Three-qubit-state preparation: Classification and explicit circuits

초록

We develop a deterministic and fully explicit framework for preparing an arbitrary three-qubit pure state from its computational-basis amplitudes. Our approach exploits bipartite Schmidt structure: we classify three-qubit states into five types with respect to a 1|2 bipartition and provide concrete, concurrence-based criteria that identify the type and extract the required Schmidt data directly from the target amplitudes. For each type, we derive an explicit circuit template built from elementary single-qubit rotations and CNOT gates, together with an end-to-end parameter map that specifies all gate angles and phases without procedural ambiguity. The resulting constructions are arranged to use only CNOT gates between adjacent qubits, making them directly deployable on restricted-connectivity hardware. As an application, we group widely used three-qubit states into four representative classes and obtain class-adapted circuits whose parameters are read off from the amplitude and phase data; in several regimes, these specialized circuits reduce entangling-gate count and overall depth relative to universal templates.

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