Quantum computation with the eigenstate thermalization hypothesis instead of wavefunction preparation

It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum systems to produce an equal superposition of eigenstates. The quantum phase estimation subroutine then allows for the computations of functions of the input operator, leading to a variety of methods in linear algebra. The algorithm circumvents the need for elaborate wavefunction preparation on the quantum computer to find the solution of the linear algebra problem in poly-logarithmic time.