--- title: Shor's Algorithm for Quantum Computing - Computerphile description: A detailed walkthrough of Shor's algorithm, covering both its classical and quantum components. The classical part reframes integer factorization as a... canonical: https://daily.dev/posts/shor-s-algorithm-for-quantum-computing---computerphile-fqraip4vy twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Shor's Algorithm for Quantum Computing - Computerphile | daily.dev og:description: A detailed walkthrough of Shor's algorithm, covering both its classical and quantum components. The classical part reframes integer factorization as a... og:url: https://daily.dev/posts/shor-s-algorithm-for-quantum-computing---computerphile-fqraip4vy og:image: https://api.daily.dev/og/posts/fQRAIP4Vy.png og:image:alt: Shor's Algorithm for Quantum Computing - Computerphile og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Shor's Algorithm for Quantum Computing - Computerphile **[Computerphile](https://daily.dev/sources/computerphile)** · 38 min read · 0 upvotes · 0 comments ## Summary A detailed walkthrough of Shor's algorithm, covering both its classical and quantum components. The classical part reframes integer factorization as a period-finding problem using modular exponentiation, demonstrated with a small example (N=15, a=2). The quantum part explains how a quantum Fourier transform efficiently extracts the period by exploiting wave interference — constructive and destructive — rather than brute-force search. The video demystifies qubits using trapped-ion quantum computers and phasors, explaining superposition as wave addition rather than parallel universes. It also addresses current practical limitations: quantum computers today can barely factor 15, and breaking real 2048-bit RSA keys may be decades away due to noise and error-correction challenges. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### How does Shor's algorithm actually break RSA encryption? Shor's algorithm reframes the hard problem of factoring RSA's large semiprime number N into an easier problem of finding the period of a modular exponentiation function. Once a quantum computer finds that period, the greatest common divisor of a simple expression derived from it and N reveals the prime factors P and Q, which let an attacker derive the private key from the public key. _Developers tracking post-quantum cryptography risks can follow deeper explainers like this on daily.dev._ ### Can current quantum computers factor RSA-sized numbers yet? No, existing quantum computers cannot reliably factor numbers much larger than 15 due to noise and the need for extensive error correction with duplicate qubits. Estimates for when a machine large enough to threaten a 2,000-bit RSA key might exist range widely, from as soon as 5 years to as long as hundreds of years. _Anyone weighing when to migrate to quantum-resistant crypto can track progress like this on daily.dev._ ### What role does the Fourier transform play in Shor's algorithm on a quantum computer? The quantum Fourier transform decomposes the periodic modular exponentiation function into its component frequencies, and the dominant peak in that spectrum directly reveals the function's period. On a trapped-ion quantum computer, this is achieved physically by controlling the phase of qubit states with microwave pulses to produce constructive or destructive interference, rather than by testing every possible factor. _Engineers curious how quantum hardware implements algorithms like this can dig into explainers on daily.dev._ ## Similar posts on daily.dev - [Why Haven’t Quantum Computers Factored 21 Yet?](https://daily.dev/posts/why-haven-t-quantum-computers-factored-21-yet--inmhkl0p3) · Hackaday · 1 upvotes · 0 comments - [Factoring an integer with three oscillators and a qubit](https://daily.dev/posts/factoring-an-integer-with-three-oscillators-and-a-qubit-rbzard0bp) · Nature · 0 upvotes · 0 comments --- Tags: [#data-science](https://daily.dev/tags/data-science), [#quantum-computing](https://daily.dev/tags/quantum-computing), [#cryptography](https://daily.dev/tags/cryptography) [View this post on daily.dev](https://daily.dev/posts/shor-s-algorithm-for-quantum-computing---computerphile-fqraip4vy) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Shor's Algorithm for Quantum Computing - Computerphile","url":"https://daily.dev/posts/shor-s-algorithm-for-quantum-computing---computerphile-fqraip4vy","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/shor-s-algorithm-for-quantum-computing---computerphile-fqraip4vy"},"datePublished":"2026-07-09T14:21:46.758Z","dateModified":"2026-09-13T18:26:13.666Z","description":"A detailed walkthrough of Shor's algorithm, covering both its classical and quantum components. 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