planted noisy kXOR algorithm

Author: anurudhp

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -91,6 +91,9 @@
 import qualtran.bloqs.gf_arithmetic.gf2_multiplication
 import qualtran.bloqs.gf_arithmetic.gf2_square
 import qualtran.bloqs.hamiltonian_simulation.hamiltonian_simulation_by_gqsp
+import qualtran.bloqs.max_k_xor_sat
+import qualtran.bloqs.max_k_xor_sat.arithmetic
+import qualtran.bloqs.max_k_xor_sat.guided_hamiltonian
 import qualtran.bloqs.mcmt.and_bloq
 import qualtran.bloqs.mcmt.controlled_via_and
 import qualtran.bloqs.mcmt.ctrl_spec_and
@@ -878,6 +881,58 @@
     ),
 ]
 
+# --------------------------------------------------------------------------
+# -----   Quartic Speedups paper  ------------------------------------------
+# --------------------------------------------------------------------------
+ALGO_QUARTIC_SPEEDUPS = [
+    # -----   Preliminaries  ------------------------------------------
+    NotebookSpecV2(
+        title='Guided (sparse) Hamiltonian Problem',
+        module=qualtran.bloqs.max_k_xor_sat.guided_hamiltonian.guided_hamiltonian,
+        bloq_specs=[
+            qualtran.bloqs.max_k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_DOC,
+            qualtran.bloqs.max_k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_PHASE_ESTIMATION_DOC,
+        ],
+    ),
+    NotebookSpecV2(
+        title='Arithmetic Primitives',
+        module=qualtran.bloqs.max_k_xor_sat.arithmetic,
+        bloq_specs=[
+            qualtran.bloqs.max_k_xor_sat.arithmetic.sort_in_place._SORT_IN_PLACE_DOC,
+            qualtran.bloqs.max_k_xor_sat.arithmetic.symmetric_difference._SYMMETRIC_DIFFERENCE_DOC,
+            qualtran.bloqs.max_k_xor_sat.arithmetic.has_duplicates._HAS_DUPLICATES_DOC,
+        ],
+    ),
+    # -----   Algorithm  ------------------------------------------
+    NotebookSpecV2(
+        title='kXOR: Instance load Oracles',
+        module=qualtran.bloqs.max_k_xor_sat.load_kxor_instance,
+        bloq_specs=[qualtran.bloqs.max_k_xor_sat.load_kxor_instance._LOAD_INSTANCE_DOC],
+    ),
+    NotebookSpecV2(
+        title='Noisy kXOR: Guiding State',
+        module=qualtran.bloqs.max_k_xor_sat.guiding_state,
+        bloq_specs=[
+            qualtran.bloqs.max_k_xor_sat.guiding_state._SIMPLE_GUIDING_STATE_DOC,
+            qualtran.bloqs.max_k_xor_sat.guiding_state._GUIDING_STATE_DOC,
+        ],
+    ),
+    NotebookSpecV2(
+        title='Noisy kXOR: Block-encoding the Kikuchi Matrix',
+        module=qualtran.bloqs.max_k_xor_sat.kikuchi_block_encoding,
+        bloq_specs=[
+            qualtran.bloqs.max_k_xor_sat.kikuchi_adjacency_matrix._KIKUCHI_MATRIX_ENTRY_DOC,
+            qualtran.bloqs.max_k_xor_sat.kikuchi_adjacency_list._KIKUCHI_NONZERO_INDEX_DOC,
+            qualtran.bloqs.max_k_xor_sat.kikuchi_block_encoding._KIKUCHI_HAMILTONIAN_DOC,
+        ],
+    ),
+    NotebookSpecV2(
+        title='Algorithm: Planted Noise kXOR',
+        module=qualtran.bloqs.max_k_xor_sat.planted_noisy_kxor,
+        bloq_specs=[qualtran.bloqs.max_k_xor_sat.planted_noisy_kxor._PLANTED_NOISY_KXOR_DOC],
+    ),
+]
+
 NB_BY_SECTION = [
     ('Basic Gates', BASIC_GATES),
     ('Chemistry', CHEMISTRY),
@@ -886,5 +941,6 @@
     ('GF Arithmetic', GF_ARITHMETIC),
     ('Rotations', ROT_QFT_PE),
     ('Block Encoding', BLOCK_ENCODING),
+    ('Paper: Quartic Quantum Speedups for Planted Inference', ALGO_QUARTIC_SPEEDUPS),
     ('Other', OTHER),
 ]

docs/bloqs/index.rst

@@ -134,6 +134,17 @@ Bloqs Library
     block_encoding/chebyshev_polynomial.ipynb
     block_encoding/lcu_block_encoding.ipynb
 
