Factoring an integer with three oscillators and a qubit

Area of Science:

• Quantum Computing
• Quantum Information Science
• Algorithm Design

Background:

• Traditional quantum algorithm design often relies on the abstraction of a universal quantum computer with scalable qubits.
• This model, while useful for device-independent development, may not fully leverage the benefits of specific physical setups.
• Hybrid qubit-oscillator systems offer an alternative framework for quantum computation.

Purpose of the Study:

• To explore the benefits of a physical setup-centered approach in quantum algorithm design.
• To develop a quantum factoring algorithm utilizing hybrid qubit-oscillator systems.
• To demonstrate native realizations of essential quantum operations within such systems.

Main Methods:

• Utilizing hybrid qubit-oscillator systems with linear optics and qubit-controlled Gaussian unitaries.
• Implementing native continuous variable Fourier transforms and arithmetic operations.
• Developing a quantum factoring algorithm based on these physical realizations.

Main Results:

• A polynomial-time quantum factoring algorithm was developed.
• The algorithm requires minimal resources: only one qubit and three oscillators.
• The algorithm's efficiency is independent of the magnitude of the number being factored.

Conclusions:

• A physical setup-centered approach can yield significant benefits in quantum algorithm design.
• Hybrid qubit-oscillator systems provide a powerful platform for efficient quantum computation.
• This work demonstrates a practical and resource-efficient quantum factoring algorithm.