Qubits Definition and 57 Threads

I have done part A so far below, but I'm a bit behind on my reading, so I don't quite understand the action of the controlled-NOT gate on a single qubit. What I have so written so far for part B is: Let ##\mathcal{H}=(\mathbb{C}^2)^{\otimes 3}##. Let ##|\psi _{q_i}\rangle_k## , ##(i\in\left...

One Qubit can be represented on the Bloch sphere. How would multiple entangled Qubits (say 2 or 3) be represented? Classically, one would think that if one Qubit is represented on a Bloch sphere, 2 Qubits would be represented on 2 Bloch spheres, but I'm pretty sure it doesn't work this way. I...

Summary:: Looking for articles/books to prepare myself for the course: Quantum computation with superconducting qubits Hello everyone. I am about to take a course in Quantum computation with superconducting qubits and I am searching for material to prepare it. I took a first course on that...

Hello! I don't know much about quantum computing beside some basic notions, but I was wondering if there are techniques used there that can be used in measuring properties more accurately compared to current laser based techniques (e.g. Ramsey interferometry, infrared interferometry)? For...

Hello! When using a Jordan-Wigner-mapping or parity-mapping to map the hydrogen molecule \mathrm{H}_2 with two electrons and 4 spin-orbitals to 4 qubits, it is possible to reduce the number of qubits down to two [1,2,3]. The reason is apparently that the molecule has a discrete...

In this paper, on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G} = \langle \mathcal{T}_C(\hat{\sigma}^{a_n}_{j_n}(t_n^*)\cdot\cdot\cdot...

Hey there, There are plenty of proposed implementations of Shor's algorithm which require different numbers of qubits, ##q##, to be able to factor a number ##N## of size ##<2^n##, i.e. a number of length at most ##n## bits. Most of these require ##q## linear in ##n##; for example, this...

Here's what I think I understand: First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab. I'm thinking the expectation values of each operator...

Hi, I'm trying to understand an outer product |1>_a<1| where |1>_a is the ket for one qubit (a) and <1| is the bra for another qubit. Does this make sense and is it possible to express it in terms of tensor products or pauli matrices?

https://arstechnica.com/science/2019/09/who-needs-qubits-factoring-algorithm-run-on-a-probabilistic-computer/

Hello, I would like to start with an assumption. Suppose a system is in the state: $$|\psi\rangle=\frac{1}{\sqrt{6}}|0\rangle+\sqrt{\frac{5}{6}}|1\rangle$$ The question is now: A measurement is made with respect to the observable Y. The expectation or average value is to calculate. My first...

From the properties of tensor product, ##H^{\otimes n} \cdot H^{\otimes n} =\left ( H_1 \cdot H_1 \right ) \otimes \left ( H_2 \cdot H_2 \right ) \otimes \cdots \otimes \left ( H_n \cdot H_n \right ) =I \otimes I \otimes \cdots \otimes I =I## where ##H_i## acts on the ##i^{th}## qubit. But I...

Due to required reversibility, classical function (f(a)=y^a \mod N) in Shor's algorithm needs a lot of auxiliary qubits. I was afraid that their later treatment might influence the computation - and just got confirmation from Peter Shor himself: that we need to "uncompute" these auxiliary...

Hello everyone, My understanding is that a two-quantum state system is simply a system that can only be in two states. That is equivalent to say that the observable of interest that is being considered can only have possible values. Is that the case? If so, a classical bit can have two values...

Hello everyone! I'm having trouble understanding a specific aspect of qubits, maybe someone among you clever guys can help me. I understand that a qubit is in superposition, we can store information (a quantum property equivalent of true or false) in it. I also understand that reading that...

Hi, I am a student from the Netherlands in 6V, the year before university, and I'm doing research on Quantum Computing. However, I have difficulty understanding the four states of two entangled qubits, $$\left|00\right> \\ \left|01\right> + \left|10\right> \\ \left|01\right> - \left|10\right>...

Hi, I am a student in the Netherlands, and I'll be attending university next year. However, I am doing some form of research on Quantum Computing with another student for our so-called "profielwerkstuk" but my understanding of Quantum Physics and math is sometimes not at the level that is...

In an article posted here: http://arxiv.org/abs/1608.00263 the authors estimate that a 50-qubit computer would be capable of computations that could not be replicated in real time by a classical computer. Interestingly, according to "New Scientists"...

Can a Markov chain be used to generate a set of qubits given their initial state?

What does one mean when one says "high-fidelity qubit readouts"?

I'm very confused as to how qubits function. I understand that qubits can represent 2^n classical bits due to superposition, but I cannot find an explanation as to how the qubit can "parallel process" if you will. How could the qubit represent 2^n bits if, whenever it is measured, you still...

Hi, I'm having trouble understanding the power of qubits relating to quantum computers. I've read a number of times that the power comes from the fact that instead of simply holding an on or off state (1/0), they can hold both at the same time (superposition). However, when we measure them...

