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Variational Hybrid Quantum Algorithms

Rényi free energy and variational approximations to thermal states

arXiv
Authors: Giacomo Giudice, Aslı Çakan, J. Ignacio Cirac, Mari Carmen Bañuls

Year

2020

Paper ID

564

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

We propose the construction of thermodynamic ensembles that minimize the Rényi free energy, as an alternative to Gibbs states. For large systems, the local properties of these Rényi ensembles coincide with those of thermal equilibrium, and they can be used as approximations to thermal states. We provide algorithms to find tensor network approximations to the 2-Rényi ensemble. In particular, a matrix-product-state representation can be found by using gradient-based optimization on Riemannian manifolds, or via a non-linear evolution which yields the desired state as a fixed point. We analyze the performance of the algorithms and the properties of the ensembles on one-dimensional spin chains.

Why This Paper Matters

  • This paper contributes to the Variational & Hybrid Quantum Algorithms research area in the Quantum Articles archive.
  • It adds a 2020 reference point for readers tracking recent quantum research.
  • We propose the construction of thermodynamic ensembles that minimize the Rényi free energy, as an alternative to Gibbs states.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.12848 [2] arXiv https://arxiv.org/abs/2012.12848 [3] Publisher https://arxiv.org/abs/2012.12848

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