Crossing a topological phase transition with a quantum computer

TL;DR

This paper demonstrates how near-term quantum computers can simulate and detect topological phase transitions in quantum many-body systems, showcasing their potential for studying complex quantum phenomena beyond classical capabilities.

Contribution

The authors construct and measure a family of states crossing a symmetry protected topological phase transition using IBM Q quantum computers, introducing methods to detect the transition.

Findings

Successful measurement of topological phase transition using quantum computers

Development of methods to measure string order parameters

Analysis of noise effects on quantum simulation accuracy

Abstract

Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One of the most apparent applications for such a device is the study of complex many-body quantum systems, where classical computers are unable to deal with the generic exponential complexity of quantum states. Even zero-temperature equilibrium phases of matter and the transitions between them have yet to be fully classified, with topologically protected phases presenting major difficulties. We construct and measure a continuously parametrized family of states crossing a symmetry protected topological phase transition on the IBM Q quantum computers. We present two complementary methods for measuring string order parameters that reveal the transition, and additionally analyse the effects of noise in the device using simple error models. The simulation that we perform is easily scalable and is a practical demonstration of the utility of near-term quantum computers for the study of quantum phases of matter and their transitions.