Questions tagged [notation]

For questions about the usage of, origin of or reasons for specific notation used in the context of quantum computing.

Filter by
Sorted by
Tagged with
1
vote
1answer
57 views

Representing a Bell measurement on non adjacent qubits

I have a state $${|\psi\rangle} = s {\Bigl(|1\rangle_1|1\rangle_2-|0\rangle_1|0\rangle_2\Bigr)}\otimes{\Bigl(|0\rangle_3|1\rangle_4-|1\rangle_3|0\rangle_4\Bigr)}\otimes{\Bigl(|0\rangle_5|1\rangle_6-|1\...
3
votes
2answers
119 views

Writing the notation when gates act on non successive registers

Suppose I have registers $|a\rangle^{l}|b\rangle^{l} |c\rangle^{l}$ and want an adder mod $l$ gate between the $a$ and $c$ registers. Let $R$ be the adder mod $l$ gate. So is this the correct ...
2
votes
0answers
62 views

Kronecker notation of an operator

Suppose I have the state $|A\rangle=|x\rangle^l\otimes |y\rangle^l \otimes |z\rangle^l \otimes |0\rangle_x^l\otimes |0\rangle_y^l\otimes |0\rangle_z^l$. I perform the transformation between the $|x\...
1
vote
1answer
107 views

Which is the correct depiction of a qubit before it collapses?

Which is the correct depiction of a qubit state showing the possibilities before it collapses? Is it like: MODEL 1: 1000 0100 0010 0001 MODEL 2: 1000 0100 0010 0001 0111 1011 1101 1110 MODEL 3: ...
2
votes
1answer
161 views

Circuit construction and Dirac notation of the following operation

I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\...
1
vote
2answers
149 views

Resources for quantum computing which do not use Dirac notation

What are some introductory textbooks and resources on quantum computing that do not use Dirac-notation, but rather ordinary mathematical notation (i.e. the notation used by mathematicians to represent ...
2
votes
0answers
60 views

Writing the transformation matrix for the following in terms of Kronecker products of elementary 2-qubit gates

I have a set of transformations that transforms $|11001\rangle\to |10101\rangle$ which is basically keeping the leftmost qubit as it is and then it is just the CNOT between the successive qubits, I ...
2
votes
1answer
169 views

What is the meaning of writing a state in its Bloch representation?

What is the meaning of writing a state $|\psi\rangle$ in its Bloch representation. Would I be correct in saying it's just writing out its Bloch vector?
4
votes
2answers
218 views

What does it mean to express a gate in Dirac notation?

When discussing the Dirac notation of an operator, for example, let's just say we have the bit flip gate $X$ if we want to write this in the Dirac notation does that just mean writing it as follows? $...
3
votes
1answer
120 views

Notation for two qubit composite product state

In my lecture notes on quantum information processing my lecturer gives an example of composite systems as $|\phi\rangle=|0\rangle |0\rangle=|00\rangle$. I understand that if we have two qubits then ...
1
vote
1answer
68 views

How to write the map $\mathbb C\ni z\mapsto zv$ in bra-ket notation?

As part of a course, I've been asked to write a map $C\rightarrow H,z \rightarrow zv$ for $v \in H=C^3\otimes C^2$, $v=[1, 0, 0, 1, 0, 1]$ in bra-ket notation. However, I never written such a map ...
2
votes
1answer
187 views

What is the meaning of the state $|1\rangle-|1\rangle$?

I don't understand it. But suppose you have a state of two qubits in superposition and it looks like $|10\rangle-|11\rangle$. Now you have in your circuits two gates one is a controlled-NOT from the ...
1
vote
0answers
42 views

Qiskit gates in LaTeX representation: notation meaning [duplicate]

I started working in Qiskit, and here is an example of how gates of a circuit are represented graphically in LaTeX format: Obviously, $R_y(\theta)$, is a y rotation by a certain angle. But all the ...
2
votes
1answer
60 views

Is there a place online where I can catch up with all the notational syntax associated with quantum computing?

