planted noisy kXOR algorithm

Author: anurudhp

dev_tools/autogenerate-bloqs-notebooks-v2.py

@@ -72,6 +72,7 @@
 import qualtran.bloqs.block_encoding.phase
 import qualtran.bloqs.block_encoding.product
 import qualtran.bloqs.block_encoding.sparse_matrix
+import qualtran.bloqs.block_encoding.sparse_matrix_hermitian
 import qualtran.bloqs.block_encoding.tensor_product
 import qualtran.bloqs.block_encoding.unitary
 import qualtran.bloqs.bookkeeping
@@ -111,6 +112,18 @@
 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.arithmetic.has_duplicates
+import qualtran.bloqs.max_k_xor_sat.arithmetic.sort_in_place
+import qualtran.bloqs.max_k_xor_sat.arithmetic.symmetric_difference
+import qualtran.bloqs.max_k_xor_sat.guided_hamiltonian
+import qualtran.bloqs.max_k_xor_sat.guided_hamiltonian.guided_hamiltonian
+import qualtran.bloqs.max_k_xor_sat.guided_hamiltonian.walk_operator
+import qualtran.bloqs.max_k_xor_sat.guiding_state
+import qualtran.bloqs.max_k_xor_sat.kikuchi_block_encoding
+import qualtran.bloqs.max_k_xor_sat.load_kxor_instance
+import qualtran.bloqs.max_k_xor_sat.planted_noisy_kxor
 import qualtran.bloqs.mcmt.and_bloq
 import qualtran.bloqs.mcmt.controlled_via_and
 import qualtran.bloqs.mcmt.ctrl_spec_and
@@ -746,6 +759,13 @@
         module=qualtran.bloqs.block_encoding.sparse_matrix,
         bloq_specs=[qualtran.bloqs.block_encoding.sparse_matrix._SPARSE_MATRIX_DOC],
     ),
+    NotebookSpecV2(
+        title='Sparse Matrix (Hermitian)',
+        module=qualtran.bloqs.block_encoding.sparse_matrix_hermitian,
+        bloq_specs=[
+            qualtran.bloqs.block_encoding.sparse_matrix_hermitian._SPARSE_MATRIX_HERMITIAN_DOC
+        ],
+    ),
     NotebookSpecV2(
         title='Chebyshev Polynomial',
         module=qualtran.bloqs.block_encoding.chebyshev_polynomial,
@@ -875,6 +895,57 @@
         ],
     ),
 ]
+# --------------------------------------------------------------------------
+# -----   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],
+    ),
+]
 
 # --------------------------------------------------------------------------
 # -----   Concepts   -------------------------------------------------------
@@ -902,6 +973,7 @@
     ('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

@@ -129,9 +129,21 @@ Bloqs Library
     block_encoding/phase.ipynb
     block_encoding/linear_combination.ipynb
     block_encoding/sparse_matrix.ipynb
+    block_encoding/sparse_matrix_hermitian.ipynb
     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/basic_gates/x_basis.py

@@ -227,13 +227,14 @@ def my_tensors(
 
     def get_ctrl_system(self, ctrl_spec: 'CtrlSpec') -> Tuple['Bloq', 'AddControlledT']:
         from qualtran.bloqs.basic_gates import CNOT, Toffoli
+        from qualtran.bloqs.mcmt import ControlledViaAnd
 
         if ctrl_spec == CtrlSpec():
             bloq: 'Bloq' = CNOT()
         elif ctrl_spec == CtrlSpec(cvs=(1, 1)):
             bloq = Toffoli()
         else:
-            return super().get_ctrl_system(ctrl_spec)
+            return ControlledViaAnd.make_ctrl_system(self, ctrl_spec)
 
         def add_controlled(
             bb: 'BloqBuilder', ctrl_soqs: Sequence['SoquetT'], in_soqs: Dict[str, 'SoquetT']

qualtran/bloqs/block_encoding/__init__.py

@@ -23,5 +23,6 @@
 from qualtran.bloqs.block_encoding.phase import Phase
 from qualtran.bloqs.block_encoding.product import Product
 from qualtran.bloqs.block_encoding.sparse_matrix import SparseMatrix
+from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import SparseMatrixHermitian
 from qualtran.bloqs.block_encoding.tensor_product import TensorProduct
 from qualtran.bloqs.block_encoding.unitary import Unitary

qualtran/bloqs/block_encoding/block_encoding_base.py

@@ -84,6 +84,14 @@ def ancilla_bitsize(self) -> SymbolicInt:
     def resource_bitsize(self) -> SymbolicInt:
         """The number of resource qubits not counted in ancillas."""
 
+    @property
+    def ctrl_bitsize(self) -> SymbolicInt:
+        """The number of control qubits, useful to define optimized custom controlled circuits.
+
+        Usually either 0 or 1, as all other control cases can be reduced to 1.
+        """
+        return 0
+
     @property
     @abc.abstractmethod
     def epsilon(self) -> SymbolicFloat: