qat.opt.NumberPartitioning

class qat.opt.NumberPartitioning(array_of_numbers, **kwargs)

Specialization of the Ising class for Number Partitioning.

This class allows for the encoding of a Number Partitioning problem for a given array of numbers. The method produce_j_h_and_offset() is automatically called. It computes the coupling matrix \(J\), magnetic field \(h\) and Ising energy offset corresponding to the Hamiltonian representation of the problem, as described in the reference. These are stored in the parent class Ising and would be needed if one wishes to solve the problem through Simulated Annealing (SA), for instance - see the Number Partitioning notebook.

Reference

“Ising formulations of many NP problems”, A. Lucas, 2014 - Section 2.1.

import numpy as np
from qat.opt import NumberPartitioning

array_of_numbers_size = np.random.randint(low=1, high=10000, size=1)[0]
array_of_numbers = np.random.randint(low=1, high=10000, size=array_of_numbers_size)

number_partitioning_problem = NumberPartitioning(array_of_numbers)

print("To anneal the problem, the solver would need "
      + str(array_of_numbers_size) + " spins.")

To anneal the problem, the solver would need 973 spins.
Parameters

numbers_array (1D numpy array) – an array with all the numbers we want to partition

get_best_parameters()

This method returns a dictionary with the best found parameters (after benchmarking) for simulated quantum annealing (SQA), available in the QLM. However, the temperature parameters could also be used for simulated annealing (SA).

Returns

6-key dictionary containing

  • n_monte_carlo_updates (int) - the number of Monte Carlo updates

  • n_trotters (int) - the number of “classical replicas” or “Trotter replicas”

  • gamma_max (double) - the starting magnetic field

  • gamma_min (double) - the final magnetic field

  • temp_max (double) - the starting temperature

  • temp_min (double) - the final temperature

qat.opt.number_partitioning.produce_j_h_and_offset(array_of_numbers)

Returns the \(J\) coupling matrix of the problem, along with the magnetic field \(h\) and the Ising energy offset.

Parameters

numbers_array (1D numpy array) – an array with all the numbers we want to partition