Related Experiment Video
Updated: Jun 1, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Circuit complexity across a topological phase transition
Fangli Liu1,2, Seth Whitsitt1,2, Jonathan B Curtis1
1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
None:
We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and nonequilibrium steady states of the Kitaev model exhibit nonanalytical behaviors at the critical points, and thus can be used to detect both equilibrium and dynamical topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and we discuss generalizations to higher dimensions. Our result opens up an avenue for using circuit complexity as a tool to understand quantum many-body systems.
Related Concept Videos
Circuit Terminology
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
Second-Order Circuits
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
First-Order Circuits
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
Phase Transitions
Network Function of a Circuit
Phase Diagram

