Exact Gravity Duals for Simple Quantum Circuits

TL;DR

This paper constructs exact gravity duals for simple quantum circuits, specifically local conformal transformations in 2D conformal field theories, advancing the understanding of holographic complexity and its gravitational representation.

Contribution

It provides a method to find exact gravity duals for circuits performing local conformal transformations, enhancing the theoretical framework of holographic complexity.

Findings

Derived the gravity dual for circuits with local conformal transformations.

Established a basis for studying gravity duals to circuit costs from first principles.

Connected circuit complexity with gravitational minimal cost principles.

Abstract

Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion of a class of circuits that, when acting on a given reference state, all produce a desired target state. In the present work we build on studies of circuits performing local conformal transformations in general two-dimensional conformal field theories and construct the exact gravity dual to such circuits. In our approach to holographic complexity, the gravity dual to the optimal circuit is the one that minimizes an externally chosen cost assigned to each circuit. Our results provide a basis for studying exact gravity duals to circuit costs from first principles.