+.. toctree::
+    :maxdepth: 2
+    :caption: Paper: Quartic Quantum Speedups for Planted Inference:
+
+    max_k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb
+    max_k_xor_sat/arithmetic/arithmetic.ipynb
+    max_k_xor_sat/load_kxor_instance.ipynb
+    max_k_xor_sat/guiding_state.ipynb
+    max_k_xor_sat/kikuchi_block_encoding.ipynb
+    max_k_xor_sat/planted_noisy_kxor.ipynb
+
 .. toctree::
     :maxdepth: 2
     :caption: Other:

qualtran/bloqs/arithmetic/sorting.py

@@ -23,6 +23,7 @@
     bloq_example,
     BloqBuilder,
     BloqDocSpec,
+    DecomposeNotImplementedError,
     DecomposeTypeError,
     QBit,
     QUInt,
@@ -222,8 +223,6 @@ def __attrs_post_init__(self):
         k = self.half_length
         if not is_symbolic(k):
             assert k >= 1, "length of input lists must be positive"
-            # TODO(#1090) support non-power-of-two input lengths
-            assert (k & (k - 1)) == 0, "length of input lists must be a power of 2"
 
     @cached_property
     def signature(self) -> 'Signature':
@@ -249,14 +248,16 @@ def is_symbolic(self):
     def build_composite_bloq(
         self, bb: 'BloqBuilder', xs: 'SoquetT', ys: 'SoquetT'
     ) -> dict[str, 'SoquetT']:
-        if is_symbolic(self.half_length):
+        k = self.half_length
+        if is_symbolic(k):
             raise DecomposeTypeError(f"Cannot decompose symbolic {self=}")
+        if (k & (k - 1)) == 0:
+            # TODO(#1090) support non-power-of-two input lengths
+            raise DecomposeNotImplementedError("length of input lists must be a power of 2")
 
         assert isinstance(xs, np.ndarray)
         assert isinstance(ys, np.ndarray)
 
-        k = self.half_length
-
         first_round_junk = []
         for i in range(k):
             xs[i], ys[k - 1 - i], anc = bb.add(Comparator(self.bitsize), a=xs[i], b=ys[k - 1 - i])

qualtran/bloqs/max_k_xor_sat/__init__.py

@@ -0,0 +1,19 @@
+#  Copyright 2024 Google LLC
+#
+#  Licensed under the Apache License, Version 2.0 (the "License");
+#  you may not use this file except in compliance with the License.
+#  You may obtain a copy of the License at
+#
+#      https://www.apache.org/licenses/LICENSE-2.0
+#
+#  Unless required by applicable law or agreed to in writing, software
+#  distributed under the License is distributed on an "AS IS" BASIS,
+#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#  See the License for the specific language governing permissions and
+#  limitations under the License.
+from .guiding_state import GuidingState, SimpleGuidingState
+from .kikuchi_adjacency_list import KikuchiNonZeroIndex
+from .kikuchi_adjacency_matrix import KikuchiMatrixEntry
+from .kikuchi_block_encoding import KikuchiHamiltonian, KikuchiMatrixEntry, KikuchiNonZeroIndex
+from .kxor_instance import Constraint, KXorInstance
+from .planted_noisy_kxor import AliceTheorem, PlantedNoisyKXOR

qualtran/bloqs/max_k_xor_sat/arithmetic/__init__.py

@@ -0,0 +1,16 @@
+#  Copyright 2024 Google LLC
+#
+#  Licensed under the Apache License, Version 2.0 (the "License");
+#  you may not use this file except in compliance with the License.
+#  You may obtain a copy of the License at
+#
+#      https://www.apache.org/licenses/LICENSE-2.0
+#
+#  Unless required by applicable law or agreed to in writing, software
+#  distributed under the License is distributed on an "AS IS" BASIS,
+#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#  See the License for the specific language governing permissions and
+#  limitations under the License.
+from .has_duplicates import HasDuplicates
+from .sort_in_place import SortInPlace
+from .symmetric_difference import SymmetricDifference