Math mode typo fix

docs/implementation.rst

@@ -12,7 +12,7 @@ A single bit gate essentially acts as a :math:`2\times2` matrix between the :mat
 
 To determine how state vector coefficients should be exchanged in register-wise operations, essentially, we form bitmasks that are applied to every underlying possible permutation state in the state vector, and act an appropriate bitwise transformation on them. The result of the bitwise transformation tells us which input permutation coefficients should be mapped to each output permutation coefficient. Acting a bitwise transformation on the input index in the state vector array, we return the array index for the output, and we move the double precision complex number at the input index to the output index. The transformation of the array indexes is basically the classical computational bit transformation implied by the operation. In general, this is again "embarrassingly parallel" over fixed bit values for bits that are not directly involved in the operation. To ease the process of exchanging coefficients, we allocate a new duplicate permutation state array vector, which we output values into and replace the original state vector with at the end.
 
-The act of measurement draws a random double against the probability of a bit or string of bits being in the :math:`1` state. To determine the probability of a bit being in the :math:`1` state, sum the probabilities of all permutation states where the bit is equal to :math:`1`. The probablity of a state is equal to the complex norm of its coefficient in the state vector. When the bit is determined to be :math:`1` by drawing a random number against the bit probability, all permutation coefficients for which the bit would be equal to :math:`0` are set to zero. The original probabilities of all states in which the bit is :math:`1` are added together, and every coefficient in the state vector is then divided by this total to "normalize" the probablity back to :math:`1` (or :math:`100%`).
+The act of measurement draws a random double against the probability of a bit or string of bits being in the :math:`1` state. To determine the probability of a bit being in the :math:`1` state, sum the probabilities of all permutation states where the bit is equal to :math:`1`. The probablity of a state is equal to the complex norm of its coefficient in the state vector. When the bit is determined to be :math:`1` by drawing a random number against the bit probability, all permutation coefficients for which the bit would be equal to :math:`0` are set to zero. The original probabilities of all states in which the bit is :math:`1` are added together, and every coefficient in the state vector is then divided by this total to "normalize" the probablity back to :math:`1` (or :math:`100\%`).
 
 In the ideal, acting on the state vector with only unitary matrices would preserve the overall norm of the permutation state vector, such that it would always exactly equal :math:`1`, such that on. In practice, floating point error could "creep up" over many operations. To correct we this, we normalize at least immediately before (and immediately after) measurement operations. Many operations imply only measurements by either :math:`1` or :math:`0` and will therefore not introduce floating point error, but in cases where we multiply by say :math:`1/\sqrt{2}`, we can normalize proactively. In fact, to save computational overhead, since most operations entail iterating over the entire permutation state vector once, we can calculate the norm on the fly on one operation, finish with the overall normalization constant in hand, and apply the normalization constant on the next operation, thereby avoiding having to loop twice in every operation.