Hypergraphstates used for optimization

convert_in_binary(number_to_convert, number_of_bits=0)

Converts an int into a string containing its bits.

Example:

>>> convert_in_binary(5,3)
101
>>> convert_in_binary(5,3)
00101

Parameters:

• number_to_convert (int) – the number that is going to be converted.
• number_of_bits (int) – the number of bits required.

Returns:

String number : The converted number.

corresponding_state_determination(n, state, hyperedges)

Determines the states corresponding to an hyperedge. That is the states

where the vertices linked by the hyperedge are equal to 1.

Parameters:

• n (int) – The number of qubits.
• state (list(int)) – The state of the vector.
• hyperedges (list(list(int))) – a list containing the lists of the vertices which are linked by an hyperedge.

Param:

boolean – True if the state is in an hyperedge.

hyperedges_computation(n, state_vector, hyperedges)

Puts the phases in the right places. Wherever there is an edge or an

hyperedge between some vertices, a minus sign is put where those vertices are all in state 1.

Example:

>>> hyperedges_computation(2, [0.5, 0.5, 0.5, 0.5], [[0,1]])
[0.5, 0.5, 0.5, -0.5]

Parameters:

• n (int) – The number of qubits.
• state_vector (list(int)) – The initialized state vector.
• hyperedges (list[list[int]) – a list containing the lists of the vertices which are linked by an hyperedge.

Returns:

list(int) – The correct state vector.

putting_in_list(number)

Puts every figure of the number in a list.

Example:

>>> putting_in_list(000)
 [0, 0, 0]

Parameters:number (int) – The number to split. Returns:list(int) – The list with every digit of the number in a case.

state_vector_initialisation(n)

Initializes the state vector; which is to create an array with the size

of 2 to the power of n. Every number in the array is equal to 1 over the square root of 2 to the power of n.

Example:

>>> state_vector_initialisation(3)
[0.35355339 0.35355339 0.35355339 0.35355339 0.35355339 0.35355339
 0.35355339 0.35355339]

Parameters:n (int) – The number of qubits. Returns:list(int) – The initialized state vector.

states_formation(n)

Calculates every state for n qubits.

Example:

>>> states_formation(3)
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1], [1, 1, 0], [1, 1, 1]]

Parameters:n (int) – The number of qubits. Returns:list(list(int)) – A list of all the possible states of the qubits which are also contained in a list.