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Exact amplitude amplification
If you’ve ever wondered whether Grover’s algorithm can amplify a desired state all the way to probability 1, the answer is yes. This capability is implemented in Classiq’s open library through the exact_amplitude_amplification function.
In the standard Grover approach, each iteration rotates the state vector toward the desired subspace by a fixed angle, determined by the ratio of good vs. bad states. Unless this angle divides pi exactly, repeated applications only approximate the desired state, never reaching it with certainty. While this suffices for search tasks, it can be limiting for state preparation.
The function implementation of the exact version is based on the paper Quantum state preparation without coherent arithmetic. By coupling the system to an ancillary qubit, the method modifies the effective rotation angle so that it divides pi exactly. As a result, after a constant number of Grover iterations, the target state is reached with probability 1.
As a toy example, consider amplifying the state ∣1⟩ from a single qubit superposition. Standard Grover overshoots, but the exact variant lands precisely on ∣1⟩. See the full example here.
For a more advanced usage example, see this community notebook (by Seungmin Jeon), where the function is used to exactly prepare and amplify a Gaussian state.
If you’ve ever wondered whether Grover’s algorithm can amplify a desired state all the way to probability 1, the answer is yes. This capability is implemented in Classiq’s open library through the exact_amplitude_amplification function.
In the standard Grover approach, each iteration rotates the state vector toward the desired subspace by a fixed angle, determined by the ratio of good vs. bad states. Unless this angle divides pi exactly, repeated applications only approximate the desired state, never reaching it with certainty. While this suffices for search tasks, it can be limiting for state preparation.
The function implementation of the exact version is based on the paper Quantum state preparation without coherent arithmetic. By coupling the system to an ancillary qubit, the method modifies the effective rotation angle so that it divides pi exactly. As a result, after a constant number of Grover iterations, the target state is reached with probability 1.
As a toy example, consider amplifying the state ∣1⟩ from a single qubit superposition. Standard Grover overshoots, but the exact variant lands precisely on ∣1⟩. See the full example here.
For a more advanced usage example, see this community notebook (by Seungmin Jeon), where the function is used to exactly prepare and amplify a Gaussian state.
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