Preparing a Thermofield Double State with Feedback Quantum Algorithms

Abstract

The efficient preparation of correlated thermal states, such as the Thermofield Double (TFD) state, is a fundamental prerequisite for simulating quantum gravity models and many-body thermodynamics on quantum processors. In this work, we investigate the ground state preparation of the Two Coupled Sachdev-Ye-Kitaev model, known as the Maldacena-Qi model, which is dual to a traversable wormhole in $AdS_2$, utilizing feedback-based quantum algorithms. We demonstrate that the standard feedback-based quantum algorithm (FALQON) and its time-rescaled variant (TR-FALQON) face severe kinetic limitations in this system, failing to converge to the highly entangled ground state when initialized in trivial product states. To overcome these barriers, we propose the hybrid ITE-TR-FALQON protocol, which integrates the imaginary-time evolution present in imaginary-time-enhanced FALQON (ITE-FALQON) with the time-rescaling mechanism. Our numerical results indicate that the introduction of non-unitary dynamics is strictly necessary to break symmetry traps and filter out excited states, while time-rescaling drastically accelerates algorithm convergence. The proposed method achieves fidelities close to unity and reproduces the von Neumann and Rényi entropy spectra of the exact TFD state with high precision.