# dwavebinarycsp.factories.csp.circuits.multiplication_circuit¶

multiplication_circuit(nbit, vartype=Vartype.BINARY)[source]

Multiplication circuit constraint satisfaction problem.

A constraint satisfaction problem that represents the binary multiplication $$ab=p$$, where the multiplicands are binary variables of length nbit; for example, $$2^ma_{nbit} + ... + 4a_2 + 2a_1 + a0$$.

The square below shows a graphic representation of the circuit:

________________________________________________________________________________
|                                         and20         and10         and00    |
|                                           |             |             |      |
|                             |┌───────────┘|┌───────────┘|             |      |
|               |┌───────────┘|┌───────────┘|             |             |      |
|  ┌───────────┘|             |             |             |             |      |
| p5            p4            p3            p2            p1            p0     |
--------------------------------------------------------------------------------

Parameters
• nbit (int) – Number of bits in the multiplicands.

• vartype (Vartype, optional, default='BINARY') –

Variable type. Accepted input values:

• Vartype.SPIN, ‘SPIN’, {-1, 1}

• Vartype.BINARY, ‘BINARY’, {0, 1}

Returns

CSP that is satisfied when variables $$a,b,p$$ are assigned values that correctly solve binary multiplication $$ab=p$$.

Return type

Examples

This example creates a multiplication circuit CSP that multiplies two 3-bit numbers, which is then formulated as a binary quadratic model (BQM). It fixes the multiplacands as $$a=5, b=3$$ ($$101$$ and $$011$$) and uses a simulated annealing sampler to find the product, $$p=15$$ ($$001111$$).

>>> from dwavebinarycsp.factories.csp.circuits import multiplication_circuit
>>> import neal
>>> csp = multiplication_circuit(3)
>>> bqm = dwavebinarycsp.stitch(csp)
>>> bqm.fix_variable('a0', 1); bqm.fix_variable('a1', 0); bqm.fix_variable('a2', 1)
>>> bqm.fix_variable('b0', 1); bqm.fix_variable('b1', 1); bqm.fix_variable('b2', 0)
>>> sampler = neal.SimulatedAnnealingSampler()
>>> response = sampler.sample(bqm)
>>> p = next(response.samples(n=1, sorted_by='energy'))
>>> print(p['p5'], p['p4'], p['p3'], p['p2'], p['p1'], p['p0'])
0 0 1 1 1 1