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

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.

Charged complexity and the thermofield double state

“…Furthermore, using both CV and CA, holographic complexity was found to grow quadratically C ∼ t 2 at early times due to the time-reversal symmetry of the charged black hole geometry. 35 Finally, the rate of change in complexity was found to vanish at all times in the extremal (vanishing temperature) limit using both the CV and the CA complexity proposals. Our analysis of the cTFD in the previous section resulted in the following features which can be tested for consistency and qualitatively compared to the holographic results.…”

“…charged black holes whose horizon radius is much larger, or of the same order as the AdS scale. 35 The charged case smoothly interpolates to the neutral case, where CA interestingly gives a neighbourhood around t = 0 where the rate of change in holographic complexity is exactly zero, then discontinuously becomes infinitely negative, only to quickly grow to a positive value in a short time [39].…”

“…TFD and cTFD states received special attention in holographic studies due to their duality to (neutral and charged) eternal black holes of the corresponding temperature [30] and chemical potential [31,32]. Outside the context of holography, a number of works have been written on building the TFD state in the laboratory [33][34][35][36][37] and these further motivate focusing on the TFD for simple quantum mechanical systems. Since charge is very natural in an experimental setup, we expect that the cTFD state is also a natural state to study in the laboratory.…”

Toward simulating superstring/M-theory on a quantum computer

“…For finite temperature state, one could use the algorithms discussed in[95,96,114] to prepare thermofield double states.…”

Cross-Platform Comparison of Arbitrary Quantum Computations

“…Here, we demonstrate a cross-platform comparison based on randomized-measurement [8][9][10] , obtained independently over different times and locations on several disparate quantum computers built by different teams using different technologies, comparing the outcomes of four families of quantum circuits. We use four ion-trap platforms, the University of Maryland (UMD) EU-RIQA system 11 (referred to as UMD 1), the University of Maryland TIQC system 12 (UMD 2), and two IonQ quantum computers 13,14 (IonQ 1, IonQ 2), as well as five separate IBM superconducting quantum computing systems hosted in New York, ibmq belem (IBM 1), ibmq casablanca (IBM 2), ibmq melbourne (IBM 3), ibmq quito (IBM 4), and ibmq rome (IBM 5) 15 . See Supplementary Information Sec.…”