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title: Shor's Algorithm: Resource Requirements description: This MicroSim visualizes the staggering hardware resources required to run Shor's algorithm for breaking RSA encryption at various key sizes. By adjusting the RSA key size slider, you can see how the image: /sims/shors-algorithm-resources/shors-algorithm-resources.png og:image: /sims/shors-algorithm-resources/shors-algorithm-resources.png

Shor's Algorithm: Resource Requirements

This MicroSim visualizes the staggering hardware resources required to run Shor's algorithm for breaking RSA encryption at various key sizes. By adjusting the RSA key size slider, you can see how the number of logical qubits, physical qubits (with error correction overhead), gate operations, and required coherence times scale with the problem size.

The bar chart compares today's best quantum computer (roughly 1,000 physical qubits) against the millions of qubits needed for cryptographically relevant factoring, making the gap between current hardware and practical threat levels immediately visible.

Shor's Algorithm Resource Requirements MicroSim

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Use the slider to explore different RSA key sizes from 16 bits up to 4,096 bits. Notice how the physical qubit requirement grows linearly with key size but remains thousands of times beyond current hardware capabilities for any cryptographically relevant key length.

Key Takeaways

  • Logical qubits scale as roughly 2n for an n-bit RSA key, meaning RSA-2048 needs about 4,096 logical qubits.
  • Physical qubits multiply the logical count by 1,000 to 10,000 for error correction, pushing the requirement into the millions.
  • Gate operations scale as n cubed, requiring trillions of operations for RSA-2048.
  • The largest number ever factored by Shor's algorithm on a quantum computer is 21 (in 2012), highlighting the enormous gap between demonstration and practical use.
  • Current quantum hardware falls short by a factor of 4,000 to 20,000 in qubit count alone, before considering gate speed and coherence requirements.