Minimum-error quantum state discrimination is usually formulated as an optimization over positive operator-valued measures, but a circuit-level formulation is useful when the measurement is implemented with an ancilla and a unitary dilation. A difficulty in such circuits is that multiplexed rotation blocks generally contain angle tables whose size grows exponentially with the number of control qubits. We introduce a Walsh-basis parametrization of these angle tables and restrict the circuit to low-order Walsh components. This gives a structured reduced-parameter family of measurement circuits while keeping the underlying ancilla-assisted architecture fixed. For linearly independent pure-state ensembles, we show that the lowest nontrivial Walsh restriction is sufficient for the part of the circuit that writes the measurement outcome, provided that the optimal measurement basis is implemented by a system-only unitary. We study the resulting models on structured and random pure-state discrimination benchmarks. The numerical experiments compare Walsh-restricted circuits with the unrestricted circuit and with random parameter-matched restrictions, and examine both linearly independent and overcomplete ensembles. In overcomplete cases, increasing the allowed Walsh order improves the observed agreement with the unrestricted circuit in the tested instances. Additional four-qubit checks compare selected Walsh-restricted circuits with the unrestricted circuit. These results support the Walsh representation as a structured approach to quantum measurement design, linking restrictions on circuit controls to discrimination performance.

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• Machine learning
• Quantum algorithms & computation