From Meta:
Qiskit 1.2, Phase Estimation; what does the value for theta - between 0 and 1 - represent?
https://meta.ai/s/DaTdepPbkVNL6XNB/
What is the purpose of controlled-U operations?
https://meta.ai/s/VNzHE4AuRrGWmY91/
Qiskit Code from IBMLearn, showing the procedure for theta=.7:
With theta set to .7, I.m getting 901 counts out of 1024 for 11. What does this mean?
In the context of Quantum Phase Estimation (QPE), the output (11, 901/1024) provides valuable information:
Interpretation:
11: This is the estimated value of the phase θ, represented as a binary fraction.
901/1024: This is the probability (or confidence) of measuring the estimated value 11.
Binary fraction to decimal conversion:
To interpret the estimated phase θ, convert the binary fraction 11 to a decimal:
11 (binary) = 3/4 = 0.75 (decimal)
Comparison to actual θ:
You set θ = 0.7. The estimated value 0.75 is close to the actual value.
Accuracy and precision:
The difference between estimated (0.75) and actual (0.7) θ values indicates an error of ≈ 0.05 (or 7%).
The high probability (901/1024 ≈ 88%) suggests that the estimation is reliable.
Implications:
This result demonstrates the Quantum Phase Estimation algorithm's ability to accurately estimate the phase θ:
The estimated value is close to the actual value.
The probability indicates a high confidence in the estimation.
Factors influencing accuracy:
Keep in mind that:
Number of qubits
Number of controlled-U operations
Measurement noise
Algorithmic limitations
can affect the accuracy of the estimation.
Would you like to explore ways to improve accuracy or discuss other QPE aspects?
Qiskit phase estimation keeps the values of the jumps on the unit circle to x*pi/4...
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