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Implements exact arithmetic for complex numbers of the form: (a + be^(ipi/4) + ci + de^(-i*pi/4)) * 2^power This representation enables exact computation of phases in ZX-calculus graphs without floating-point errors.

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class ExactScalarArray

ExactScalarArray(coeffs: Array, power: Array | None = None)
Exact scalar array for ZX-calculus phase arithmetic using dyadic representation. Represents values of the form (c_0 + c_1·ω + c_2·ω² + c_3·ω³) × 2^power where ω = e^(iπ/4). This enables exact computation without floating-point errors.

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prod

prod(axis: int = -1) -> ExactScalarArray
Compute product along the specified axis using associative scan. Returns identity (1+0i with power 0) for empty reductions. Parameters:
  • axis (int) — The axis along which to compute the product.
Returns:
  • ExactScalarArray — ExactScalarArray with the product computed along the axis.

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sum

sum(axis: int = -1) -> ExactScalarArray
Sum elements along the specified axis using normalized pairwise adds. Parameters:
  • axis (int) — The axis along which to sum.
Returns:
  • ExactScalarArray — ExactScalarArray with the sum computed along the axis.

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to_complex

to_complex() -> jax.Array
Convert to complex number.