Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Strongly correlated condensed matter systems are among those for which quantum simulation should be able to give an advantage. Here, the authors use a translationally invariant tensor network technique to simulate a quantum critical system on a superconducting quantum processor. The phenomena of quantum criticality underlie many novel collective phenomena found in condensed matter systems. They present a challenge for classical and quantum simulation, in part because of diverging correlation lengths and consequently strong finite-size effects. Tensor network techniques that work directly in the thermodynamic limit can negotiate some of these difficulties. Here, we optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.

Automated summary

In this paper, the authors propose a method to simulate quantum critical systems using a superconducting quantum processor. By using tensor network techniques and sequential quantum circuits, they successfully simulate quantum critical phenomena and the groundstate of the quantum Ising model.