Hello. Quantum computer calculations are being improved day by day. In this article, I would like to give an overview of how to do numerical integration, which is available in blueqat tutorial.
Numerical integration can be used to find a certain area in a quantum computer. Numerical integration approximates the area by a collection of rectangles, which are then added together.
To do this with a quantum computer, the above y = f(x) needs to be expressed in a quantum circuit, which is a circuit made of logical qubits. To find the area, we need to add up the small rectangles, and we do this using the amplitude of the quantum state of the qubits. Taking it from the tutorial
In this quantum state, we can prepare the probability amplitude from the superposition state, and then create a state that has the square root of f(x) as its amplitude, so that we can estimate the amplitude of the|1> state to find the area.
Since the initial state starts from superposition, the denominator is 2^n, but if the partition interval is complicated, the initial state may need to be a reasonably complicated quantum state.
In this case, the root 2^n becomes the denominator from the superposition, and f(x) corresponds to the numerator. As a quantum circuit, in the example
In this case, the root 2^n is the denominator and the numerator is f(x). This allows us to find the area using numerical integration by estimating the amplitude of the|1> state of q0. This is the amplitude estimation.
In the tutorial, we use two different methods to find the area of sinx^2 by estimating the amplitude, so please read on. That's all.
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