimal strategies.
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Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization
A general conic optimization solver computes finite-size QKD rates from Rényi entropies more reliably than prior Frank-Wolfe methods.
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Finite-size general security for differential phase shift keying via variable-length quantum key distribution
Finite-size general security for DPSK QKD is achieved with positive key rates for 10^5 signals beyond 12 dB loss via variable-length entropy accumulation and conic optimization.
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Beyond collective fluctuations: probing micro-image swarms in lensed quasars with intensity interferometry
Intensity interferometry offers a way to measure micro-image swarm sizes in lensed quasars, revealing stellar and compact dark matter mass functions beyond collective intensity fluctuations.
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A Framework for Quantum Simulations of Energy-Loss and Hadronization in Non-Abelian Gauge Theories: SU(2) Lattice Gauge Theory in 1+1D
A quantum simulation framework is developed and demonstrated for energy loss and hadronization of a heavy quark in 1+1D SU(2) lattice gauge theory on 18 qubits of IBM hardware, with results matching classical simulations.
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Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.
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Deployable probabilistic programming
Design guidelines and a Go library (Infergo) for deploying probabilistic programming in production systems, with benchmark comparisons.
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Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
PySR delivers a distributed evolutionary symbolic regression tool with a new EmpiricalBench for recovering historical scientific equations from data.