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What makes a QSVT polynomial admissible?
PostedJul 15, 2026
Question: In standard Quantum Singular Value Transformation, why can we not simply choose any real polynomial p(x) and apply it to the singular values of a block-encoded matrix?
A) Because QSVT works only for exactly linear polynomials
B) Because the polynomial must satisfy structural constraints such as boundedness and parity conditions compatible with a unitary phase sequence
C) Because QSVT can transform eigenvalues but not singular values
D) Because the block-encoding normalization α must always equal one
Correct: B
Explanation: QSVT implements polynomial transformations through unitary signal-processing sequences. The target polynomial must be physically realizable inside a unitary construction, so boundedness and parity-type constraints matter. Arbitrary polynomials must usually be approximated by admissible ones.
Topic: advanced quantum computing / QSVT / polynomial constraints