By name: quantum-prime-identification description: "Quantum protocol for prime number identification using entanglement dynamics on real quantum processors. Links primality testing to Fourier components of quantum circuit measurements. Use when: prime number testing with quantum hardware, quantum number theory, entanglement-based primality detection, quantum arithmetic algorithms, Shor algorithm alternatives, noise mitigation for quantum processors, rescaling-based error mitigation." license: Complete terms in LICENSE.txt metadata: arxiv_id: "2605.28964" published: "2026-05-29" tags: [quantum, number-theory, prime-numbers, entanglement, noise-mitigation]
Quantum Prime Number Identification
Core Methodology
Implements a quantum protocol for prime number identification based on entanglement dynamics, demonstrated on IBM quantum processors. The method links the primality of an integer to specific Fourier components generated by the entanglement evolution of a quantum system.
Key Insights
- Entanglement-as-Primality: Prime numbers produce distinct Fourier signatures in the measurement distribution of entangled quantum states
- Rescaling-Based Noise Mitigation: New technique that rescales measurement outcomes to counteract hardware noise, enabling reliable prime detection on NISQ devices
- Hardware Demonstrated: Successfully implemented on actual IBM quantum processors, not just simulation
Algorithm Steps
- Encode integer n into quantum state preparation
- Apply entangling gate sequence that generates periodic dynamics
- Measure output distribution and compute Fourier transform
- Identify primality via characteristic frequency peaks in Fourier spectrum
- Apply rescaling-based noise mitigation to correct for hardware errors
When to Use
- Testing primality of large integers on quantum hardware
- Exploring quantum approaches to number-theoretic problems
- Demonstrating quantum advantage for arithmetic tasks
- Benchmarking quantum processors with number-theoretic circuits
Noise Mitigation
The rescaling technique works by:
- Running circuits at multiple noise levels (via gate stretching)
- Fitting a linear model to the noisy measurement outcomes
- Extrapolating to the zero-noise limit via rescaling
- This is simpler than full zero-noise extrapolation and works well for periodic observables
Related Approaches
- Shor's algorithm (factoring, not primality testing)
- Classical AKS primality test (polynomial time, no quantum needed)
- Quantum phase estimation for period-finding