Generation of thermofield double states and critical ground states with a quantum computer

D Zhu; S Johri; N M Linke; K A Landsman; C Huerta Alderete; N H Nguyen; A Y Matsuura; T H Hsieh; C Monroe

doi:10.1073/pnas.2006337117

Generation of thermofield double states and critical ground states with a quantum computer

Proc Natl Acad Sci U S A. 2020 Oct 13;117(41):25402-25406. doi: 10.1073/pnas.2006337117. Epub 2020 Sep 28.

Authors

D Zhu^{1

2

3}, S Johri⁴, N M Linke^{1

2}, K A Landsman^{1

2}, C Huerta Alderete^{1

2

5}, N H Nguyen^{1

2}, A Y Matsuura⁴, T H Hsieh⁶, C Monroe^{7

2

3

8}

Affiliations

¹ Joint Quantum Institute, University of Maryland, College Park, MD 20742.
² Department of Physics, University of Maryland, College Park, MD 20742.
³ Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742.
⁴ Intel Labs, Intel Corporation, Hillsboro, OR 97124.
⁵ Óptica y Electrónica, Instituto Nacional de Astrofísica, Puebla 72840, Mexico.
⁶ Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada.
⁷ Joint Quantum Institute, University of Maryland, College Park, MD 20742; monroe@umd.edu.
⁸ Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742.

Abstract

Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum-classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

Keywords: Ising model; quantum computing; quantum simulation; thermofield double state; trapped ions.