Stop col_norm early for < max hamming distance

mthree/compute.pxd

@@ -28,3 +28,6 @@ cdef void compute_col_norms(double * col_norms,
                             unsigned int num_bits,
                             unsigned int num_elems,
                             unsigned int distance) nogil
+
+cdef unsigned int hamming_terms(unsigned int num_bits,
+                                unsigned int distance) nogil

mthree/compute.pyx

@@ -130,8 +130,55 @@ cdef double _inner_col_norm_loop(unsigned int col,
     """
     cdef size_t row
     cdef double col_norm = 0
+    cdef unsigned int num_terms = hamming_terms(num_bits, distance)
+    cdef unsigned int terms = 0
 
     for row in range(num_elems):
         if MAX_DIST or within_distance(row, col, bitstrings, num_bits, distance):
             col_norm += compute_element(row, col, bitstrings, cals, num_bits)
+            terms += 1
+        if terms == num_terms:
+            break
     return col_norm
+
+
+@cython.cdivision(True)
+cdef unsigned int binomial_coeff(unsigned int n, unsigned int k) nogil:
+    """Computes the binomial coefficient n choose k
+
+    Parameters:
+        n (unsigned int):  Number of terms
+        k (unsigned int): Number to choose
+
+    Returns:
+        unsigned int: Resulting number of possibilities
+
+    """
+    if k > n:
+        return 0
+    elif k == 0 or k == n:
+        return 1
+    elif k ==1 or k == (n-1):
+        return n
+    elif k+k < n:
+        return (binomial_coeff(n-1, k-1) * n) / k
+    else:
+        return (binomial_coeff(n-1, k) * n) / (n-k)
+
+
+@cython.boundscheck(False)
+cdef unsigned int hamming_terms(unsigned int num_bits, unsigned int distance) nogil:
+    """Compute the total number of terms within a given Hamming distance
+
+    Parameters:
+        num_bits (unsigned int): Number of bits in bit-strings
+        distance (unsigned int): Hamming distance to consider
+
+    Returns:
+        unsigned int: Number of terms
+    """
+    cdef unsigned int out = 0
+    cdef unsigned int kk
+    for kk in range(distance+1):
+        out += binomial_coeff(num_bits, kk)
+    return out 

mthree/test/test_hamming.py

@@ -0,0 +1,107 @@
+# This code is part of Mthree.
+#
+# (C) Copyright IBM 2023.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Test Hamming distance truncation"""
+import numpy as np
+
+from qiskit.providers.fake_provider import FakeKolkata
+import mthree
+
+
+def test_hamming_equiv():
+    """Test Hamming truncation is same for direct and iterative methods"""
+    # This test is valid because for the direct method, we do not stop
+    # when all the elements within the Hamming distance are found, i.e
+    # we check them all since the problem size is small.  However, for
+    # the iterative method, we explicitly compute the number of terms
+    # and break when we hit that number.  Thus, this test validates
+    # that break via the computed column norms
+    backend = FakeKolkata()
+    mit = mthree.M3Mitigation(backend)
+    mit.cals_from_system()
+    for kk in range(8+1):
+        _, details = mit.apply_correction(COUNTS, list(range(8)),
+                                          details=True,
+                                          method='iterative',
+                                          distance=kk)
+        _, details2 = mit.apply_correction(COUNTS, list(range(8)),
+                                           details=True,
+                                           method='direct',
+                                           distance=kk)
+
+        assert np.linalg.norm(details2['col_norms']-details['col_norms']) < 1e-15
+
+
+COUNTS = {'11100010': 591,
+          '01010111': 119,
+          '10101101': 758,
+          '00101011': 488,
+          '10010001': 291,
+          '01100011': 622,
+          '10111000': 421,
+          '11100000': 1226,
+          '11100101': 957,
+          '11111100': 261,
+          '11101010': 482,
+          '01000100': 385,
+          '11111101': 281,
+          '10101000': 1094,
+          '00000010': 286,
+          '01101010': 455,
+          '11000100': 376,
+          '01110011': 369,
+          '00001000': 565,
+          '00010001': 296,
+          '01101111': 295,
+          '01000000': 718,
+          '01010100': 147,
+          '00101110': 230,
+          '10101110': 255,
+          '00010011': 197,
+          '00100001': 1536,
+          '01000001': 939,
+          '10001001': 682,
+          '00100000': 1142,
+          '11111111': 182,
+          '00101001': 1389,
+          '01100010': 575,
+          '01100001': 1603,
+          '11001010': 275,
+          '11110000': 472,
+          '11101001': 1532,
+          '00100101': 896,
+          '10100101': 917,
+          '01110000': 441,
+          '00000101': 429,
+          '10110011': 369,
+          '11110011': 366,
+          '01110111': 151,
+          '10000010': 278,
+          '11100001': 1662,
+          '11011011': 205,
+          '01110101': 306,
+          '01111101': 225,
+          '00110111': 147,
+          '10110010': 223,
+          '00111010': 184,
+          '11000001': 995,
+          '11111001': 527,
+          '11000000': 754,
+          '10101001': 1492,
+          '01100110': 257,
+          '01101000': 1051,
+          '01011000': 232,
+          '11010011': 216,
+          '00000011': 330,
+          '00101101': 772,
+          '01100000': 1257,
+          '00101111': 248}