TE-PAI: Exact Time Evolution by Sampling Random Circuits

Understand

Simulating time evolution under quantum Hamiltonians is one of the most natural applications of quantum computers.

• We introduce TE-PAI, which simulates time evolution exactly by sampling random quantum circuits for the purpose of estimating observable expectation values at the cost of an increased circuit repetition.
• The approach builds on the Probabilistic Angle Interpolation (PAI) technique and we prove that it simulates time evolution without discretisation or algorithmic error while achieving shallow circuit depths with optimal scaling that saturates the Lieb-Robinson bound.
• Another significant advantage of TE-PAI is that it only requires executing random circuits that consist of Pauli rotation gates of only two kinds of rotation angles $\pm\Delta$ and $\pi$, along with measurements.