Most Popular
1500 questions
13
votes
2 answers
What are the possible non-entangling two-qubit gates?
The non-entangling gates in $ SU_4 $ contains the entire group of gates of the form
$$
SU_2 \otimes SU_2.
$$
It also contains
$$
\zeta_8 SWAP= \zeta_8 \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1…
Ian Gershon Teixeira
- 3,722
- 3
- 21
13
votes
3 answers
What are the possible ways to visualise large, entangled states?
What are the prominent visualizations used to depict large, entangled states and in what context are they most commonly applied?
What are their advantages and disadvantages?
SLesslyTall
- 1,626
- 8
- 26
13
votes
1 answer
How to implement a matrix exponential in a quantum circuit?
Maybe it is a naive question, but I cannot figure out how to actually exponentiate a matrix in a quantum circuit.
Assuming to have a generic square matrix A, if I want to obtain its exponential, $e^{A}$, i can use the series
$$e^{A} \simeq I+…
FSic
- 859
- 5
- 18
13
votes
1 answer
How can classical bits be copied if qubits cannot be copied?
The no-cloning theorem of quantum mechanics tells us there can be no general quantum circuit that can copy arbitrary qubit states, i.e. a quantum gate or circuit cannot send $|0\rangle |\psi\rangle\mapsto|\psi\rangle |\psi\rangle$ for arbitrary…
Maximal Ideal
- 359
- 1
- 8
13
votes
2 answers
Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm
I have been trying to get my head around the famous(?) paper Quantum algorithm for linear systems of equations (Harrow, Hassidim & Lloyd, 2009) (more popularly known as the HHL09 algorithm paper) for some time, now.
On the very first page, they say:…
Sanchayan Dutta
- 17,497
- 7
- 48
- 110
13
votes
2 answers
What is a Haar random quantum state?
Can somebody please explain me what is a Haar random state? I am not able to find any friendly resource to read about it.
Shweta Aggrawal
- 329
- 2
- 5
13
votes
1 answer
What is the relationship between the Toffoli gate and the Popescu-Rohrlich box?
Background
The Toffoli gate is a 3-input, 3-output classical logic gate. It sends $(x, y, a)$ to $(x, y, a \oplus (x \cdot y))$. It is significant in that it is universal for reversible (classical) computation.
The Popescu-Rohrlich box is the…
Evan Jenkins
- 518
- 3
- 7
13
votes
2 answers
Quantum XNOR Gate Construction
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is the quantum XNOR gate a CCNOT gate?
user820789
- 3,302
- 12
- 42
13
votes
6 answers
Resources for quantum algorithm basics
I have just started to learn about quantum computing, and I know a little bit about qubits. What is a resource where I can learn a basic quantum algorithm and the concepts behind how it works?
Vashi
- 177
- 7
13
votes
2 answers
How can one define contextuality within the circuit model?
It is in general believed that contextuality is one of the quantum resource that provides the quantum advantage. A context is usually defined in terms of a set of commuting observables. The quantum algorithms are usually describe employing the…
madeel
- 321
- 1
- 5
13
votes
1 answer
What are min and max overlaps of a maximally entangled state with a separable state?
Let $A,B$ be Hilbert spaces of dimension $d$. Let $\rho$ be some separable quantum state of the composite system $AB$. Given a maximally entangled state:
$$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=1}^d \vert i\rangle_A\vert…
Jules
- 133
- 4
13
votes
2 answers
Degeneracy of Quantum Error Correction Codes
The feature of quantum error correcting codes called degeneracy is that they can sometimes be used to correct more errors than they can uniquely identify. It seems that codes exhibiting such characteristic are able to overcome the performance of…
Josu Etxezarreta Martinez
- 3,916
- 13
- 39
13
votes
2 answers
Using a fractional number of classical bits within quantum teleportation
Recently, I heard that there can be transfer of rational classical bits (for example 1.5 cbits) from one party to another via quantum teleportation. In the Standard Teleportation Protocol, 2 classical bits and 1 maximally entangled shared resource…
Vijeth Aradhya
- 361
- 1
- 7
13
votes
2 answers
What is the minimum integer value to make quantum factorization to be worthwhile?
Let us assume that we have quantum and classical computers such that, experimentally, each elementary logical operation of mathematical factorization is equally time-costing in classical and in quantum factorization:
Which is the lowest integer…
SalvaCardona
- 673
- 3
- 12
13
votes
2 answers
How do you rotate a Fock state qubit?
I read that a qubit can be encoded in a Fock state, such as the presence or absence of a photon. How do you perform single qubit rotations on Fock states?
Daniel Tordera
- 885
- 5
- 13