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Add tapering QPE - #113
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BrendanKKrueger
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Oct 13, 2026
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- Fix ancilla qubit counts
scipy is imported directly in several modules but was only installed transitively.
Prepares any 2^n-amplitude state with uniformly controlled Ry/Rz trees. Gate counts depend only on n and on whether the amplitudes are real, so costs are available without the angles.
Window states can now be built from any two of num_phase_qubits, num_precision_qubits and num_confidence_qubits (or num_phase_qubits alone), with informative errors otherwise. The default uses only the total; windows whose shape depends on the split can override it.
DPSSWindowState prepares the exact DPSS taper of arXiv:2403.18927 on l precision plus m confidence qubits. from_requirements picks the smallest m whose Theorem 1 bound meets the probability of failure; tests check the worst case over phases meets it too.
TruncatedDPSSWindowState keeps only the 2K + 1 lowest frequencies of the DPSS (arXiv:2403.18927 eq. 92) and prepares them with the paper's App. A circuit: an m-qubit state preparation, a phase ramp, sign-extending CNOTs and a QFT. Its failure probability is at most 4x that of the DPSS (eq. 107), for far fewer rotations when l is large.
BandwidthOptimizedWindowState is the taper on the same 2K + 1 frequencies as the truncated DPSS with the smallest average failure probability (arXiv:2403.18927 Sec. VII B), using the same circuit. It is found with an SVD of the out-of-band energy, which stays accurate below the 1e-16 floor of an eigensolver.
qpe_from_pauli_file now passes any algorithm settings through to the config, so other end-to-end tests can reuse it with different window states.
"QPE: QHAT flexible" now accepts ancilla_prep = "dpss", "truncated dpss" or "bandwidth-optimized", sized from energy_error and probability_of_failure or from explicit num_precision_qubits and num_confidence_qubits (either may be replaced by num_phase_qubits). Invalid combinations raise errors that name the config settings. An end-to-end test through a Pauli file checks that the tapered QPE meets its requirements where a rectangular window of the same size does not.
For amplitudes (0.6, 0, 0, 0.8) the second-level angle for prefix 1 is pi (sending |0> to |1>), not 0.
…m, P The tapering paper's symbols for the precision, confidence and total phase qubit counts are specific to that paper. Code, docstrings, the README and tests now say num_precision_qubits, num_confidence_qubits and num_phase_qubits (or N and K where those suffice).
1 - (probability of the 2K + 1 closest estimates) rounded to -2e-16 for the 4-point DPSS at theta = 0 on CI (Python 3.14, Linux), and its square root in test_truncation_bound_pointwise was NaN. Summing the other estimates' probabilities is never negative.
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