RobustPhaseEstimation operation

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Warning

This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.

Please see https://aka.ms/qdk.api for the API documentation for the Modern QDK.

Namespace: Microsoft.Quantum.Characterization

Package: Microsoft.Quantum.Standard

Performs the robust non-iterative quantum phase estimation algorithm for a given oracle U and eigenstate, and provides a single real-valued estimate of the phase with variance scaling at the Heisenberg limit.

operation RobustPhaseEstimation (bitsPrecision : Int, oracle : Microsoft.Quantum.Oracles.DiscreteOracle, targetState : Qubit[]) : Double

Input

bitsPrecision : Int

This provides an estimate of $\phi$ with standard deviation $\sigma \le 2\pi / 2^\text{bitsPrecision}$ using a number of queries scaling like $\sigma \le 10.7 \pi / \text{# of queries}$.

oracle : DiscreteOracle

An operation implementing $U^m$ for given integer powers $m$.

targetState : Qubit[]

A quantum register that $U$ acts on. If it stores an eigenstate $\ket{\phi}$ of $U$, then $U\ket{\phi} = e^{i\phi} \ket{\phi}$ for $\phi\in(-\pi,\pi]$ an unknown phase.

Output : Double

Remarks

In the limit of a large number of queries, Cramer-Rao lower bounds for the standard deviation of the estimate of $\phi$ satisfy $\sigma \ge 2 \pi / \text{# of queries}$.

References

  • Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation Shelby Kimmel, Guang Hao Low, Theodore J. Yoder https://arxiv.org/abs/1502.02677