Efficient Quantum Simulation for Translationally Invariant Systems

Area of Science:

• Condensed matter physics
• Quantum computation
• Lattice gauge theories

Background:

• Discrete translational symmetry is crucial in condensed matter physics and lattice gauge theories.
• Quantum simulations offer insights but are hindered by device connectivity constraints and long computation times.

Purpose of the Study:

• To extend the application of spatial symmetry from physical systems to the quantum circuits used for simulation.
• To algorithmically alleviate device connectivity constraints in quantum simulations.

Main Methods:

• Applying spatial symmetry principles to quantum circuit design.
• Developing algorithmic approaches to optimize circuit layout based on system symmetry.

Main Results:

• Significant reduction in quantum computational time (several orders of magnitude) for simulations.
• Feasibility of complex simulations for condensed matter systems and lattice gauge theories.
• Enhanced performance even before hardware improvements.

Conclusions:

• Spatial symmetry in quantum circuits is a powerful tool for overcoming hardware limitations.
• This approach substantially enhances quantum computer capabilities for scientific simulations.
• Provides a foundation for using spatial symmetry in quantum error correction and other quantum computation areas.