Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

Area of Science:

• Quantum Information Science
• Photonic Quantum Computing
• Quantum Simulation

Background:

• Quantum walk applications are constrained by particle number, symmetry, indistinguishability, and graph topology.
• Existing quantum walk implementations often lack full control over these crucial parameters.
• Developing programmable quantum devices is essential for advancing quantum computation.

Purpose of the Study:

• To demonstrate a silicon photonics device for realizing quantum walks with tunable properties.
• To achieve full control over particle number, exchange symmetry, and indistinguishability in quantum walks.
• To explore the application of this device in quantum algorithms and simulations.

Main Methods:

• Utilized an entanglement-driven scheme in silicon photonics to implement two-photon quantum walks.
• Developed a device capable of simulating quantum walks on any five-vertex graph.
• Continuously tuned particle exchange symmetry and indistinguishability to control walk properties.

Main Results:

• Successfully implemented entangled two-photon quantum walks with full control over particle properties.
• Demonstrated the simulation of single-particle walks on larger, controlled graphs.
• Applied the device to quantum walk algorithms for graph searching and isomorphism testing, simulating 100 time steps on 292 graphs.

Conclusions:

• The developed silicon photonics device offers unprecedented control over quantum walk parameters.
• This work paves the way for large-scale, programmable quantum walk processors.
• Enables tackling classically intractable problems through advanced quantum walk simulations and algorithms.