Quantum Circuits for Scale Transformations

TL;DR

This paper develops quantum circuits to simulate thermal properties and scale transformations of integrable lattice models like the quantum XY/Ising chain, linking quantum computing with renormalization group concepts.

Contribution

It introduces quantum circuits for exact thermal state simulation, coarse graining, and local scale transformations in integrable lattice models.

Findings

Quantum circuits for thermal property simulation

Circuit analogy for Wilsonian renormalization group flow

Implementation of local scale transformations

Abstract

In this note we develop quantum circuits for exactly simulating the thermal properties of the quantum XY/Ising chain. These circuits are applicable to the simplest integrable lattice models for which the exact momentum-space scattering-matrix can be constructed in terms of local two-body gates. We discuss a circuit analogy for Wilsonian renormalization group flow and show how it can be used to simulate a global coarse graining transformation. We then construct a circuit that transforms the ground state of these models into the thermo-field double state, and show how it can be used to implement a local scale transformation.