Generation of Thermofield Double States and Critical Ground States with\n a Quantum Computer

Abstract

Finite-temperature phases of many-body quantum systems are fundamental to\nphenomena ranging from condensed-matter physics to cosmology, yet they are\ngenerally difficult to simulate. Using an ion trap quantum computer and\nprotocols motivated by the Quantum Approximate Optimization Algorithm (QAOA),\nwe generate nontrivial thermal quantum states of the transverse-field Ising\nmodel (TFIM) by preparing thermofield double states at a variety of\ntemperatures. We also prepare the critical state of the TFIM at zero\ntemperature using quantum-classical hybrid optimization. The entanglement\nstructure of thermofield double and critical states plays a key role in the\nstudy of black holes, and our work simulates such nontrivial structures on a\nquantum computer. Moreover, we find that the variational quantum circuits\nexhibit noise thresholds above which the lowest depth QAOA circuits provide the\nbest results.\n