Issue with Factoring with D-Wave Quantum Computers example

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  Ed C  (Report)

  September 05, 2022 22:08

  Nasser,

  The factoring example in the Notebook is set up as a CSP for a multiplication circuit for multiplying two 3-bit numbers. Since 22 and 24 have factors which need more than 3 bits (that is outside the range 0-7), it cannot return a correct solution.

  To try factoring other numbers, increase the number of bits in the multiplicands (a and b) and the product (p).

  I hope this helps answer your question.

  Ed

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  Nasser E  (Report)

  September 06, 2022 13:35

  Thank you very much. But I tested it with 4bits and it always gave bad results.

  This is the whole code:

  P = 22  

  from dimod.generators import multiplication_circuit 

  bqm = multiplication_circuit(4)

  p_vars = ['p0', 'p1', 'p2', 'p3', 'p4', 'p5', 'p6', 'p7']

  fixed_variables = dict(zip(reversed(p_vars), "{:08b}".format(P)))

  fixed_variables = {var: int(x) for(var, x) in fixed_variables.items()}

  for var, value in fixed_variables.items():

      bqm.fix_variable(var, value)

  from dwave.system import DWaveSampler

  sampler = DWaveSampler() 

  from dwave.system import EmbeddingComposite

  embedding_sampler = EmbeddingComposite(sampler)

  sampleset = embedding_sampler.sample(bqm, num_reads=100, label='Notebook - Factoring')

  from helpers.convert import to_base_ten

  a, b = to_base_ten(sampleset.first.sample)

   

  print("Given integer P={}, found factors a={} and b={}".format(P, a, b))

  Thanks again.

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  Ed C  (Report)

  September 07, 2022 00:29

  Thanks for including your code. From that, I can see the problem is not in your code in the main notebook. The extra bits (a3, b3) for handling 4-bit multiplicands also need to be added in the to_base_ten function in convert.py. Your sampler was finding the correct solution, but it was being printed incorrectly.

  Also, contrary to what the notebook says, I found I needed to increase the num_reads from the value of 100 to 1000 to make it more likely I would get a correct solution in the sample.

  If this does not solve it for you, please let us know what results you are seeing.

  Ed

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  Nasser E  (Report)

  September 07, 2022 01:54

  Thanks a lot. It finally worked. I defined and changed  the convert function and increased the number of reads function in the code:

  P = 22  

  from dimod.generators import multiplication_circuit 

  bqm = multiplication_circuit(4)

  p_vars = ['p0', 'p1', 'p2', 'p3', 'p4', 'p5', 'p6', 'p7']

  fixed_variables = dict(zip(reversed(p_vars), "{:08b}".format(P)))

  fixed_variables = {var: int(x) for(var, x) in fixed_variables.items()}

  for var, value in fixed_variables.items():

      bqm.fix_variable(var, value)

  from dwave.system import DWaveSampler

  sampler = DWaveSampler() 

  from dwave.system import EmbeddingComposite

  embedding_sampler = EmbeddingComposite(sampler)

  sampleset = embedding_sampler.sample(bqm, num_reads=1000, label='Notebook - Factoring')

  def to_base_ten(sample):
      a = b = 0
      
      # we know that multiplication_circuit() has created these variables
      a_vars = ['a0', 'a1', 'a2','a3']
      b_vars = ['b0', 'b1', 'b2','b3']
      
      for lbl in reversed(a_vars):
          a = (a << 1) | sample[lbl]
      for lbl in reversed(b_vars):
          b = (b << 1) | sample[lbl] 
          
      return a,b

  
  a, b = to_base_ten(sampleset.first.sample)

   

  print("Given integer P={}, found factors a={} and b={}".format(P, a, b))

  You were of great help.

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