  We introduce Port-Based State Preparation (PBSP), a teleportation task where
Alice holds a complete classical description of the target state and Bob's
correction operations are restricted to only tracing out registers. We show a
protocol that implements PBSP with error decreasing exponentially in the number
of ports, in contrast to the polynomial trade-off for the related task of
Port-Based Teleportation, and we prove that this is optimal when a maximally
entangled resource state is used.
  As an application, we introduce approximate Universal Programmable Hybrid
Processors (UPHP). Here the goal is to encode a unitary as a quantum state, and
the UPHP can apply this unitary to a quantum state when knowing its classical
description. We give a construction that needs strictly less memory in terms of
dimension than the optimal approximate Universal Programmable Quantum Processor
achieving the same error. Additionally, we provide lower bounds for the optimal
trade-off between memory and error of UPHPs.
