Shor's Factoring Quantum Algorithm Emulation Using Polychronous CMOS Oscillators

Richelle L. Smith

doi:10.1109/tcsii.2026.3718387

Shor's Factoring Quantum Algorithm Emulation Using Polychronous CMOS Oscillators

2026-07-30

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DOI：10.1109/tcsii.2026.3718387

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This brief presents emulation of Shor’s factoring quantum algorithm using polychronous oscillatory cellular neural networks. We emulate a set of universal quantum gates using a network of ring oscillators and switches in a standard CMOS process. We apply impulse sensitivity function (ISF) theory to model the injection locking behavior of the oscillators. Using this set of universal gates, we then show the emulation of Shor’s algorithm (quantum period finding algorithm). We demonstrate prime factorization of $N = 15$ with oscillator circuits. Next, we propose a compiled quantum circuit and design oscillator circuits for prime factorization of $N = 21$ . Spectre simulation results show close agreement with the quantum theory.

Keywords:

CMOS

cellular neural network (CNN)

computing

integer factorization

neuromorphic computing

polychronization

Shor’s factoring algorithm

Shor's Factoring Quantum Algorithm Emulation Using Polychronous CMOS Oscillators

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