Mixed s-sourcery: Building many-body states using bubbles of Nothing

TL;DR

This paper extends the concept of s-sourcery to mixed states, particularly thermal states, using quantum circuits and thermofield double states, establishing the widespread presence of mixed s-source fixed points.

Contribution

It introduces a generalized framework for s-sourcery applicable to mixed states and proves the existence of mixed s-source fixed points, expanding the original formalism.

Findings

Mixed s-sourcery applies to thermal states of local Hamiltonians.

Thermofield double states are instrumental in the constructions.

Theorems demonstrate the prevalence of mixed s-source fixed points.

Abstract

In arXiv:1407.8203, we introduced the idea of s-sourcery, a general formalism for building many-body quantum ground states using renormalization-group-inspired quantum circuits. Here we define a generalized notion of s-sourcery that applies to mixed states, and study its properties and applicability. We prove a number of theorems establishing the prevalence of mixed s-source fixed points. For our examples we focus on thermal states of local Hamiltonians. Thermal double states (also called thermofield double states) and the machinery of approximate conditional independence are used heavily in the constructions.