Minimal resources for open-system universality

Determine the minimal resources required for open-system state and channel universality, including the number of auxiliary qubits, preparable environment states, and coherent control parameters.

Background

The paper constructs open-system protocols that achieve universal state preparation and channel synthesis using comparatively small coherent control groups, including a single interaction Hamiltonian with repeated preparation and trace-out of a one-qubit environment. It also establishes exponential lower bounds on worst-case approximation lengths, showing that universality does not by itself make synthesis efficient.

The authors explicitly note that their constructions may not be resource-optimal. The unresolved problem is to identify the minimum number of auxiliary qubits, preparable environment states, and coherent control parameters sufficient for universal state preparation and channel universality in open quantum systems.