Using quantum computers to identify prime numbers via entanglement dynamics

Abstract

Recently, the entanglement dynamics of two harmonic oscillators initially prepared in a separable-coherent state was demonstrated to offer a pathway for prime number identification. This article presents a generalized approach and outlines a deterministic algorithm making possible the implementation of this theoretical concept on scalable fault-tolerant qubit-based quantum computers. We prove that the diagonal unitary operations employed in our algorithm exhibit a polynomial-time complexity of degree two, contrasting with the previously reported exponential complexity of general diagonal unitaries.

References in corpus (7)

• Physics of the Riemann Hypothesis
• Landau levels and Riemann zeros
• Entanglement Monotones from Complementarity Relations
• Prime Suspects in a Quantum Ladder
• Strengthening the Baillie-PSW primality test
• The Prime state and its quantum relatives
• Identifying primes from entanglement dynamics

Cited by in corpus (1)

• Prime Number Identification Demonstrated with Quantum Processors Using a New Rescaling-Based Noise Mitigation Technique