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Quantum State Preparation

State preparation algorithms are essential building blocks in quantum simulation and optimization. The present folder explores advanced quantum state preparation techniques, including adaptive variational eigensolvers and block-encoding–based Gibbs state generation. The examples emphasize both practical hybrid workflows and algorithmic primitives.

  • ADAPT VQE - The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) is a variational hybrid algorithm. It constitutes an extension of the Variational Quantum Eigensolver (VQE) framework, constructing problem-specific solution in an adaptive manner. By increasing the number of measurements, the algorithms produces shallower circuit relative to the standard VQE algorithm.

  • Gibbs state preparation - An important quantum primitive employed as a subroutine in higher-level algorithms, including quantum methods for solving semidefinite programs, Boltzmann sampling, and Metropolis-type algorithms. The procedure prepares a quantum thermal (Gibbs) state by implementing a block-encoding of the Lindbladian superoperator, which generates the open-system dynamics of a quantum system coupled to a thermal bath. Applying this block-encoding effectively drives the initial state toward thermal equilibrium, thereby producing the corresponding Gibbs state. The implementation relies on an operator Fourier transform combined with mid-circuit weak measurements, leveraging the quantum Zeno effect to enhance runtime performance and improve overall algorithmic efficiency.