PhaseE

 Like it, or not, any procedure to compute various mathematical operations

in polynomial time on a quantum computer will need to use phase estimation.

And that is what the first part of the lesson on Schor's algorithm seeks to define.

Below, AI clearing things up on the matter.

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You

Quantum omputing with qiskit; can you explain the phase estimation problem to me, in simple terms?

Copilot

Sure! The phase estimation problem is a fundamental task in quantum computing, especially useful in algorithms like Shor’s algorithm for factoring large numbers. Here’s a simplified explanation:

What is Phase Estimation?

Phase estimation is about finding the “phase” (a specific value) associated with an eigenvalue of a unitary operator. In simpler terms, it’s like trying to figure out a hidden angle that a quantum state has been rotated by.

How Does It Work?

Superposition: First, we put some qubits into a superposition state using Hadamard gates. This means they are in a mix of 0 and 1 states.

Apply Unitary Operations: We then apply a series of controlled unitary operations to another set of qubits. These operations are like rotations, and the amount of rotation is related to the phase we want to estimate.

Inverse Quantum Fourier Transform (QFT): After applying the rotations, we use an inverse Quantum Fourier Transform on the qubits. This step helps to decode the phase information from the superposition state.

Measurement: Finally, we measure the qubits. The result gives us a binary number that we can convert to the phase value.

Example

Imagine you have a qubit that has been rotated by an angle (\theta). Phase estimation helps you find out what (\theta) is. If (\theta) is (\pi/2) (90 degrees), the algorithm will help you determine this angle.

Why is it Important?

Phase estimation is crucial because it forms the basis of many quantum algorithms, including those for solving complex mathematical problems and simulating quantum systems12.

If you want to dive deeper, you can check out tutorials and resources on Qiskit, which is a popular quantum computing framework by IBM12.

Does this help clarify things? Feel free to ask more questions if you have any!