Tagged Questions
2
votes
0answers
37 views
What is three-photon interference?
Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
7
votes
1answer
92 views
Positivity in the Pauli/Bloch/coherence vector representation
Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
7
votes
1answer
105 views
How are qubits better than classical bit?
WHAT I KNOW:
classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states.
Now ...
0
votes
0answers
38 views
Deutsch-Jozsa algorithm [closed]
How many calls are required to determine is the function balanced or not on the classical computer with probability of error < 50%.
Ref: Deutsch-Jozsa algorithm.
1
vote
2answers
63 views
Qubit projections
Given the qubit:
$$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$
What is the corresponding point on the extended complex plane and Bloch sphere?
How to perform calculations and get the point representing ...
0
votes
1answer
56 views
Two qubits problem [closed]
Given the 2 qubit state:
(a/b) |00> + (c/b) |01> + (c/b) |10> + (d/b) |11>
What is the probability that 2 qubits are equal?
Thanks much!
0
votes
0answers
43 views
Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
0
votes
0answers
33 views
The physical implementation of quantum annealing algorithm
From that question about differences between Quantum annealing and simulated annealing, we found (in comments to answer) that physical implementation of quantum annealing exists (D-Wave quantum ...
1
vote
1answer
153 views
I am interested in learning Quantum Computing what should I do? [closed]
I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
13
votes
3answers
367 views
Does quantum computing rely on particular interpretations of quantum mechanics?
It is my understanding that quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed.
...
-2
votes
1answer
44 views
2 following gates, inverse circuit
I have a circuit that has 4 wires and 2 following each other Toffoli gates.
The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below.
What will look ...
1
vote
1answer
97 views
2 following gates, permutation matrix
I have a circuit that has 4 wires and 2 following each other Toffoli gates.
I have permutation matrix for each Toffoli gate (A and B).
Do I have to multiply that 2 matrices to get the entire ...
4
votes
0answers
61 views
fixed input qubit state to an arbirary pure state using two variable rotations and one fixed rotation
It is a theorem that any arbitrary unitary transformation in SU(2) can be factored into the following form:
$ O = U_X(\theta) U_Y(\phi) U_X(\delta) $
Where $U_X$ is a Bloch sphere rotation. I ...
9
votes
2answers
307 views
Entropy of a state subject to the action of a set of random unitaries
Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
0
votes
2answers
95 views
Quantum gate: Phase shift
I dont undestand how to apply a phase shift gate to a qubit. By example how to map $|\psi_0\rangle = \cos (30^\circ) |0\rangle + \sin (30^\circ) |1\rangle$ to $|\psi_1\rangle = \cos(-15^\circ) ...
2
votes
2answers
472 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
0
votes
0answers
47 views
Finding out resulting state [closed]
Suppose we have two qubits in the state $x|00\rangle+y|11\rangle $.
What is the resulting state of the second qubit in that case? Use and to denote and respectively.
2
votes
2answers
153 views
Constructing a Toffoli gate with 2-and 1-qubit gates?
I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
3
votes
1answer
134 views
Quantum computing problem
Suppose that a qubit is in the state $|\varphi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle$, where $a\in[-1,1]$.
If we first perform a standard basis measurement on this qubit and then perform a
...
2
votes
2answers
110 views
Non-destructive measurement of qbits
Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says:
"The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
3
votes
1answer
106 views
Qubit, one or two complex numbers?
I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent qubits.
It is often stated that a qubit is represented as $a|0\rangle + ...
1
vote
1answer
110 views
NOT Universal Operator and Computational basis
This is the relationship between density operator and Bloch vector:
$$\rho= \frac{1}{2}({\bf{\hat{1}}}+{\bf{b}}.\boldsymbol{\hat{\sigma}})$$
We define the NOT Universal Operator in the following way:
...
6
votes
1answer
189 views
Why do we want to entangle qubits?
The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
1
vote
1answer
59 views
How is a qubit realized in a cavity?
Considering a single photon in a cavity, how is a qubit realized in this setup? How is the qubit $|0\rangle$ or $|1\rangle$ manipulated? I.e. how are the transitions $|0\rangle \to |1\rangle$ and ...
0
votes
1answer
148 views
Will quantum computers ever work? [duplicate]
Possible Duplicate:
Why do some physicists believe that scalable quantum computing is possible?
The idea of a quantum computer is that a quantum system can be in a Quantum Superposition of ...
3
votes
3answers
142 views
How can quantum (Internet) network be possible?
According to the knowledge I have, there are routers, switches etc. Therefore, packets would have to be "measured" before continuing on. (If not, how will anyone know the damn IP address?)
But this ...
4
votes
1answer
107 views
Fast algorithm for maximizing the quantum fidelity
Consider the following optimization problem: Given a quantum state $\sigma$, a constant $b$ and a Hermitian operator $A$, find
$\underset{\rho} \max F(\rho,\sigma)$
subject to $\text{Tr}(\rho ...
3
votes
3answers
273 views
what breakthrough Physics needs to make quantum computers work?
