# What is Qubit: Definition and 80 Discussions

In quantum computing, a qubit () or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

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1. ### I Qbit pure vs mixed state space

According to this Wikipedia entry a quantum pure qbit state is a ray in the Hilbert space ##\mathbb H_2## of dimension 2. In other words a qbit pure quantum state is a point in the Hilbert projective line. Now my question: is an arbitrary vector in ##\mathbb H_2## actually a "mixed" state for...
2. ### Questions from Quantum Measurements

[Mentor Note: Two similar thread starts merged] The questions are from MIT OCW. First of all, I cannot understand what is the meaning of the measurement outcome being 0. How can an eigenvalue be 0? I tried doing the problems guessing that by 0 they mean the posterior state will be |0>. The only...
3. ### Model for a Qubit system using the Hamiltonion Operator

Hi, unfortunately, I am not sure if I have calculated the task a correctly. I calculated the eigenvalues with the usual formula ##\vec{0}=(H-\lambda I) \psi## and got the following results $$\lambda_1=E_1=-\sqrt{B^2+\nabla^2}$$ $$\lambda_2=E_2=\sqrt{B^2+\nabla^2}$$ I'm just not sure about...
4. ### I What causes qubit superpositions to form?

When I observe a qubit's state, decoherence happens such that I find the qubit in a particular state. After I cease observing a qubit's state, what physical process causes a fresh superposition of states to develop? Is zero-point energy at least a contributor?
5. ### Calculate qubit states with Schrodinger's equation

Summary:: How to calculate qubit states with the Schrodinger eq I'm writing something about the relation between quantum computers and the Schrodinger equation. One of the requirements is there has to be an experiment. So I thought I could measure some qubits that have results and then do the...
6. ### I Measurement of a qubit in the computational basis - Phase estimation

Hello, I have a question about the measurement of a qubit in the computational basis. I would like to first state what I know so far and then ask my actual question at the end.What I know: Let's say we have a qubit in the general state of ##|\psi\rangle = \alpha|0\rangle + \beta|1\rangle##. Now...
7. ### I Information content of a qubit

I have just started reading Neilson and chuang's book on quantum computing and two times already have they said that when a qubit is not observed, it can contain infinite information. "How much information is represented by a qubit? Paradoxically, there are an infinite number of points on the...
8. ### A Translating/encoding a continuous variable model into a qubit model

I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...
9. ### How can I apply single qubit gates and CNOT to 8x1 column vectors?

I know |GHZ>=(1/sqrt(2))[1; 0; 0; 0; 0; 0; 0; 1], and |000>= the tensor product |0> x |0> x |0> = [1; 0; 0; 0; 0; 0; 0; 0]. Can I apply single qubit gates (i.e. 2x2 matrices) and CNOT (a 4x4 matrix) to 8x1 column vectors? If so, does anyone know a good starting point or a hint to get me moving...
10. ### Controlled-Z gate as a product of exponentials

I have numerous points of confusion: what does it mean that the matrices are within the exponential? How do I go about doing the matrix multiplication to prove the given form of CZ matches the common form, the 4x4 matrix? Update: using the fact that exp(At)=∑ ((t^n)/n!)*A^n, where A is a...
11. ### Projective measurements of quantum processor

Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be: |<0|1>|^2= 0 |<1|1>|^2= 1 |<+x|1>|^2= |(1/√2)|^2 = 1/2 |<-x|1>|^2= |(-1/√2)|^2 = 1/2 |<+y|1>|^2= |(-i/√2)|^2 = 1/2 |<-y|1>|^2= |(i/√2)|^2...
12. ### Qubit Operations: Finding U Gates & Probabilities

Part a: Gate H X Y Z S T R_x R_y Theta pi pi pi pi pi/2 pi/4 pi/2 pi/2 n_alpha (1/sqrt(2))*(1,0,1) (1,0,0) (0,1,0) (0,0,1) (0,0,1) (0,0,1) (1,0,0) (0,1,0) Using the info from the table and equation 1, I find: U_H=(i/sqrt(2))*[1,1;1,-1] U_X=i*[0,1;1,0] U_Y=i*[0,-i;i,0] U_Z=i*[1,0;0,-1]...
13. ### A How to build a qubit (theoretically)?

