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This function performs a rotation on a series of mm target qubits, where the rotation angle is a linear function of an nn-qubit control register, as follows: ∣x⟩n∣q⟩m→∣x⟩n∏k=1m(cos⁡(ak2x+bk2)−isin⁡(ak2x+bk2)Pk)∣qk⟩\left|x\right\rangle _{n}\left|q\right\rangle _{m}\rightarrow\left|x\right\rangle _{n}\prod_{k=1}^{m}\left(\cos\left(\frac{a_{k}}{2}x+\frac{b_{k}}{2}\right)- i\sin\left(\frac{a_{k}}{2}x+\frac{b_{k}}{2}\right)P_{k}\right)\left|q_{k}\right\rangle where ∣x⟩\left|x\right\rangle is the control register, ∣q⟩\left|q\right\rangle is the target register, each PkP_{k} is one of the three Pauli matrices XX, YY, or ZZ, and aka_{k}, bkb_{k} are the user given slopes and offsets, respectively. For example, the operation of a linear YY rotation on a zero-input qubit is ∣x⟩n∣0⟩→∣x⟩n(cos⁡(a2x+b2)∣0⟩+sin⁡(a2x+b2)∣1⟩)\left|x\right\rangle _{n}\left|0\right\rangle \rightarrow\left|x\right\rangle _{n}\left( \cos\left(\frac{a}{2}x+\frac{b}{2}\right)\left|0\right\rangle +\sin\left(\frac{a}{2}x+\frac{b}{2}\right)\left|1\right\rangle \right) Such a rotation can be realized as a series of controlled rotations as follows: [Ry(2n−1a)]xn−1⋯[Ry(21a)]x1[Ry(20a)]x0Ry(b)\left[R_{y}\left(2^{n-1}a\right)\right]^{x_{n-1}}\cdots \left[R_{y}\left(2^{1}a\right)\right]^{x_{1}} \left[R_{y}\left(2^{0}a\right)\right]^{x_{0}}R_{y}\left(b\right) Function: linear_pauli_rotations Arguments:
  • bases: CArray[int]
  • List of Pauli Enums.
  • slopes: CArray[float]
  • Rotation slopes for each of the given Pauli bases.
  • offsets: CArray[float]
  • Rotation offsets for each of the given Pauli bases.
  • x: QArray[QBit]
  • Quantum state to apply the rotation based on its value.
  • q: QArray[QBit]
  • List of indicator qubits for each of the given Pauli bases.
Notice that bases, slopes, offset and q should be of the same size.

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Example: Three Y Rotations Controlled by a 6-Qubit State

This example generates a quantum program with a 66-qubit control state and 33 target qubits, acted upon by Y rotations with different slopes and offsets.