I read some posts on this forum and some articles which repeatedly state that it is not impossible to build q-comps but to make it successful, physics needs a great breakthrough.
I tried finding but ...
4
votes
2answers
319 views
Shor's algorithm and Bohmian Mechanics
Do quantum computer's tell us anything about the foundations of quantum theory? In particular Shor argued in the famous thread by 't Hooft
Why do people categorically dismiss some simple quantum ...
1
vote
0answers
50 views
Efficiently distinguishing mixed quantum states?
Assume we know two different mixed states, p and q, and an efficient (quantum) algorithm for creating such two. Does it follow that there exists a computationally efficient method/measurement for ...
4
votes
1answer
226 views
Entanglement of qubits circuit- Bell states
I know that the quantum circuit $\text{CNOT}\; (H \otimes I)$, where $\text{CNOT}$ is the controlled-not gate and $H$ the Hadamard gate, takes the computational basis of two qubits ...
1
vote
3answers
367 views
Can I study Quantum Computing or Quantum Mechanics with an Engineering background?
Sir,
I am studying Electrical & Elctronics Engg. now. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. & then pursue ...
0
votes
1answer
208 views
Existence of quantum computer
At time there are talks about quantum computers and lot of talks and discussion on its exponential speed. But studying in some more details it makes reference to "Heisenberg uncertainty principle", ...
6
votes
1answer
158 views
partial trace with sparse matrices
Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space.
For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
1
vote
1answer
141 views
Quantum Coin Flipping Protocol
$\newcommand{\ket}[1]{\left|#1\right>}$
I have the next protocol:
$A$ tosses a fair coin $a\in \{0,1\}$, if $a=0$, $A$ sends to $B$ $\ket{\psi_0}=\ket0$, if $a=1$ $A$ sends to $B$, ...
4
votes
1answer
138 views
Transpose Map Positive, But Not Completely Positive?
I am reading Introduction to Quantum Computing by Kaye, Laflamme, and Mosca. Here is a question I am struggling with:
Exercise 3.5.6: Prove that the transpose map, which maps $\rho \mapsto ...
0
votes
0answers
19 views
Is the universe a quantum computer - is light speed barrier a computational constraint [duplicate]
Possible Duplicate:
Is the universe a quantum computer - is light speed barrier a computational constraint
Cross-posting this question, since physics.stackexchange has not provided any ...
12
votes
3answers
930 views
Is the universe a quantum computer - is light speed barrier a computational constraint
There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
1
vote
1answer
154 views
Quantum Cryptography
First question was a little bit ambiguous.
Photons are passed through a linear polarizer that is oriented $\theta$ degrees again the photon passes through another linear polarizer that also have a ...
6
votes
2answers
451 views
Quantum Computing, Qubit Creation/Entanglement
I am currently a high school student researching quantum computing. I was referred to this site by Google and a friend. Currently I am researching the qubit part of quantum computing. My question is ...
12
votes
4answers
208 views
direct sum of anyons?
In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally.
There is then supposed to be a braided fusion ...
11
votes
1answer
49 views
Principle behind fidelity balance in quantum cloning
If we do optimal state estimation on an unknown qubit, we can recreate a state with fidelity $F_c=2/3$ with respect to the original. Let us define the "quantum information content" $I_q=1-2/3=1/3$ as ...
14
votes
2answers
50 views
Counting complete sets of mutually unbiased bases composed of stabilizer states
Consider $N$ qubits. There are many complete sets of $2^N+1$ mutually unbiased bases formed exclusively of stabilizer states. How many?
Each complete set can be constructed as follows: partition the ...
11
votes
1answer
51 views
Stabilizer formalism for symmetric spin-states?
This question developed out of conversation between myself and Joe Fitzsimons. Is there a succinct stabilizer representation for symmetric states, on systems of n spin-1/2 or (more generally) n higher ...
30
votes
3answers
311 views
What is the use of a Universal-NOT gate?
The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
16
votes
3answers
147 views
Quantum computing and quantum control
In 2009, Bernard Chazelle published a famous algorithms paper, "Natural Algorithms," in which he applied computational complexity techniques to a control theory model of bird flocking. Control theory ...
3
votes
1answer
1k views
What is quantum discord?
What is quantum discord? I stumbled upon this term on Quantum Computing: The power of discord, but have never heard of it before. Can you give a bit more mathematical explanation of the term here?
1
vote
0answers
110 views
Quantum circuit decomposition
I need to construct a universal quantum circuit decomposition for a three-qubit operation where one qubit is the control bit, and a two-qubit unitary operator acts on the other two
depending on the ...
8
votes
3answers
743 views
Is “analog” quantum-computation not useful?
I understand what a qubit-based quantum computer by the current definition is and how they are constructed. I read another thread where someone suggested encoding a computation into a dual-slit ...
6
votes
2answers
665 views
Recent breakthroughs in quantum computing?
Can anyone explain to me why we have had no major breakthroughs in the theory of quantum computation in the past 15 years?
Shor's algorithm set the standard, since then we've had Grover's algorithm ...
