Questions tagged [terminology-and-notation]
For questions about the usage of, origin of or reasons for specific notation used in the context of quantum computing.
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GHZ Definition - Does it all have to be $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\rangle$
Trying to dig a bit into GHZ States and the proper definition.
Trying to determine if GHZ state is strictly $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\...
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Quantum Cryptography without Bell's Theorem -- Brassard - Bennett - Mermin
It is an old paper but I'm trying to understand one of their argument. They say that if
$$U|u\rangle |a\rangle = |u\rangle |a^\prime\rangle \ \ \ \mathrm{and} \ \ \ U|v\rangle |a\rangle = |v\rangle |a^...
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What is the origin of the term POVM?
In Nielsen Chuang section 2.2.6 as they are introducing POVMs they write “The acronym POVM stands for ‘Positive Operator-Valued Measure’, a technical term whose historical origins we won’t worry about....
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Different notations for measurement gates: what is meant by $0$ after a measurement?
I am relatively new to quantum computing I am confused with different notations for measurement gates in quantum computing as shown below https://arxiv.org/pdf/2205.00081
I really donot understand ...
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Quantum error detection
I'm a bit confused regarding the definition of error detection. Let $H$ be a Hilbert space, $C$ a subspace, $P\colon H\to C$ the projection, and $E$ a linear operator on $H$. Consider these two ...
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What exactly is the change in domain for the Quantum Fourier Transform?
The (classical) Fourier Transform is famous for the reversible switch between the time-domain and frequency-domain of time dependent functions. Likewise there would be a change in domain associated ...
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Are commuting unitary operators related to commuting Hamiltonians?
TL/DR: Can unitary operators:
$$U_a=e^{-it(H_{a1}+H_{a2}+\cdots)}$$
and
$$U_b=e^{-it(H_{b1}+H_{b2}+\cdots)}$$
commute, even though $[H_{aj},H_{ak}]\ne 0$ and $[H_{bj},H_{bk}]\ne 0$ for all $j,k$?
...
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What's the distinction between "quantum computation" and "quantum computing"?
Is there a distinction between usage of the terms "quantum computation" and "quantum computing" or are they completely interchangeable?
For example, it is conceivable that "...
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In the QFT, do the basis states $\{|k\pmod N\rangle\}_{k=0}^N$ only make sense when $N=2^n$?
When I started learning quantum computing, I learned that for an $n$ qubit system, the basis states look like $$ \bigg\{ |\text{n-bit strings}\rangle\bigg\}\,.$$ So an $n$ qubit system has $2^n$ basis ...
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What is the oracle in every quantum algorithm?
There is a machine called oracle which appears in a lot of algorithm of quantum computing, such as Deutsch's algorithm, QFT period-finding. This oracle machine really makes me confused. I've read ...
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What is the difference between symmetric states and geometrically uniform states?
On the one hand, in this article, symmetric states are defined as:
The $M$ symmetric quantum states which should be distinguished by means of the quantum measurement are described by statistical ...
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How is geometric frustration different from (not) being frustration free?
In the context of Ising models, some Hamiltonians can be described as geometrically frustrated - such as, I think, the antiferromagnetic kagome lattice, as well as a one-dimensional anisotropic, next-...
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What mathematical object is the set of quantum states of a qudit? How should one write this?
It is tempting to write $|\psi\rangle \in \mathbb{C}^d$ for a qudit state, but this isn't very precise because of global phases.
What's a better notation for the set of states of a qudit?
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What is the difference between shot and iteration of the quantum circuit?
Hi this question is stem from What is meant with "shot" in quantum computation?.
If we just look for the distribution of the result, is there any theoretical difference between method 1 and ...
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Why is the word amplitude used in quantum computing?
Apparently no one has asked why the word "amplitude" is used to refer to the complex numbers that determine the probability of a quantum object to be found in a certain state. The word ...
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How can I simplify tensor product expressions quickly?
Suppose I have a 2-qubit system in the first Bell state, $\left| \beta_{00} \right>$. I want to make the measurement in the computational/$Z$-basis on the first qubit, say qubit $A$. That means I ...
