Hamiltonian dynamics and computational utility of half-qubits

Determine whether there exists a Hamiltonian acting on half-qubits whose fused evolution reproduces a prescribed qubit channel more economically than direct evolution in the qubit description, thereby establishing whether fractional quasi-probability degrees of freedom provide a useful computational resource.

Background

The paper’s fractionalization scheme is kinematical: it constructs half-qubits, their fusion into pure qubits, and their associated local and fused observable structures, but it does not specify a dynamical theory for half-qubits. The open problem asks whether suitable Hamiltonians can reproduce arbitrary prescribed qubit channels after fusion and whether doing so offers a genuine efficiency advantage over ordinary qubit dynamics, rather than merely providing a structural reformulation.