And I was asked to include the deviation and the inherent process of the effective Hamiltonian of the charge qubit and the equation as well. And some of the derivation of the Hamiltonian as well. P.S The effective Hamiltonian formula is from the reference of ...
14. ### A The cnot with outer product control qubit

I have a simple question...the control qubit is A and the the target is B. The cnot is applied on |1A> <0A|⊗|0B0C>. ... How does it work. Thanks in advance.
15. ### A Qubit Energy Level Required to be Unevenly Separated

I been reading up on quantum computers and in particular ones based on quantum harmonic oscillators. In all the articles, I have come across they mention a regular, linear LC oscillator cannot be used for a Qubit because it's energy levels are evenly spaced. Therefore, they use a non-linear...
16. ### Understand the Outer Product of two qubits

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?
17. ### Trace of a subsystem of a two qubit system

Consider the first qubit (subsystem A): First, the density operator for the system AB is ## \rho ^{AB} =\frac { \left |00 \right > \left <00 \right |+ \left |01 \right > \left < 01\right |+\left | 11\right > \left < 11\right | } 3 ##. Then, the reduced density operator of subsystem A is ##...
18. ### I Vector Notation of Quantum States for 2 Qubit System

I am confused about the vector notation of quantum states when I have a 2 qubit system. For 1 qubit, I just write l1> = (0 ;1 ) for representing 1, and l0> = (1;0) for representing 0. Dirac notation is straightforward However when it comes to representing two qubits in linear algebra I...
19. ### Insights A Classical View of the Qubit - Comments

Greg Bernhardt submitted a new blog post A Classical View of the Qubit Continue reading the Original Blog Post.
20. ### A Finding E_J Value of a Qubit: Step-by-Step Guide

Hi everyone, I’ve performed microwave measurements on a 3D transmon and want to find the E_J value of the qubit. I’ve tried searching through many papers, particularly Koch et al, about how to do this, but I am stumped. Could someone please help me out? Thanks in advance.
21. ### A How to measure the first qubit in two qubit system? QC

I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>? A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
22. ### I Schmidt decomposition and entropy of the W state

Hello, The state | W \rangle = \frac { 1 } { \sqrt { 3 } } ( | 001 \rangle + | 010 \rangle + | 100 \rangle ) is entangled. The Schmidt decomposition is : What would the Schmidt decomposition be for | W \rangle ? I am also intersted in writing the reduced density matrix but I need the basis...
23. ### I Exploring Epistemic Models of Qubits: Finite or Infinite Ontic States?

I'm reading the following paper. https://arxiv.org/abs/1409.1570 Is there an epistemic model of a qubit in which the number of ontic states is finite? I realize Spekkens toy bit discussed in the paper has only 4 ontic states, but it seems to only model a qubit that was prepared in one of 3...
24. ### 2017 Article on Qubit Flipflops

I found this interesting article on theory work done to create qubit flipflops that can be adjusted via electric fields making them easier to integrate into existing computing systems...
25. ### I What exactly is Weizsäcker's ur-alternatives theory?

What is exactly Weizsäcker's ur-alternatives theory? How is it related to digital physics theories? Is it related to pancomputationalism? Does it defend that a universe can be described as being fundamentally made of qubits? Would this mean that that universe would be fundamentally made by...
26. ### I Clarification on what we can consider a qubit to be

In a 2 level quantum system, should I consider the states |0> and |1|> to be qubits by themselves? Or is only the SUPERPOSITION of these two states, \alpha |0> + \beta |1> considered to be a qubit?
27. ### Measure the state of the second qubit

Homework Statement For the state ##(4|00\rangle+3i|11\rangle)\otimes (|0\rangle+i|1\rangle) + (2|01\rangle -i|10\rangle)\otimes(|0\rangle-|1\rangle)## What's the probability of zero being the outcome of measuring the second bit and what is the state of the other two qubits after measurement...
28. ### A Qubit error rate of QKD BB84 protocol

Hello everyone, I don't know how to measure the QBER of BB84 protocol in a realistic experiment.In the most paper show the data which is only the number but do not show the unit of data, what is the unit of these data?
29. ### I Does 'Phase Inversion' grow exponentially?

Hi! So I'm studying Gover's Algorithm and I have this doubt: Does 'Phase inversion gate' grows exponentially? I mean, if I want to signal the one combination that is the answer, I must be able to represent all 2^N states, where N is the number of qubits in the system. How do I do this without...
30. ### I Qubit mixed state density matrix coordinates on a Bloch ball

What are the coordinates on the 3D Bloch ball of a qubit's mixed state of the form: ##\rho=p_{00}|0\rangle \langle 0|+p_{01}|0\rangle \langle 1|+p_{10}|1\rangle \langle 0|+p_{11}|1\rangle \langle 1|##
31. ### I Is a Qubit in a Quantum Superposition or a Mixed State?