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Quantum error correction terminology
I'm asking for help to clear up something, but instead of asking a question, I'm just writing my attempt of a definition below. I assume it's not this simple, and the below is not the correct ...
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Notation: Hamiltonian Simulation of Pauli Gates
Let $\sigma^j_x$ describe the following unitary over $n$ qubits: on the $j$-th qubit, it acts as the Pauli $x$ operator; instead, on any other qubit, it acts as the identity. A paper states now that
\...
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Terminology: Parameterized Quantum Circuits vs Data Encoding Unitary vs Variational Form
This question is about identifying the correct and widely accepted terminology.
Consider a function $U: \mathbb{R}^m \to \mathcal{U}(2^n)$ mapping a vector of $m$ real numbers to an element of the ...
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Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?
My doubt arises from page 99, 101 of the book Quantum Computation and Quantum Information by Michael A.Nielson and Issac L.Chung.
Let {${p_{i}, | \psi_{i} \rangle }$} be an ensemble of pure states.
...
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Are quantum channels bounded linear maps?
I've been reading about quantum channels from a couple of sources and have some doubts regarding some mathematical perspectives and properties of quantum channels. I've listed them below:
It is known ...
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Bra-ket notation in cryptography example
I was watching a presentation and I run into this example.
What does $\phi$ with the (x)t on the exponent mean?, similarly for the other symbol
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Is there non-fault-tolerant quantum error correction?
See this sectino on Wikipedia for Quantum error correction
Peter Shor's 9-qubit-code, a.k.a. the Shor code, encodes 1 logical qubit in 9 physical qubits and can correct for arbitrary errors in a ...
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how to write electron spins using bra-ket notation?
An electron has two spins $1/2$ and $-1/2$
I wanted to represent them using bra-ket notation. I used the following…
\begin{align}
1/2 &\to |0\rangle \\
-1/2 &\to |1\rangle
\end{align}
is this ...
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Name of quantum gate that cycles the Paulis
Background: There is a single qubit quantum gate of the form
$$
\frac{1}{\sqrt{2}}\begin{pmatrix}
1 & -i \\ 1 & i
\end{pmatrix}.
$$
As far as I know, this was originally introduced as the $T$ ...
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How to denote the action of a unitary transformation on a register?
Suppose we have a quantum register $\lvert ab \rangle = \frac{1}{\sqrt{2}} (\lvert 00 \rangle + \lvert 11 \rangle)$. I want to denote the action of the transformation $X \otimes I_2$ on this register. ...
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Do the following circuits violate the principle of "no fast-forwarding"?
The no fast-forwarding principle states roughly that, given that we can simulate a Hamiltonian for time $t$ using $r$ gates, in order to perform the Hamiltonian simulation for time $2t$, we must in ...
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What is the correct way to represent the CNOT gate on a circuit drawing where the target is an arbitrary qubit in a register? [closed]
Suppose we have a circuit composed of a single ancillary qubit and a $|{\psi}\rangle$ registry with n qubits. I want to draw a CNOT controlled on the ancilla and targeted on the last qubit of the $|{\...
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Best free online application for making notes containing quantum computing math notation? [closed]
This I hope, is not a trivial question. I am sure many like me struggle while making personal notes online and face difficulty in write linear algebra expressions & Dirac notations to explain ...
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How to write CNOT within a tensor product expression of operations on the whole system
If I have an $n$ qubit register and I act on the $k^{\mathrm{th}}$ qubit with an arbitrary operator $\hat{G}$, I can write the operation on the whole register as the operation,
$$\underbrace{\mathbb{1}...
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Clarification defining/finding the relative phase of a qubit
Let the vector $ |V\rangle = r_0 e^{i\theta_0} |0\rangle + r_1 e^{i\theta_1} |1\rangle $ correspond to the state of a qubit where $r_0,r_1,\theta_0,\theta_1 \in \mathbb{R}$.
According to p. 22 of ...
