Questions concerning computations performed on a quantum-computer. DO NOT USE THIS TAG just because the question concerns a computation of a quantum-system!
30
votes
3answers
319 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 ...
23
votes
9answers
556 views
Examples of number theory showing up in physics
My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics?
This probably sounds like rather strange question, or rather like one of the ...
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 ...
16
votes
3answers
148 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 ...
14
votes
1answer
319 views
If the ground states of interacting QFTs are so complicated, how did Nature find them?
My question was inspired by trying to understand the paper Quantum Algorithms for Quantum Field Theories, by Jordan, Lee, and Preskill. The main result of that paper is that scattering experiments in ...
14
votes
2answers
52 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 ...
13
votes
3answers
373 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.
...
13
votes
1answer
508 views
How Does a Quantum Computer Work?
I've read Wikipedia, I've read How Stuff Works, I've read The Singularity is Near, but I still just don't get it. How does a Quantum Computer work? It sounds very intriguing, but I just can't wrap my ...
12
votes
4answers
210 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 ...
12
votes
3answers
935 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 ...
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 ...
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 ...
11
votes
1answer
828 views
How many qubits are needed for useful computation?
Seeing the news about 14 entangled states today @ Innsbruck:
I haven't found a clear guide online to how many qubits we are aiming for a first practical quantum computer,
e.g.
Factorization,
Search ...
10
votes
2answers
487 views
Basic questions in Majorana fermions
Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
10
votes
2answers
827 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 ...
9
votes
2answers
660 views
How much is quantum computation changing the interpretation of quantum theory, and, if at all, how?
At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot ...
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 $\rho$ ...
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?
...
8
votes
3answers
751 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 ...
8
votes
1answer
255 views
Which qubit states are accessible with linear optics operations?
Given a quantum state of $n$ qubits, and being restricted to linear optics (that is, the output annihilation operators are linear combinations of the input annihilation operators):
Which states are ...
8
votes
1answer
329 views
Are there any applications of quantum information theory to physics?
Are there any applications of quantum information theory to physics?
7
votes
3answers
2k views
Can a parallel computer simulate a quantum computer? Is BQP inside NP?
If you have an infinite memory infinite processor number classical computer, and you can fork arbitrarily many threads to solve a problem, you have what is called a "nondeterministic" machine. This ...
7
votes
4answers
182 views
If quantum computation is reversible, what is the point of Grover's search algorithm?
Wikipedia et al say the following about Grover's algorithm:
Although the purpose of Grover's algorithm is usually described as
“searching a database”, it may be more accurate to describe it as
...
7
votes
1answer
96 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
4answers
682 views
Dirac equation on general geometries?
I have a numerical method for computing solutions to the Dirac equation for a spin 1/2 particle constrained to an arbitrary surface and am interested in finding applications where the configuration ...
7
votes
1answer
109 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 ...
7
votes
1answer
175 views
Computability of physics
As far as I understand a Universal Quantum Simulator can simulate any quantum system and thus anything that exists in the universe. Also, a quantum computer can implement such a quantum simulator. ...
7
votes
1answer
491 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 ...
6
votes
2answers
455 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 ...
6
votes
2answers
666 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 ...
6
votes
2answers
323 views
Probabilistic quantum cloning
I have a question with regard to probabilistic quantum cloning - see for example http://prl.aps.org/abstract/PRL/v80/i22/p4999_1.
It does seems like I can use the proof for no-cloning theorem to ...
6
votes
1answer
198 views
Ground state degeneracy of a variation of Toric Code model
We know that the ground state degeneracy of Toric Code model is 4. An easy way of seeing this is the following:
Consider a 2D spin model where all the spins live on the links. The Hamiltonian is ...
6
votes
1answer
187 views
Has anyone actually produced any braided anyons (quasi-particles) yet? (quantum computer)
Quasiparticles theoretically can form braids on a 2D surface. The braids apparently are quite stable for reasonably long periods, allowing a superposition state more time before it decoheres through ...
6
votes
1answer
191 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.
6
votes
2answers
319 views
What nonstandard theory forbids quantum computers?
What would a nonstandard model which reproduces all experimental quantum data so far but still cause quantum computers to fail when implementing Shor's algorithm look like? Would it have to be very ...
6
votes
2answers
434 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 ...
6
votes
1answer
162 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 ...
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 ...
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
...
5
votes
1answer
57 views
Scaling of quantum error correction
I'm having a question regarding quantum error correction.
Using a large number of imperfect (but already very good) quantum gates, it is in theory possible to build an equivalent, error-corrected ...
5
votes
2answers
487 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 ...
5
votes
1answer
282 views
If quantum mechanics is ultimately deterministic, would Shor's factorization algorithm still work for large integers?
Victor Stenger argues that the apparent randomness in quantum mechanics is a result of the randomness in the macroscopic detectors (similar to the randomness in the laws of thermodynamics) and is not ...
4
votes
5answers
589 views
Why do some physicists believe that scalable quantum computing is possible?
If you drop a glass cup on the ground, it will break and shatter into pieces. This happens all the time and is consistent with quantum mechanics. But it never happens that a shattered glass cup ...
4
votes
1answer
193 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?
4
votes
2answers
187 views
What is the most natural classical polynomial complexity class that includes all of BQP and NP?
Since we know that there are some oracle problems which can be solved on a quantum computer, but not on an NP machine with the same oracle, the idea of nondeterministic (i.e. infinitely parallel) ...
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 ...
4
votes
1answer
60 views
Do error checking costs of quantum computing shrink BQP?
BQP is the set of problems solvable in polynomial time for a given error tolerance, and it is suspected to be larger than P (and BPP, which is probably equal to P). However, inability for the gates to ...
4
votes
1answer
230 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
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
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 ...
