2019 October « Math Scholar

Quantum supremacy has been achieved; or has it?

IBM’s “Q” quantum computer; courtesy IBM

Google’s quantum computing achievement

For at least three decades, teams of researchers have been exploring quantum computers for real-world applications in scientific research, engineering and finance. Researchers have dreamed of the day when quantum computers would first achieve “supremacy” over classical computers, in the sense that a quantum computer solving a particular problem faster than any present-day or soon-to-be-produced classical computer system.

In a Nature article dated 23 October 2019, researchers at Google announced that they have achieved exactly this.

Google researchers employed a custom-designed quantum processor, named “Sycamore,” consisting of programmable quantum

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Pi as the limit of n-sided circumscribed and inscribed polygons

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Credit: Ancient Origins

Introduction In a previous Math Scholar blog, we presented Archimedes’ ingenious scheme for approximating $\pi$, based on an analysis of regular circumscribed and inscribed polygons with $3 \cdot 2^k$ sides, using modern mathematical notation and techniques.

One motivation for both the previous blog and this blog is to respond to some recent writers who reject basic mathematical theory and the accepted value of $\pi$, claiming instead that they have found $\pi$ to be a different value. For example, one author asserts that $\pi = 17 – 8 \sqrt{3} =

Continue reading Pi as the limit of n-sided circumscribed and inscribed polygons

Math Scholar

Quantum supremacy has been achieved; or has it?

Pi as the limit of n-sided circumscribed and inscribed polygons

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