[WIP] Algorithm for Planted Noisy kXOR

[anurudhp]

A work-in-progress implementation of the paper Quartic quantum speedups for planted inference

Once the algorithm is implemented, I will pull out changes and library updates into separate PRs.

Individual PRs:

• Sparse state preparation via alias sampling #1067
• Permutation Bloq #1110
• Support arbitrary CtrlSpec to single qubit control #1137
• Sparse state preparation via Dense + Permute #1205
• Use symbolics for computing register bitsizes #1353
• HammingWeightCompute: replace ArbitraryClifford with CNOT, support symbolic bitsizes #1355
• Add some missing self-adjoints, use CtrlSpec instead of control_values #1360
• Support more symbolic decompositions #1369
• Flatten nested controls in ControlledViaAnd #1373
• sparse state prep: allow user to pick target bitsize if needed #1430
• Improve interface for bloqs with specialized single-qubit-controlled versions #1451
• Default Bloq.get_ctrl_system: Use And ladder to reduce multiple controls to single control #1456
• Add SparseMatrixHermitian block-encoding #1479
• Simplify QubitizationWalkOperator: remove specializations for control/adjoint and use defaults instead  #1481
• Self adjoint for MCX and MCZ #1502
• Add list primitives from Quartic speedups paper #1503
• Implement Kikuchi guiding state preparation #1504