State
Polynomial approximation
Chebyshev coefficients, a degree, and the bound the polynomial obeys before anyone rescales it. The degree is the query count a circuit will pay, so this is where an error budget turns into a runtime.
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Work that arrives here
- Polynomial approximation
Given a target function, a domain and an error , return a polynomial of definite parity, bounded on , that is -close to the target on that domain, with an explicit degree.
Work that starts here
- QSP phase factors
Given an admissible polynomial, compute the phase sequence that makes the quantum-signal-processing product reproduce it to accuracy in classical finite-precision arithmetic.