Is it in a Quantum superposition, and then only in a mixed state when finding the reduced state of a qubit from an entanglement of multiple qubits?
32. ### I Qubits: Can We Store Information Again After Read?

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...
33. ### B Exploring Qubits: The Basics of Quantum Information and Computing

https://en.wikipedia.org/wiki/Qubit (copy and paste) "In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit (sometimes qbit) is a unit of quantum information—the quantum analogue of the classical bit. A qubit is a two-state quantum-mechanical system, such as the polarization of a single...
34. ### A What Are Advanced Dissertation Topics in Quantum Computing?

Hi! I'm going on to the masters year of a theoretical physics course and I need some inspiration for my dissertation. Last year I did a one semester long project on quantum computation. (More specifically I discussed the general idea of a qubit, a simple method of realising a qubit using spin...
35. ### How does a qubit represent the number two in quantum computing?

Qubit can be ZERO and ONE at the same time. Right? 1 and 0 can represent TWO (10) in a binary system. Right? Therefore one qubit can represent number 2. Right? My question. When this qubit is used to give a result of a calculation (is measured/evaluated somehow at the end of a calculation) it...
36. ### A Single qubit coherence time record

Is it possible yet to store a single qubit for an extended period of time? If I only care about storing a BB84 state, is it possible to take (say) 128 of these single qubit storages? They're not entangled and I don't need to send them through any general quantum circuitry.
37. ### Can the Markov chain be used in qubit manipulation?

Can a Markov chain be used to generate a set of qubits given their initial state?
38. ### Understanding the optimal approximate qubit cloning method

The paper Optimal Cloning of Pure States by R. F. Werner describes a method for approximately expanding an unknown state ##\rho## containing n copies of a qubit, so ##\rho = (\alpha \left| 0 \right\rangle + \beta \left| 1 \right\rangle)^{\otimes n}##, into a larger state with d more qubits...
39. ### High-Fidelity Qubit Readouts: Definition & Overview

What does one mean when one says "high-fidelity qubit readouts"?
40. ### Understanding Interference of Qubits with Varying Density Matrices

Hi PF I wonder how qubits interfere in interferometers when they are not in pure states. Let us take qubits with density matrix = Id/2. There lay at the center of the Bloch sphere. Half of them can travel unchanged through the left arm. In the other arm they become ##UP_Z##. Then there is...
41. ### CNOT Quantum Gate Schematics: Physical Implementation

Hi everyone. I'm just looking for schematics of cnot quantum gate, but on the Internet it only talks about it from a mathematical point of view. I want to ask you if you have some drawing, or schematics of it, from a "Physical" implementation, in the sense, how are the spins prepared, how we...
42. ### Complementing a Qubit in the Bloch-Sphere

Hi :-) for my master thesis I'm working with qubits in the Bloch-sphere representation ##|q\rangle = cos(\frac{\theta}{2})|0\rangle + e^{i\phi}sin(\frac{\theta}{2})|1\rangle##. Side question: why is only the second amplitude complex? But let's move to my main question. I need to know how the...
43. ### Qubit Probabilities and Angles between the measurements

Homework Statement Suppose that two measurements are made on a qubit in rapid succession. The first is δz and the second is δn. Suppose the first results is always +1. Calculate the probabilities of obtaining the results +/- 1 for the second measurement in terms of the angle θ between z and n...
44. ### Exploring Quantum Computing: Making a Qubit with Josephson Junctions

I am working on a project for our local science fair and decided on researching quantum computers. (This is what my focus will be in college.) Though, I expect to work on this far past the time allotted for that. I would like to build a superconductor based qubit using Josephson Junctions. The...
45. ### Multiple Measurements of a single Qubit

Hi :-) I'm working on my master thesis in the field of quantum theory; currently I investigante No-Go-Theorems like the No-Cloning, No-Deleting, No-Hiding, No-Communication-Theorems ans so on. There is a fundamental question which is somehow linked to the No-Communication-Theorem. Is it - in...
46. ### Rotations in Bloch Sphere, and Free Parameters of a Qubit

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...
47. ### Additional Phase factors in SU(2)

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...
48. ### A "false" superimposed qubit vs a "real one"

<< 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...
49. ### Exploring Qubits and Multiple Qubit Systems

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...
50. ### Measurement of a Hydrogen qubit?

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