# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.08257