Contents
- 1 Which is the best algorithm for quantum amplitude estimation?
- 2 How is amplitude estimation used in approximate counting?
- 3 How to estimate the amplitude of a sinusoid?
- 4 How does the quantum phase estimation algorithm work?
- 5 Which is the most important subroutine in quantum computation?
- 6 Which is the most elegant quantum adder for addition?
Which is the best algorithm for quantum amplitude estimation?
Quantum Amplitude Estimation (QAE) 1 is a fundamental quantum algorithm with the potential to achieve a quadratic speedup for many applications that are classically solved through Monte Carlo (MC) simulation.
How is amplitude estimation used in approximate counting?
We apply amplitude estimation to the problem of *approximate counting*, in which we wish to estimate the number of $x\\in X$ such that $\\chi(x)=1$. We obtain optimal quantum algorithms in a variety of settings. Comments: 32 pages, no figures
How to calculate the amplitude of a quantum superposition?
Consider also a quantum algorithm $\\mathcal A$ such that $A |0angle= \\sum_{x\\in X} \\alpha_x |xangle$ is a quantum superposition of the elements of $X$, and let $a$ denote the probability that a good element is produced if $A |0angle$ is measured.
How to estimate the amplitude of a sinusoid?
Assume you want to estimate the amplitude of a known frequency sinusoid in additive Gaussian (white or pink) noise. Also assume mainlobe width/sidelobe decay doesn’t matter. Windows should be compared such that the time latency of the resulting amplitude estimate is equal.
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.
What does oblivious amplitude amplification do in quantum?
Oblivious amplitude amplification allows the probability of success of this measurement to be boosted to 100% 100 % using the above reasoning. Further, ordinary amplitude amplification corresponds to the case where the system register is empty.
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:
Which is the most elegant quantum adder for addition?
The Draper adder is arguably one of the most elegant quantum adders, as it directly invokes quantum properties to perform addition. The insight behind the Draper adder is that the Fourier transform can be used to translate phase shifts into a bit shift.