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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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-...
Mark Spinelli's user avatar
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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 ...
user1145880's user avatar
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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 ...
requiemman's user avatar
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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 ...
Tron's user avatar
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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 \...
user20374's user avatar
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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. ...
Physkid's user avatar
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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
graphtheory92's user avatar
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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 ...
Jagerber48's user avatar
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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 ...
reza's user avatar
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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 $T$ ...
Eric Kubischta's user avatar
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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 ...
Mark Spinelli's user avatar
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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 $|{\...
thespaceman's user avatar
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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 ...
QuantumNeeraj's user avatar
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1 answer
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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}...
Adrien Amour's user avatar
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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 ...
RyRy the Fly Guy's user avatar
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Notation for Lindblad operators

I was reading the paper Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation . The claim is that universal quantum computation can be achieved using the ...
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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://...
A. K. M. Fakhrul Hossain's user avatar
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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 \...
Loic Stoic's user avatar
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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 $|1\rangle$ ...
Rayhan's user avatar
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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 ...
banercat's user avatar
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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 here is Lemma 9 of the paper: Let $T_d\in R[x]$ be the d-th Chebyshev polynomial of the first kind. Let $Φ\in R_d$ be ...
Jadzia's user avatar
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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 ...
김시윤's user avatar
2 votes
3 answers
154 views

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 ...
bburd's user avatar
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1 answer
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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 ...
Quantum Guy 123's user avatar
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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 ?
Vinay Sharma's user avatar
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1 answer
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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 about nonadiabatic holonomic quantum computation and met the condition eq.(2) states that $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ is the ...
Sherlock's user avatar
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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 ...
Vinay Sharma's user avatar
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0 answers
93 views

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,...
misanek123's user avatar
4 votes
1 answer
174 views

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 ...
BBB's user avatar
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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 ...
Marco Fellous-Asiani's user avatar
5 votes
2 answers
117 views

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
Mike Vasmer's user avatar
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2 answers
130 views

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 ...
Maximal Ideal's user avatar
3 votes
2 answers
363 views

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 ...
Sherlock's user avatar
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Is the $|00\rangle$ basis the same as the $|\phi^+\rangle$ basis?

I am working on a problem where I have 4 entangled qubits. I want to trace out 2nd and 3rd qubits by projecting them onto the $|00\rangle$ basis. Is the $|00\rangle$ basis the same as the $|\phi^+\...
Ganesh M's user avatar
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What's a nice, intuitive notation for indicating that two operators can or should be run in parallel?

Suppose I have a unitary operator acting on a state $|\psi\rangle$, such as: $$\big (\sqrt A\sqrt B\sqrt C\sqrt D\big)|\psi\rangle.$$ Conventionally, $\sqrt D$ is performed first, then $\sqrt C$, then ...
Mark Spinelli's user avatar
8 votes
2 answers
646 views

What is (formally) a transversal operator?

This question concerns about a formal definition of transversal operator. I understood that transversal operator are a group of operators which are efficient in terms of circuit depth and can be used ...
Daniele Cuomo's user avatar
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1 answer
81 views

What does $I$ represent in the expression $A\otimes I$?

This paper states: Suppose a two qubit system is in the state $|\psi\rangle=a|00\rangle+b|11\rangle$, and consider the expectation value of any observable $A \otimes I$ that is nontrivial only on the ...
mish's user avatar
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7 votes
3 answers
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What is a "maximally mixed state"?

What is meant by maximally mixed states? Does this mean that there are partially mixed states? For example, consider $\rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right|$ and $\rho_W =...
Bekaso's user avatar
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Why are slice states called so?

The "slice" states are defined by equation 50 in this (freely available) article. I wonder why they call them so!
User101's user avatar
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Which unicode character should be used for the angle brackets in braket notation?

When the use of LaTeX or MathJax or other typesetting system is not an option, one can still type the braket notation $\left<\psi\right|$ and $\left|\psi\right>$. The simplest way is probably to ...
mhucka's user avatar
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1 answer
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What are "unbounded loss functions" and "unbounded operators"?

I am reading this paper: Quantum Generative Training Using Rényi Divergences. In it, the authors mention the following multiple times: "...an unbounded loss function can circumvent the existing ...
karolyzz's user avatar
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1 answer
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What does the expression $\langle y^{(n)}|\otimes𝟙 \,|\Psi_b\rangle$ mean?

I'm trying to understand the following paper, https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.013167, but I'm new to quantum computing. In it they use this expression: $$\langle ...
G Aker's user avatar
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Is there a convention in quantum circuit diagrams for specific quantum measurements?

Is there a convention in quantum circuit diagrams for specific quantum measurements? For example, how could one express the measurement $|0\rangle \langle 0|$ in a circuit diagram?
James Ellis's user avatar