Interpretation of Qudit measurement output in cirq

Question

Here [+1] represents X gate for qutrit. How the Counter value is coming to 5? which is the measurement outcome(q0q1q2->102). Even for (q0q1q2->101) also counter value is 5. In total, for this 3 qutrits composite system, we have access to 27 levels (0,1,_ _ _ 26) but the counter value is not exceeding more than 7(q0q1q2->222).

Can someone suggest how to get true levels in Cirq for qudits after measurement? as well as what does counter value represent?

Answer 1

The histogram function has a default value for the fold_func parameter that calculates the integer value for the binary big endian number got from measurement results assuming qubits, not qudits. Thus:

1. I guess one could argue that it's a bug that it doesn't fail for non-bool values (you can open an issue for that to save time for future qudit users) and instead returns the "binary value" of the array, e.g. [1,0,2] -> [1,0,1] -> 5 is the reason you're getting 5, and why for 3 bits it never goes above 7=2^3-1.

2. You can create your own function instead for d=3 case and pass it like this for example:

def big_endian_dits_to_int(dits, dim: int) -> int:   
    result = 0
    for e in dits:        
        result *= dim
        result += e
    return result

samples.histogram(key='out',fold_func=lambda v: big_endian_dits_to_int(v, 3))