  Non-local higher-energy auxiliary states have been successfully used to
entangle pairs of qubits in different quantum computing systems. Typically a
longer-span non-local state or sequential application of few-qubit entangling
gates are needed to produce a non-trivial multiqubit gate. In many cases a
single non-local state that span over the entire system is difficult to use due
to spectral crowding or impossible to have. At the same time, many multiqubit
systems can naturally develop a network of multiple non-local higher-energy
states that span over few qubits each. We show that continuous time quantum
walks can be used to address this problem by involving multiple such states to
perform local and entangling operations concurrently on many qubits. This
introduces an alternative approach to multiqubit gate compression based on
available physical resources. We formulate general requirements for such walks
and discuss configurations of non-local auxiliary states that can emerge in
quantum computing architectures based on self-assembled quantum dots, defects
in diamond, and superconducting qubits, as examples. Specifically, we discuss a
scalable multiqubit quantum register constructed as a single chain with
nearest-neighbor interactions. We illustrate how quantum walks can be
configured to perform single-, two- and three-qubit gates, including Hadamard,
Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs
involved in these gates are investigated.
