How does the quantum phase estimation algorithm work?

How does the quantum phase estimation algorithm work?

The quantum phase estimation algorithm uses phase kickback to write the phase of UU (in the Fourier basis) to the tt qubits in the counting register. We then use the inverse QFT to translate this from the Fourier basis into the computational basis, which we can measure.

How to estimate phase value of two qubits?

Estimate a phase value on a system of two qubits through Iterative Phase Estimation (IPE) algorithm.

How to calculate the phase of an eigenvector?

Given a unitary operator UU, the algorithm estimates θθ in U | ψ⟩ = e2πiθ | ψ⟩U |ψ⟩ = e2πiθ|ψ⟩. Here | ψ⟩|ψ⟩ is an eigenvector and e2πiθe2πiθ is the corresponding eigenvalue.

Which is the most important subroutine in quantum computation?

Quantum phase estimation is one of the most important subroutines in quantum computation. It serves as a central building block for many quantum algorithms. The objective of the algorithm is the following:

How to calculate the pI of a quantum state?

At its core, QPE solves a fairly straightforward problem: given an operator U U and a quantum state |ψ⟩ | ψ ⟩ that is an eigenvalue of U U with U |ψ⟩= exp(2πiθ)|ψ⟩ U | ψ ⟩ = exp ( 2 π i θ) | ψ ⟩, can we obtain an estimate of θ θ?

How to calculate the phase of a qubit?

When we use a qubit to control the UU -gate, the qubit will turn (due to kickback) proportionally to the phase e2iπθe2iπθ. We can use successive CUCU -gates to repeat this rotation an appropriate number of times until we have encoded the phase theta as a number between 00 and 2t2t in the Fourier basis.

Which is the result of applying a quantum Fourier transform?

Inverse Fourier Transform: Notice that the above expression is exactly the result of applying a quantum Fourier transform as we derived in the notebook on Quantum Fourier Transform and its Qiskit Implementation. Recall that QFT maps an n-qubit input state |x⟩ into an output as

How are quantum algorithms used to solve stochastic processes?

We present quantum algorithms for solving two problems regarding stochastic processes.

Performs the quantum phase estimation algorithm for a given oracle U and targetState , reading the phase into a big-endian quantum register. An operation implementing U m U m for given integer powers m.

How to write a quantum program in Q #?

Q# functions: classical subroutines used within the quantum algorithm. The entry point used to call the quantum program and specify the target machine on which it should be run. This can be done directly from the command prompt, or through a host program written in a classical programming language like Python or C#.