Preparing High-Fidelity Thermofield Double States

TL;DR

This paper proposes a method to prepare high-fidelity thermofield double states on quantum computers using a parent Hamiltonian approach and adiabatic evolution, applicable to various models and system sizes.

Contribution

It introduces a gapped parent Hamiltonian construction for TFD states and demonstrates its effectiveness through numerical studies on different models.

Findings

High overlap of the parent Hamiltonian ground state with TFD states for small system sizes.

An additional penalty term can mitigate the exponential decay of overlap with system size.

Method is broadly applicable beyond specific models or temperature regimes.

Abstract

A major promise of quantum computers is the controlled preparation of many-body quantum states beyond the reach of efficient classical computation. Among the most important targets are thermal mixed states and their thermofield double (TFD) purifications, which play central roles in quantum many-body physics and quantum gravity. For target systems with a bounded energy spectrum that obey the eigenstate thermalization hypothesis (ETH), we present a parent Hamiltonian built from two copies of the target Hamiltonian and ultra-local couplings between the copies, which we argue is gapped with a ground state that approximates a TFD state of the target Hamiltonian. By adiabatically evolving down from strong coupling, we can thus prepare a high-fidelity TFD state. We study two variants of the parent Hamiltonian using numerical methods in two classes of models: mixed field Ising models in one and two dimensions and non-local "spin Sachdev-Ye-Kitaev'' models. In the simpler variant, the parent Hamiltonian ground state has high overlap with a TFD for system sizes accessible to near-term quantum devices. However, the global overlap decays exponentially with the number of qubits, with a small error per degree of freedom. The second variant introduces an additional penalty term which can be tuned to reduce or remove the decay of the overlap with system size. Together with a general ETH-based analysis, these results suggest a broadly applicable method for TFD preparation that is not limited to particular temperatures or geometric locality.