Qualtran
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Phase estimation module improvements
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Add bloqs for https://arxiv.org/abs/2303.12503 - This is a 2 qubit version of the LPResourceState based QPE which we already have. This would also require adding a bloq for semiclassical QFT, which can be useful for other contexts.
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Add phase estimation bloqs for optimising confidence intervals instead of minimizing Holevo variance (like done in (1) and our existing bloqs). This was useful in, for example, amplitude estimation for https://arxiv.org/pdf/2209.13581 (Appendix D). The main contribution here would be to add a new bloq for preparing another special initial state.
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Most importantly, write a notebook which explains the existence and utility of these different variations for phase estimation; i.e. (a) Uses of different initial states for optimizing different properties of the estimator like holevo variance / confidence intervals etc. (b) Use of the semiclassical QFT to use 2 ancilla qubits instead of using K ancilla qubits and (c) Use of the doubling trick to apply U and U^\dagger (qubitization qpe bloq) instead of U and I (textbook version) for further optimizing the constant factors and "doubling" the phase difference.
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Maybe also add unary iteration based phase estimation. cc - https://github.com/quantumlib/Qualtran/issues/590