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1500 questions
11
votes
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How is Grover's algorithm used to estimate the mean and median of a set of numbers?
On the Wikipedia page for Grover's algorithm, it is mentioned that:
"Grover's algorithm can also be used for estimating the mean and median of a set of numbers"
So far I only knew how it can be used to search a database. But not sure how to…
Sanchayan Dutta
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2 answers
Are true Projective Measurements possible experimentally?
I have heard various talks at my institution from experimentalists (who all happened to be working on superconducting qubits) that the textbook idea of true "Projective" measurement is not what happens in real-life experiments. Each time I asked…
Dr. T. Q. Bit
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What are the real advantages of superdense coding?
In superdense coding, two qubits are prepared by Eve in an entangled state; one of them is sent to Alice and the other is sent to Bob. Alice is the one who wants to send (to Bob) two classical bits of information. Depending on what pair of classical…
user72
11
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1 answer
Block encoding technique: what is it and what is it used for?
I was wondering if someone could explain to me what this technique called "block encoding" does, and what it is used for at a high level, found in arXiv:1806.01838.
It is in section 4.1, definition 43; shown below.
I encountered this topic while…
chois3
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Who was the first to call the phase gates $P(\pi/2)$ and $P(\pi/4)$ the $S$ and $T$ gates, and were they motivated by generators of the modular group?
Within the theory of quantum gates, a common pair of single-qubit phase gates are the $P(\pi/2)=S$ and $P(\pi/4)=T$ gates, with
$$S= \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix},\:T = \begin{bmatrix} 1 & 0 \\ 0 & e^{i \frac{\pi}{4}}…
Mark Spinelli
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11
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1 answer
Does anyone know the list of all known universal sets of quantum gates?
Does anyone know the list of all known universal sets of quantum gates? I know only two such sets: Cliffords + $T$ and rotations + CNOT.
Игорь Токарев
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2 answers
Characteristics of the IBM quantum computer
On the IBM Quantum Composer website, there are characteristics of qubit computers. For example, ibmq_16_melbourne.
But there is no description anywhere of what:
T1(us),
T2(us),
Frequency (GHz),
Readout assignment error,
Prob meas0 prep1,
Prob meas1…
alexhak
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What is the complexity of estimating the expectation value of an observable?
The average value of an operator $O$ in the state $\left.|\psi\right>$ is
$$\overline{O}=\left<\psi|O|\psi\right>$$
Now for simplicity let $\left.|\psi\right>=\left.|0\right>^n$ and assume we have a circuit that prepares $O$. How many times one has…
Nikita Nemkov
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What is the relation between POVMs and observables (as Hermitian operators)?
Let $\renewcommand{\calH}{{\mathcal{H}}}\calH$ be a finite-dimensional Hilbert space.
An observable $A$ is here a Hermitian operator, $A\in\mathrm{Herm}(\calH)$.
A POVM is here a collection of positive operators summing to the identity: $\{\mu(a):…
glS
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Is there any general statement about what kinds of problems can be approximated more efficiently using a quantum computer?
As the name already suggests, this question is a follow-up of this other. I was delighted with the quality of the answers, but I felt it would be immensely interesting if insights regarding optimization and approximation techniques were added, but…
fr_andres
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5 answers
What is quantum entanglement, and what role does it play in quantum error correction?
I want to understand what quantum entanglement is and what role does it play in quantum error correction.
NOTE:
As per the suggestions of @JamesWootton and @NielDeBeaudrap, I have asked a separate question for the classical analogy here.
Chinni
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11
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1 answer
What is stopping FACTORING from being BQP-complete?
Classical complexity theory makes much of the study of so-called intermediate problems - that is, problems that are in $\mathsf{NP}$ but are nonetheless not known to be in $\mathsf{P}$ and further not expected to be $\mathsf{NP}$-complete.
Commonly…
Mark Spinelli
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11
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2 answers
In shadow tomography, how is the state reconstructed from its shadows?
I'm reading Huang et al. (2020) (nature physics), where the authors present a version of Aaronson's shadow tomography scheme as follows (see page 11 in the arXiv version):
We want to estimate a state $\rho$. We apply a number of random unitary…
glS
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2 answers
Is qsphere an actual term representing 5 qubits?
I'm a total beginner, I've been brought here by the featured stackoverflow blog post so I started studying.
Watching this youtube video (A Beginner’s Guide To Quantum Computing (3:58), I saw this slide where it talks about superposition:
At first I…
Adelin
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What kinds of ions do trapped ion quantum computers use?
Trapped ion quantum computers are among the most promising approaches to achieve large-scale quantum computation.
The general idea is to encode the qubits into the electronic states of each ion, and then control the ions via electromagnetic…
glS
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