Tagged Questions
7
votes
1answer
93 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
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
1
vote
0answers
48 views
Creating matrix Hamiltonian for Feynman's CCNOT
I'm trying to read Quantum Mechanical Computer and to implement the CCNOT logical gate with Mathematica.
Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized that i need to ...
7
votes
1answer
108 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
59 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
44 views
Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
1
vote
1answer
154 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 ...
2
votes
1answer
89 views
Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$?
Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$, where $k$ is the number of "hits" in a total of $N$ possible values for $|\,x\rangle$?
If we know $k$, and know ...
-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 ...
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
97 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
488 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
3
votes
2answers
190 views
Quantum Teleportation Fidelity
I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
3
votes
1answer
50 views
Reversible gates
Is it possible to make any gate reversible merely by retaining the input bits in the
output and introducing ancilla bits as necessary? That is, given an irreversible
gate with $k$ inputs and $l$ ...
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 ...
0
votes
0answers
22 views
Finding all marked element by Grover search(not in superposition)
Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, ...
6
votes
2answers
425 views
Quantum Computing Power Advantages
Currently, the world's fastest supercomputer runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some ...
2
votes
2answers
114 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, ...
5
votes
3answers
117 views
Controlled-measurement of a quantum register
Given a state vector $\left[\alpha,\beta,\gamma,\delta\right]$ which is not known a priori, does there exist an operation, which I will call "controlled-measurement", which results in the ensemble
...
1
vote
1answer
117 views
How is a Qubit in two states under Superposition?
I have read a little about Quantum computing.
From what I understand, Quantum Superposition is when a qubit is in a state $\alpha|0\rangle$ + $\beta|1\rangle$, where $\alpha$ and $\beta$ are ...
3
votes
4answers
263 views
Why is quantum entanglement so important?
Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
0
votes
1answer
101 views
Latest advances in experimental quantum processors?
I'm and undergraduate student and I'm doing a report on Quantum computing. As a conclusion of my report I'd like to highlight the latest experimental advances in Quantum Computing, especially in ...
6
votes
1answer
190 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
88 views
Using wavepackets instead of photons in quantum computer
Why does a photonic quantum computer require photons? Why wouldn't wave packets work just as well, better in fact since it would get away from the use of fragile single photons? (Article)
4
votes
1answer
192 views
How many states can a n qubit quantum computer store?
A classical computer composed of '0' or '1' transistors stores $2^n$ states.
Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
3
votes
2answers
230 views
Mathematically challenging areas in Quantum information theory and quantum cryptography
I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
3
votes
1answer
67 views
Does quantum fingerprinting really argue for the exponential size of wavefunctions?
Does quantum fingerprinting really argue for the exponential size of wavefunctions? Quantum fingerprinting is the idea that an exponentially long classical string can be encoded in a linear number of ...
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 ...
4
votes
1answer
229 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 ...
4
votes
1answer
253 views
Areas of computer science required for quantum computing
What knowledge of computer science should I have, to be able to pursue research in quantum computing. I am a Physics undergrad and would take three core courses in QM, before the completion of my ...
5
votes
2answers
486 views
What is “code” in “toric code”?
When I first heard people talking about using Kitaev's toric code to do topological quantum computation, I was thinking how many lines does the toric code have. Then I was told that
the "code" really ...
3
votes
1answer
120 views
How can you distinguish between projections of quantum states?
Consider this problem in quantum cryptography:
We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which ...
0
votes
0answers
142 views
Quantum Compting or DNA computing [closed]
My friend and me are working on DNA computing and on some improvements to it.
Of course, we are working on computing aspects of this branch. So, we have insufficient knowledge about physics and ...
0
votes
1answer
52 views
Building some measurement appratus that distinguish between two mixtures
We have a measurement $M$ that distinguishs between $\rho_1$ and $\rho_0$, if it has three possible answers 1,2,3 and whenever it answers something different than 3 it's correct.
$M$ succeeds with ...
6
votes
1answer
161 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
0answers
46 views
Looking for description of Helstrom's measurement
I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook Quantum Detection and Estimation Theory.
...
2
votes
1answer
129 views
Shor's Algorithm: Why throw away the f(x)?
I'm having a little trouble understanding Shor's algorithm - namely, why do we throw away the result f(x) that we get after applying the F gate? Isn't that the answer we need?
My notation:
...
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 $B$, ...
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
934 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 ...
10
votes
2answers
823 views
Quantum memories: What are they?
Searching the literature for the term "quantum memory" seems to bring up results from two different communities.
On the one hand there are quantum opticians, who see a quantum memory as something ...
8
votes
3answers
37 views
Depolarizing threshold for CSS codes
Many years ago, when CSS codes were first invented, the error threshold of p=0.11 was found when bit and phase flips are independent. Has a threshold yet been found for the case of depolarizing noise?
...
6
votes
2answers
453 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 ...
5
votes
3answers
3k views
Quantum entanglement faster than speed of light?
recently i was watching a video on quantum computing where the narrators describes that quantum entanglement information travels faster than light!
Is it really possible for anything to move faster ...
30
votes
3answers
318 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 ...
7
votes
1answer
489 views
Can quantum annealing be used for factorization?
It is known that there is a famous quantum factorization algorithm by Peter Shor. The algorithm is thought to be suitable only for quantum gate computer.
But can a an adiabatic quantum computer ...
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?
23
votes
2answers
3k views
What can the D-Wave quantum computer do?
The media are reporting the commercially sold 128-bit quantum computer from D-Wave
http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n
which of course ...
