Quantum parallel algorithm for the thermal canonical ensemble*

Calculating the thermal average of a physical quantity for quantum many-body systems in the canonical ensemble is one of the most important tasks in computational physics, which requires, however, formidable computational resources for large systems because (i) the dimension M of a state vector increases exponentially as the system size N increases, and (ii) the number of excited states to be included in the sum increases exponentially as temperature T increases. In this talk, I propose an algorithm ( https://arxiv.org/abs/2006.14459 ) that is embarrassingly parallel and expected to work extremely efficient on massive parallel classical supercomputers such as Fugaku, where tensor network representation [1] is introduced as the solution of the first difficulty, and quantum parallelization of METTS algorithm [2] using random state method [3] is introduced as the solution of the second difficulty.

[1] R. Orus, Annals of Physics 349, 117 (2014).
[2] S. R. White, Phys. Rev. Lett. 102, 190601 (2009).
[3] T. Iitaka, and T. Ebisuzaki, Phys. Rev. Lett. 90, 047203 (2003).