Seminar at CPHT February 27th Friday

Classical simulation of quantum computation faces an immediate storage problem: a system of n qubits requires 2^n complex numbers to describe, an amount that grows exponentially beyond the reach of a modern supercomputer. To address this issue, we utilize tensor network representations (MPS) coupled with quantum trajectories to efficiently represent our state. These trajectories describe stochastic numerical evolutions that replace a single, massive density matrix with an ensemble of individual "paths".

 

However, this computational efficiency comes at a statistical price. Indeed, efficient MPS representation requires low entanglement, so we tend to try and minimize it. By doing so during each trajectory, we observed empirically that the statistical variance of the measured observable explodes. We then have cheaper individual simulations, but the need for a larger ensemble of trajectories to have a trustworthy physical measure. How can we characterize and understand this tradeoff?