Optimizing for an arbitrary perfect entangler: I. Functionals

TL;DR

This paper introduces a new functional for optimal control that specifically targets the full set of two-qubit perfect entanglers, aiding the design of entangling quantum gates across various platforms.

Contribution

A novel functional based on local invariants is derived to identify and optimize two-qubit perfect entanglers in quantum control problems.

Findings

Functional effectively identifies perfect entanglers

Optimization improves quantum gate design

Applicable to multiple quantum platforms

Abstract

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally-entangled state out of some initial product state. The functional depends on easily-computable local invariants and uniquely determines when a gate evolves into a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.