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Quantum In-place Modular Addition Circuit
Can anyone explain this in-place modular addition circuit from the paper "Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms" by Martin Roetteler et. al
(https://...
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What's the symbol $\circ$ called, and what does it mean?
I see the quantum gate
$U_1^{-1}\circ U_1\circ U_0=U_0$, what is the $\circ$ called and mean?
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What does the notation $\sum_\lambda \lambda \left | \lambda \right > \left < \lambda \right |$ mean?
In many places, I see a form of representing a matrix with:
$A = \sum_\lambda \lambda \left | \lambda \right> \left < \lambda \right |$
Where $\lambda$ is an eigenvalue, and $\left | \lambda \...
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Why is Dirac notation used for quantum states?
I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ ...
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What does the centered dot notation mean in the expression $|+\rangle|+\rangle\otimes(\cdot)$?
In the expression $|+\rangle|+\rangle \otimes(\cdot)$, what does the centered dot represent? I have come across a definition of the centered dot previously, similar to the one given here, but I am ...
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How to write down product operators acting on non-adjacent subsystems?
Given the following fusion gate (type-2) which is projecting 2 qubits to an even state
$$F_{ZZ}=(\langle00|+\langle|11|)$$
I would like to find the operator for the bigger space. For example, if I ...
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Meaning of the notation $[d]$ in scientific paper
Here in this paper (and several others), the notation $[d]$ is used. For instance, Lemma 9 of the paper reads:
Let $T_d\in R[x]$ be the d-th Chebyshev polynomial of the first kind. Let $Φ\in R_d$ be ...
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What is fidelity in quantum computing?
As I studied quantum computing, I saw term 'Fidelity' in many papers that related to quantum algorithm. So, I really wonder about following two things.
What is the real meaning of 'Fidelity' (As I ...
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Dirac notation for classic bits?
I'm writing about Quantum Computing, and in my preliminary sections on classical computing, there are too many things going by the names 0 and 1. Would it be awful to denote the values of classical ...
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In what contexts are different notations used for indicating measurement outcomes?
I have seen a few different notations for denoting measurement outcomes. Does anyone know of which notation is more widely used in various contexts?
For instance, I like referring to this Wikipedia ...
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What is the difference between "maximally entangled" and "entangled" states?
when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
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Why does the condition $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ called parallel transport condition?
I'm reading this paper (arXiv) about nonadiabatic holonomic quantum computation. Therein, it is stated that $\langle \varphi_k( t ) |\dot{\varphi}_l( t ) \rangle =0$ Eq.(2) is the parallel transport ...
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What is dual space, and why is it required?
I recently started QC/QM and came across something called dual space? How do we explain concept of dual space to a layman. why do we need dual space?
I tried to read and watch some resources on dual ...
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What is the correct name of this quantum gate? Possibly state control gate
Let $\vec v \in \mathbb{C}^2 $ be the following quantum state:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
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Representation of a vector in the HHL algorithm
Reading about the HHL algorithm, which is used to solve the equation $Ax=b$, on Wikipedia, they say to represent $b$ as
$|b\rangle=\sum_{i \mathop =1}^N b_i|i\rangle.$
I'm assuming $b$ is a vector ...
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What is the definition of $n$-local commuting circuit?
In this paper and this one, they talk about commuting quantum circuits that are only composed of "$n$-local commuting circuits", typically for $n=2$ or $n=3$.
However they don't provide a ...
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Standard name for CZ gate conjugated by Hadamards?
Is there a standard name for a $CZ$ gate conjugated by $H \otimes H$ gates? See below for circuit
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What is meant by "local isometry" in this paper?
I apologize for such a basic question here. I've been reading this paper, and I am wondering what is the usage of the term "local isometry" in the paper? The paper is open access, so you can ...
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What is the difference between "permutationally invariant" and "symmetric" states?
In this paper: ArXiv and PRL links, the authors give the definition of two $d\times d$ qudits to be permutationally invariant states if $\varrho$ is invariant under exchanging the particles. This can ...
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