Why do we measure and count the distribution when using quantum algorithm with Qiskit? — Answer by Perplexity Pro
So, I was wondering why we measure and count the distribution when using quantum algorithm with frameworks such as Qiskit.
Here’s the answer from Perplexity Pro
Measurement and counting of the output distribution are essential components when implementing quantum algorithms using Qiskit or other quantum computing frameworks. Here are the key reasons why measurement and counting are necessary:
1. Extracting classical information: Quantum algorithms ultimately need to produce classical outputs that can be interpreted and used[1]. Measurement collapses the quantum state into classical bits, allowing us to extract usable information from the quantum system.
2. Probabilistic nature of quantum algorithms: Many quantum algorithms, including those based on the quantum Fourier transform, rely on the output probability distribution[1]. Measuring multiple times and counting the results allows us to estimate this distribution.
3. Verifying results: Repeated measurements and counting help verify that the quantum circuit is behaving as expected and producing consistent results.
4. Error mitigation: Real quantum devices are prone to errors. Taking multiple measurements and analyzing the distribution can help identify and mitigate some types of errors.
5. Algorithm-specific requirements: Some algorithms, like Grover’s search or quantum counting, specifically require measurement and counting of results to determine the final answer[3][6].
6. Quantum state cannot affect the classical world without measurement: For a quantum computation to be useful, it must ultimately lead to or contribute to a measurement somewhere[1].
7. Sampling for statistical analysis: In many cases, we need to run the quantum circuit multiple times (shots) to gather statistics on the output distribution, which is crucial for interpreting the results accurately[2].
It’s important to note that while measurement is necessary for obtaining useful results, it’s not always required at every step of a quantum algorithm. Many quantum algorithms transform quantum information without measuring it as part of larger computations[1]. The timing and placement of measurements in a quantum circuit are often crucial to the algorithm’s success.
In Qiskit specifically, measurement operations are typically added at the end of quantum circuits, and the `execute()` function allows you to specify the number of shots (repetitions) to run. The results are then collected and can be analyzed using Qiskit’s built-in tools or custom classical post-processing.
Citations:
[1] https://quantumcomputing.stackexchange.com/questions/26800/is-measurement-necessarily-required-for-every-quantum-algorithm
[2] https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.012412
[3] https://people.ohio.edu/diao/papers/QC_AAM.pdf
[4] https://www.nature.com/articles/s41467-021-27922-0
[5] https://www.studysmarter.co.uk/explanations/physics/quantum-physics/quantum-measurement/
[6] https://en.wikipedia.org/wiki/Quantum_counting_algorithm
[7] https://arxiv.org/abs/2308.01255
[8] https://www.cl.cam.ac.uk/teaching/2223/QuantComp/Quantum_Computing_Lecture_4_2023.pdf
[9] https://www.linkedin.com/pulse/thoughts-quantum-counting-constantin-gonciulea
[10] https://docs.quantum.ibm.com/api/migration-guides/qiskit-runtime-examples
[11] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8613231/
[12] https://en.wikipedia.org/wiki/Quantum_algorithm
[13] https://docs.quantum.ibm.com/start/hello-world
[14] https://quantumcomputing.stackexchange.com/questions/15678/if-quantum-computing-always-return-random-measurement-or-uncertain-measurement
[15] https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics
[16] https://quantumcomputing.stackexchange.com/questions/32766/quantum-algorithms-and-binomial-distributions-and-probabilities
[17] https://quantumcomputing.stackexchange.com/questions/33281/how-do-we-measure-the-probability-of-outcomes-in-a-quantum-computer-if-qubits-co
[18] https://phys.org/news/2022-07-importance-science-quantum-revolution.html
[19] https://quantumcomputinguk.org/tutorials/modelling-probability-distributions-in-qiskit
[20] https://arxiv.org/pdf/2402.10745.pdf
