Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions

Area of Science:

• Quantum computing
• Quantum simulation
• Computational physics

Background:

• Continuous-time quantum walks (CTQWs) are a powerful tool for quantum simulation.
• Simulating multiparticle CTQWs often requires large Hilbert spaces, especially for indistinguishable particles.
• Current methods for simulating fermionic CTQWs face challenges with state space size.

Purpose of the Study:

• To develop a method for simulating interacting fermionic CTQWs with a reduced state space.
• To address the computational challenges associated with simulating indistinguishable quantum particles.
• To modify the graph structure used in CTQW simulations for fermionic systems.

Main Methods:

• Developing an algorithm to systematically remove redundant and forbidden quantum states.
• Modifying the Cartesian graph product structure used for multiparticle CTQWs.
• Applying fermionic statistics to the propagated state vector.

Main Results:

• A significant reduction in the effective dimension of the Hilbert space for fermionic CTQWs.
• The classical computational resources required do not increase exponentially with the number of interacting fermions.
• Enabling more efficient classical simulations of fermionic quantum systems.

Conclusions:

• The proposed algorithm offers a more efficient approach to simulating interacting fermionic CTQWs.
• This method overcomes the exponential scaling issue of computational resources.
• It paves the way for simulating larger and more complex fermionic quantum systems.