planted noisy kXOR algorithm

Author: anurudhp

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -93,6 +93,8 @@
 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.guided_hamiltonian
 import qualtran.bloqs.mcmt.and_bloq
 import qualtran.bloqs.mcmt.controlled_via_and
 import qualtran.bloqs.mcmt.ctrl_spec_and
@@ -904,6 +906,49 @@
     ),
 ]
 
+# --------------------------------------------------------------------------
+# -----   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,
+        ],
+    ),
+    # -----   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),
@@ -912,5 +957,6 @@
     ('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

@@ -137,6 +137,16 @@ 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/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/max_k_xor_sat/__init__.py

@@ -12,4 +12,8 @@
 #  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/guided_hamiltonian/__init__.py

@@ -0,0 +1,15 @@
+#  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 .guided_hamiltonian import GuidedHamiltonian, GuidedHamiltonianPhaseEstimation
+from .walk_operator import QubitizedWalkOperator