There is a vast amount of new notations which would be new even to Ph.D. in math. How on Earth can I catch up with all of this? Is there a place online which is devoted to the QC syntax? I would ...
0
votes
1answer
100 views

How to read Dirac notation (without algebra)?

I have no idea how to read Dirac notation. $$\left|↑↑ \right\rangle \tag{1}$$ $$\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}$$ $$\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}$$ $$\left|↓...
1
vote
1answer
55 views

Why is correlation in the $X$ basis represented as $X\otimes X = 1$?

As far as I know, correlation of two qubits in the $X$ basis implies that under a simultaneous bit flip, the composite quantum state must be invariant. For instance, $A$ and $B$ can be said to be ...
2
votes
2answers
105 views

What is the notational convention for the single-qubit states $\lvert0\rangle\pm i\lvert1\rangle$?

The features of major search engines (looking at you, google!) prevent me from searching for an answer to this question, so I will poll the community here. Is the state $|{\pm} i\rangle$ generally ...
5
votes
1answer
247 views

Problem with the mathematical formulation of “qubitization”

In this research paper, the authors introduce a new algorithm to perform Hamiltonian simulation. The beginning of their abstract is Given a Hermitian operator $\hat{H} = \langle G\vert \hat{U} \...
1
vote
2answers
72 views

A question about notation for quantum states

I am reading an article on representation of digital images using qubits. But I am not able to understand the notations of the article. Can somebody help me: $|0\rangle$: It means the first basis ...
2
votes
1answer
190 views

Notation for two entangled registers

Suppose I have two registers x and y, of length m and n bits respectively. I want to initialize my system to contain an equal superposition of all $2^{n+m}$ states, then apply an oracle function (in ...
3
votes
1answer
68 views

Convention for expressing measurement in non-standard basis

If we're measuring in common bases like $|0\rangle$, $|1\rangle$ or $|+\rangle$, $|-\rangle$ we express this by saying we're measuring with $\sigma_z$ or $\sigma_x$, or measuring in the computational ...
12
votes
6answers
3k views

Quantum states are unit vectors… with respect to which norm?

The most general definition of a quantum state I found is (rephrasing the definition from Wikipedia) Quantum states are represented by a ray in a finite- or infinite-dimensional Hilbert space over ...
3
votes
1answer
104 views

What does the notation $\lvert \underline{x} \rangle$ mean?

I recently read hand-written notes about the "secret mask" or "secret string" algorithm (which I can't share here) with the following notation $\lvert \underline{x} \rangle$, i.e. a letter with a line ...
4
votes
1answer
148 views

What do we mean by the notation $\lvert \mathbf{x}, 0\rangle$?

In quantum computation, a common operation performed between two quantum states is the tensor product, which allows us to create a new and higher-dimensional state from two lower-dimensional states. ...
8
votes
2answers
258 views

What does quantum error correction code notation stand for?

I understand the notation for classical error correcting codes. E.g., "Hamming(7,4)" stands for a Hamming code that uses 7 bits to encode blocks of 4 bits. What does the notation for quantum error ...
5
votes
2answers
410 views

How to compute the average value $\langle X_1 Z_2\rangle$ for a two-qubit system?

Show that the average value of the observable $X_1Z_2$ in a two-qubit system measured in the state $(|00\rangle + |11\rangle)/\sqrt{2}$ is zero. How would we approach this question? I understand ...
10
votes
1answer
188 views

What do double wires mean in quantum circuits, and how do they relate to if statements?

The circuit can be translated to the following code: ...
27
votes
5answers
9k views

How does bra-ket notation work?

Quantum algorithms frequently use bra-ket notation in their description. What do all of these brackets and vertical lines mean? For example: $|ψ⟩=α|0⟩+β|1⟩$ While this is arguably a question about ...