Efficient generation of random multipartite entangled states using time optimal unitary operations

TL;DR

This paper explores the efficient generation of random multipartite entangled states through time-optimal two-qubit gates, analyzing how different optimality criteria and entanglement measures influence the process.

Contribution

It introduces a framework for generating multipartite entangled states using time-optimal unitary operations based on the quantum brachistochrone formalism.

Findings

Optimal quantum gates depend on the chosen optimality criterion.

Convergence to Haar-random entanglement varies with entanglement measures.

Different Hamiltonians yield different time-efficient entangling operations.

Abstract

We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.