Parent Hamiltonian Reconstruction via Inverse Quantum Annealing

TL;DR

This paper introduces inverse quantum annealing, a numerical method to reconstruct parent Hamiltonians from a given wavefunction by simulating an adiabatic evolution based on local expectation values.

Contribution

The paper presents a novel inverse quantum annealing approach that efficiently reconstructs parent Hamiltonians using local expectation values and adiabatic state deformation.

Findings

Successfully applied to Kitaev fermionic chain and quantum Ising chain.

Produces approximate parent Hamiltonians with locality depending on state correlations.

Requires only local expectation values, making it computationally efficient.

Abstract

Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|\psi\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a numerical method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the states $|\psi(\lambda(t))\rangle$, starting from a simple state $|\psi_0\rangle$ with a known $\hat{\mathcal{H}}_0$, generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. The method, implemented through a projection onto a set of local operators, only requires the knowledge of local expectation values, and, for long annealing times, leads to an approximate parent Hamiltonian whose degree of locality depends on the correlations built up by the states $|\psi(\lambda)\rangle$. We illustrate the method on two paradigmatic models: the Kitaev fermionic chain and a quantum Ising chain in longitudinal and transverse fields.