Quantum Yang-Mills theory: an overview of a programme

Understand

We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective.

• Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice.
• Firstly, inspired by recent constructions for $\mathbb{Z}/2\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter.
• We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points.