What type of study is this?

This is a Quantitative Study study.

October 9, 2025Open Access

Lower bounds on the complexity of preparing mixed states

Key Points

Lower bounds on circuit depth are established based on correlations in mixed states and mutual information.
As temperature decreases, the required circuit depth for preparing thermal states of one-dimensional quantum critical systems diverges.
The intersection of past lightcones of subsystems is necessary for preparing mixed states, linking entanglement and complexity.
Preparation error settings define cutoffs for circuit depth in thermal state preparation, as derived from conformal field theory.

Abstract

We establish a relationship between the correlations in a many-qubit mixed state and the minimum circuit depth needed for its preparation. If the mutual information between two subsystems exceeds the mutual information between one of those subsystems and the environment, which purifies the mixed state of the system, then the past lightcones of the subsystems must intersect one another. This results in a lower bound on the circuit depth of any ensemble of geometrically local unitaries that prepares the state to some specified degree of approximation. As an application, we derive lower bounds on the circuit depth needed to prepare thermal states of one-dimensional quantum critical systems described by conformal field theory, showing that the depth diverges as temperature is decreased up to a cutoff set by the preparation error.

Lower bounds on the complexity of preparing mixed states

Key Points

Abstract

Cite This Study

Also Consider

Also Consider