Hi, Does anybody know why we have complex scalers to represent qubits..I mean why they are not real numbers. Thanks

I'm aware that this is a very basic question, yet I hope to get a non-trivial answer :wink: Let's assume to have an apparatus A (to make measurements) that is oriented in space. We first point it along the z axis and measure a spin σz = 1. Then we rotate the apparatus through an angle of ½π...

<< All caps removed from post by Moderator >> 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 |0> or...

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...

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...

Hello, I have a problem where I'm given the following H=-\frac{\hbar\Omega}{2}\sigma_x\quad\quad\quad\textrm{and}\quad\quad\quad\Psi(0)=\left|0\right\rangle\quad Where \sigma_x=\begin{pmatrix}0 &...

I've been following the EdX course on Quantum Computing by Prof. Vazirani and I don't understand how one physically can create a superimposed state of the ground and 1st excited state of an hydrogen atom. He mentions "the use of light," but doesn't explain the frequency of the light, nor the...

Hi All, I'm in the beginning stages of writing a quantum computer emulator, primarily to get all the concepts down. I've got an excellent Bloch sphere with a Bloch vector that I can duplicate as many times as I like. However, I'm now tackling entangled states. I'm struggling with identifying...

Hi All, I'm working out a program to emulate a quantum computer (definitely in a nascent stage), and I'm struggling with a piece of the math. I looked at the math sections in these forums, but thought this might be more appropriate to post it. I'll try to conceptually outline the problem, and...

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 guys, my quesion is quite simple but I think I need to give some background... Let's suppose I have 3 qubits, so the basis of the space is: \left\{{\left |{000}\right>,\left |{001}\right>,\left |{010}\right>,\left |{100}\right>,\left |{011}\right>,\left |{101}\right>,\left...

[Superdense coding](http://en.wikipedia.org/wiki/Superdense_coding) is a way to send 2 classical bits by sending only 1 qubit and 'consuming' a previously shared entangled qubit. (Normally you could only send 1 classical bit per qubit.) My question is: why doesn't this work (or does it?) for...

Forming the matrix representation of say 1><1 is no problem but how does one calculate the matrix representation of 11><11 ? Is it 0 0 0 0 0 1 0 1...

I'm a programmer who is trying to figure out if there is any possible way to implement a pseudo-quantum cryptography algorithm without quantum computers, or is Bell's Inequality something that is going to get in the way of that goal? Or if I am anywhere in the ballpark. I wouldn't be surprised...

How can we measure the "reality" in quBits? Hello All matter is based in information, and quantum computing use quBits, so I was wondering how can we measure the reaility in quBits? A certain solid objet, let's imagine an apple, it has a weight and we can calculate (approximately) the number...

Qubits are mentioned for use for factorizing big numbers, for search engines, etc. But, what about common calculations as multiplications etc? Why they are not mentioned for this, are not appropriate or they are too less economic for use of this?

Hello Forum, is someone able to explain, conceptually, in layman terms, the difference and benefits of qubits compared to regular bits? thanks, fisico30

I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...

I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...

I am reading an introduction to quantum computing and I have a question about one thing I don't understand. "In classical physics, the possible states of a system of n particles, whose individual states can be described by a vector in a two dimensional vector space, form a vector space of 2*n...

I have a general question about extracting information from measurement of a qubit. Theoretically a qubit in a superposition state contains an infinite amount of information, but when measured collapses to a definite state and result. My question is this: Is there a way to obtain a value from...

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.

Recently the NIST group demonstrated a two qubit programmable quantum computer, http://arxiv.org/abs/0908.3031 And another consortium used a two qubit computer in an iterative fashion to compute some properties of the hydrogen molecule. http://arxiv.org/abs/0905.0887 How many qubits...

Can someone give me a layman's explanation for the Qubit? And, like the bit, does it represent an intangible, or does it have some material quality to it?

Homework Statement If I was given a general Werner state: u |001> + v |010> + w |100>, where u, v and w are just arbitrary constants. Now, the question is, what is the state of the first two qubits if the third is measured to be |1>? Homework Equations The Attempt at a Solution...

Guys, I'm stuck with a simple and stupid question... We have a spin "up" and "down" as a qubit 1 and 0 states. Now can we consider a state perpendicular to this basis direction as a (0+1)/sqrt(2) state? If not then what is the sense of the phase shift x in the state (0+exp(ix)1)/sqrt(2)?

Quantum Computers use Qubit with Up Down spin to holds bits |0> and |1> for entangled particles in a Bell state. Is this the only way of doing it?

Suppose you have a general state of n-qubits, and you have a second copy with the same state, but with the qubits permuted in some order. Suppose you have given lots of copies of these pairs. What is the minimum number of such copies needed to find the permutation with high certainty as a...