  A physical platform for nodes of the envisioned quantum internet is
long-sought. Here we propose such a platform, along with a conceptually simple
and experimentally uncomplicated quantum information processing scheme,
realized in a system of multiple crystal-phase quantum dots. We introduce novel
location qubits, describe a method to construct a universal set of all-optical
quantum gates, and simulate their performance in realistic structures,
including decoherence sources. Our results show that location qubits can
maintain coherence 5 orders of magnitude longer than single-qubit operation
time, and single-qubit gate errors do not exceed 0.01%. Our scheme paves a
clear way towards constructing multi-qubit solid-state quantum systems with a
built-in photonic interface, such as a multi-qubit quantum register -- a key
building block of the forthcoming quantum internet.
