Commit 5005b543 authored by Lotshaw, Phil's avatar Lotshaw, Phil
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Update States/how_to_read_states.txt

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Each row in a file lists the graph number followed by the real and imaginary components of the expansion coefficients c_z = <z|psi>.  

For states of n qubits, in each row the second through 2^n+1'th entries are the real parts of the coefficients, the next 2^n entries are the imaginary parts of the coefficients.  

The basis is ordered as |z_{n-1}, z_{n-2}, ... , z_0> such that z_{n-1},...z_0 for the z'th basis state gives the binary expansion of z.  

For example, with n=3:
0th basis state: |0,0,0>
1st basis state: |0,0,1>
2nd basis state: |0,1,0>
3rd basis state: |0,1,1>
4th basis state: |1,0,0>
5th basis state: |1,0,1>
6th basis state: |1,1,0>
7th basis state: |1,1,1>

For example, the first row of state_n=3_p=2.txt reads

1	-2.2009153888280508E-008   2.3433567536231681E-008   2.3433567623941675E-008  0.67084105521580439       0.67084105521580439        2.3433567623941675E-008   2.3433567536231681E-008  -2.2009153888280508E-008   5.6767305522953393E-008   1.9460947995374837E-010   1.9460947668619967E-010 -0.22354480230356799      -0.22354480230356799        1.9460947668619967E-010   1.9460947995374837E-010   5.6767305522953393E-008

This separates into real parts for the second to 2^n+1'th entries and imaginary parts for the next 2^n entries. 

Real parts:   -2.2009153888280508E-008   2.3433567536231681E-008   2.3433567623941675E-008  0.67084105521580439       0.67084105521580439        2.3433567623941675E-008   2.3433567536231681E-008  -2.2009153888280508E-008

Imag parts: 	5.6767305522953393E-008   1.9460947995374837E-010   1.9460947668619967E-010 -0.22354480230356799      -0.22354480230356799        1.9460947668619967E-010   1.9460947995374837E-010   5.6767305522953393E-008

All the entries are effectively zero except the fourth and fifth entries, corresponding to the basis states 
3rd basis state: |0,1,1>
4th basis state: |1,0,0>

These each have coefficients c_z = 0.67084105521580439 + i * (-0.22354480230356799)

These states are the two symmetry-related solutions to the MaxCut problem for the graph, with edges 0,2 and 1,2, seen in the first adjacency matrix of Graphs/graph3c.txt.