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The power statement applies the unitary operation raised to some integer power, where the unitary is specified as a nested statement block.

Syntax

Semantics

  • If the statement block specifies the unitary operation UU on some quantum object, power applies UexponentU^{exponent}.
  • In the general case, the statement block is iterated over exponent times, but in some important special cases the operation is implemented more efficiently.
  • Quantum variables declared outside the power statement and used inside its nested block must be initialized prior to it and remain initialized subsequently.
  • Quantum variables declared inside the power statement, including in nested function calls, must be uninitialized at the end of the statement.

Examples

In the following example power is applied 3 times - to gate-level functions H and RX, and to a user-defined function foo. It demonstrates both special and general treatment of the power operation.
Synthesizing this model creates the quantum program shown below. Because two consecutive applications of H cancel each other out, raising H to the power of 5 is equivalent to applying H once. Raising RX with rotation angle π/8\pi / 8 to the power 5 is equivalent to applying RX with rotation angle 5×π/85 \times \pi / 8. However, raising foo to the power 2 requires 2 consecutive applications of foo. visualization of the power example bright