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 Quantum Annealing (SQA) via the SQAQPU - see the Number Partitioning notebook. This QPU also requires a few additional parameters, the specification of which may vary the quality of the solution. We therefore provide the best parameters found thus far through the method get_best_parameters().

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 4273 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 annealing parameters found thus far after benchmarking. The parameters are needed to produce the entries of the SQAQPU used to solve a Number Partitioning problem via Simulated Quantum Annealing (SQA).

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