Adaptive variational algorithms for quantum Gibbs state preparation

Abstract

The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ansätze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effectiveness of our approach, we numerically demonstrate that our algorithm can prepare high-fidelity Gibbs states across a broad range of temperatures and for a variety of Hamiltonians.[1] M. Kieferová and N. Wiebe, Tomography and generative training with quantum Boltzmann machines,

Markov chain Monte Carlo enhanced variational quantum algorithms

“…Likewise, while classical MCMC methods have been used to simulate quantum computing routines [40,41], our work is unique in that it uses classical MCMC to enhance the performance of variational quantum algorithms. Similarly, while the preparation of a Gibbs state on a variational quantum computer had been previously proposed via an approximate Fourier series [42] and free energy minimization [43], and has been suggested since the release of this work using time evolution [44] and efficient free energy minimization [45], these methods do not employ MCMC techniques.…”

How Much Entanglement Do Quantum Optimization Algorithms Require?

“…To improve the performance of QAOA, one can modify it with the ADAPT approach [37,38]. This algorithm, dubbed ADAPT-QAOA, builds up the ansatz layer by layer.…”