Quantum Advantage Formally Proved for Short-Depth Quantum Circuits @ InfoQ
what is proven?
"parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are probably better at solving certain linear algebra problems associated with binary quadratic forms."
Quantum advantage with shallow circuits | Science
Quantum supremacy - Wikipedia
"Quantum supremacy or quantum advantage is the potential ability of quantum computing devices to solve problems that classical computers practically cannot.[1] In computational complexity-theoretic terms, this generally means providing a superpolynomial speedup over the best known or possible classical algorithm"
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