Qubit Definition and 82 Threads

This question is mostly about group theory but I would like to understand it in the context of qubits rotating in a Bloch Sphere. What my understanding of things are right now: In the rotation Lie Group ##SO(3)##, we have three free parameters (##\frac{n(n-1)}{2}##), and this is also why we end...

I am curious as to the meaning of, and name given to the phase ##\xi(t)## which may be added as a prefix to the time evolution operator ##\hat{U}(t)##. This phase acts to shift the energy of the dynamical phase ##<{\psi(t)}|\hat{H}(t)|\psi(t)>##, since it appears in the Hamiltonian along the...

<< All caps removed from post by Moderator >> [/color] A "false" (equally superimposed qubit) is created by mechanically firing with 50/50 probability a resonance photon at a Hydrogen atom qubit in the ground state. This qubit is sent to Alice and it now has 50/50 probability of being in state...

At first, good evening. I want you to know that Eng is not my first language, so you could find many errors while reading my posts. I was reading something about qubit and multiple qubit systems, which combined can create a powerful processor for a new type of computer. I'm not sure of how...

Given a 2 state hydrogen atom in a superimposed state, how does one measure it for either of its two states?

Hi guys! I have an unsolved problem. I'm going to calculate the concurrence for pure 2-qubit states: |Ψ>=a| up up >+b|up down> +c|down up> +d | down down > where up and down stay for uparrow and downarrow. The concurrence is defined as: C = 2|ad-bc|≥0 I have found the vector Ψ3= 1/2 (1,1, cos...

Firstly, I apologise for any lack of understanding, incorrect assumptions or misinterpretations of the very little I know about physics, quantum mechanics & quantum computing. I am not an academic, scientist or mathematician, but a software engineer with an interest in quantum computing and...

This is undoubtedly one of the more basic (not to say stupid) questions ever to appear in this rubric. But here goes: Suppose you have v= 0.6|0> + 0.8|1>. This means that there is 36% chance of measuring |0> and 64% chance of measuring |1>. Otherwise put, given a million particles in this...

If you have a two-qubit system |x>[(|0>-|1>)/√2], whereby x∈{0,1}, and you want to just know x, do you (a) assume that this means that |x> belongs to one particle, (|0>-|1>)/√2 to another particle, so you just measure the first particle? or (b) if you can't tell the particles apart, pass this...

I undertand that measuring a qubit's spin along a particular axis yields one of the eigenstates of the corresponding pauli matrices. I'm a little confused about what this type of measurement looks like mathematically. i.e how do you show the actual act of observing the qubits spin using the...

Hi All, I'm gradually teaching myself quantum computing, being an excellent programmer and fair at linear algebra and geometry. To learn it, I'm writing a quantum computer emulator (complete with graphical representations). I'll share it when I get to some level of completion. The following...

Homework Statement Determine which qubits are entangled: ##|\psi\rangle=\frac{1}{2}(|000\rangle+i|010\rangle+i|101\rangle-|111\rangle)## Homework EquationsThe Attempt at a Solution [/B] My idea was to first calculate the density operator ##\rho = |\psi\rangle \langle\psi|## and then find...

Hi I'm going through some course notes for QM. A state for a 2 qubit system is called non-entangled (or separable) if it can be decomposed in a tensorproduct of 2 single qubit states. If we write a general state as |\psi> = a_{00}|00>+a_{01}|01>+a_{10}|10>+a_{11}|11> A theorem states...

I have seen numerous articles referencing the teleportation of information over a distance of 3 meters using quantum entanglement. I don't believe it. That would contradict special relativity, would it not? You could, for example, decide which of two observers moving relatively to one...

Homework Statement See attachment Homework Equations The Attempt at a Solution (i) |\Psi(t)_{1}>=e^{{-itE_{1}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>+|z^{-}>) |\Psi(t)_{2}>=e^{{-itE_{2}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>-|z^{-}>) where...

Good day everyone, I apologize if this is not the correct forum; in some way it is a homework question but not of the ordinary form. This semester I will be writing a ~3000 word paper on the topic of the current standing in qubit research, where I will be describing and comparing various...

Hi I read this information about the Qubit: "N Qubits are equivalent 2^N classical bits (2^N states)" But I couldn't understand that, because I know that each single Qubit could be one and zero at the same time, so each single Qubit is equivalent two classical bits (two states) That...

I am having trouble understanding the following: Uf: |x>|y> → |x>|y \oplusf(x)> \oplus being a mod 2 operation (nand)? I suppose I don't understand how to read the "ket" states so well. As far as I understand we have that since x and y can be 0,1 only if |x=1>|y=1> then if f(x) = 1 then...

I have seen four two qubit entangled states of the form: $ \frac{1}{\sqrt{2}} \left | 00 \right > \pm \left | 11 \right >$ $ \frac{1}{\sqrt{2}} \left | 01 \right > \pm \left | 10 \right >$ I want to write a most general two qubit entangled state. I presume it can be of the form: $...

Hi guys having a little trouble with two-qubit state multiplication. Could you tell me how you work out the following? (not only the answers but the working out) I need to be able to understand these calculations before I can move on to the next step of an entanglement question. I understand...

This is a bit embarrassing, but by convention does |0> = (1,0)^T and |1>=(0,1)^T, where we are in the basis of the eigenvectors of \sigma_{z}?

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 to do this, or how to verify it (fig 4.8 in his book) I've attached a photo of the diagram...

Hello! I am new here and I will try my best to clarify my questions and not violate the forum rules. Just for the record, I am not particularly good at understanding equation-saturated explanations because I am not an expert. However, I did a lot of searching and I still don't understand...

I just had a weird thought. One qubit is a 2-d complex vector space which is isomorphic to a 4-d real vector space. Why can't we model the 4-manifold of space-time universe using one qubit?

Whats most scalable qubit candidate so far ? - - Thanks, Vvk

Hi, I would like to ask some questions in regards to preparing mixed states. Assuming I am allowed to prepary any pure quantum state, perform measurements and apply unitaries, I am asked to prepare a single qubit quantum state of maximum entropy. As I understand, a 1-qubit quantum...

Quantum optics, 2 qubit gates acting on 2 qubits - cannot be factorized?? Hi, I'm struggling to understand why two qubit gates acting on two qubits cannot be factorized, i.e. G12 \neq G1 \otimes G2, where G1 acts on qubit 1 only and G2 acts on qubit 2 only.

From the http://physicsworld.com/cws/article/news/23637 How can that be possible? Isn't that a violation of the No-cloning theorem?

What requirements must an observable A meet to be usefull as a qubit for quantum computers? I think that the wave function must have time independent coefficients in the base of A (when we are not applying quantum gates). This means that expected value <A> must be constant, so the...

What is the arbitrary density matrix of a mixed state qubit?

Hi, One can describe a pure qubit in two ways (onto the bloch-sphere): 1.) one take a (\alpha,\beta) , where \alpha,\beta are complex numbers and \left|\alpha\right|^{2}+\left|\beta\right|^{2}=1. 2.) with a real 3-dimensional unit vector. Bob wants that Alice generate one million random...

ok I just read something that doesn't make much sense to me. It said that quantum computers can only use reversible logic gates because irreversible gates generate heat/lost information. It makes sense to me that everything in physics is reversible and that NAND gates produce heat because...