Quantum Measurement Simulator
Quantum Measurement Simulator computes and visualizes probabilities of qubit measurement outcomes in superposition, simulating multiple measurements for quantum studies.
Formulas Used in Quantum Measurement Simulator
The simulator uses the following formulas for a single qubit measurement:
Qubit State:
\\[ |\psi\rangle = \alpha |0\rangle + \beta |1\rangle \\]Normalization:
\\[ |\alpha|^2 + |\beta|^2 = 1 \\]Measurement Probabilities:
\\[ P_{|0\rangle} = |\alpha|^2 = \alpha_{\text{real}}^2 + \alpha_{\text{imag}}^2 \\] \\[ P_{|1\rangle} = |\beta|^2 = 1 – |\alpha|^2 \\]Where:
- \\( \alpha \\): Complex amplitude of |0⟩
- \\( \beta \\): Complex amplitude of |1⟩
- \\( P_{|0\rangle} \\): Probability of measuring |0⟩
- \\( P_{|1\rangle} \\): Probability of measuring |1⟩
Example Calculations
Example 1: Equal Superposition
Input: α Real = 0.707, α Imag = 0, Number of Measurements = 1000
Simulated 1000 measurements: ~500 |0⟩, ~500 |1⟩
Result: P_{|0\rangle} = 0.5, P_{|1\rangle} = 0.5, Counts ~ [500, 500]
Example 2: Biased State
Input: α Real = 0.894, α Imag = 0, Number of Measurements = 1000
Simulated 1000 measurements: ~800 |0⟩, ~200 |1⟩
Result: P_{|0\rangle} = 0.8, P_{|1\rangle} = 0.2, Counts ~ [800, 200]
Example 3: Large Number of Measurements
Input: α Real = 0.707, α Imag = 0, Number of Measurements = 10000
Simulated 10000 measurements: ~5000 |0⟩, ~5000 |1⟩
Result: P_{|0\rangle} = 0.5, P_{|1\rangle} = 0.5, Counts ~ [5000, 5000]