Computing geometric entanglement via quantum hueristics on near-term spin qubit hardware

Entanglement is one of the fundamental properties of a quantum state

and is a crucial differentiator between classical and quantum computation.

Various definitions and measures of entanglement exist,

tailored to different contexts and applications in quantum information theory,

yet few methods for computing these measures are viable on near-term quantum hardware.

We present a quantum adaptation of the iterative higher-order power method for

estimating the geometric measure of entanglement of multi-qubit pure states.

This approach is a hueristic for the NP-hard problem "rank-1 tensor approximation".

We demonstarate the praciticality of this method by showing the steps to

implement it on a silicon spin quantum computer.

This algorithm has several properties that make it suitable for near-term quantum hardware.

In particular the algorithm still converges despite the effect of noise (up to 1%).

We analsyse the effect of noise and show it causes a shift in the converged value.

We then derive a simple formula to mitigate the effect of noise on the computation.