Qubit Regularization of Asymptotic Freedom.

Area of Science:

• Quantum Field Theory
• Condensed Matter Physics
• Quantum Information

Background:

• The (1+1)-dimensional nonlinear O(3) sigma model is a fundamental model in quantum field theory.
• Regularizing this model is crucial for theoretical studies and potential applications.
• Previous methods faced challenges in achieving large correlation lengths and demonstrating asymptotic freedom.

Purpose of the Study:

• To introduce and validate a novel quantum lattice Hamiltonian, the
• Heisenberg comb,
• for regularizing the (1+1)-dimensional nonlinear O(3) sigma model.
• To explore the potential of near-term quantum computers in demonstrating asymptotic freedom.
• To investigate the emergence of the continuum limit from a quantum lattice description.

Main Methods:

• Implementation of a quantum lattice Hamiltonian (Heisenberg comb) acting on a two-qubit Hilbert space per site.
• Utilizing a world-line Monte Carlo method to simulate the model.
• Developing a quantum circuit description for the time evolution.

Main Results:

• The Heisenberg comb successfully reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 lattice units.
• Strong evidence is provided for the model's ability to regularize the (1+1)-dimensional nonlinear O(3) sigma model.
• The study outlines a pathway for the emergence of the continuum limit.

Conclusions:

• The Heisenberg comb offers a viable and efficient method for regularizing the (1+1)-dimensional nonlinear O(3) sigma model.
• Near-term quantum computers may be capable of simulating this model and demonstrating asymptotic freedom.
• This work bridges quantum field theory and quantum computation, opening new avenues for research.