What is Qubits: Definition and 57 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. cwill53

    Basic Quantum Circuit: States of Individual Qubits

    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...
  2. P

    I How can multiple entangled Qubits be represented and visualized?

    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...
  3. J

    Preparing for a Quantum Computation Course: Superconducting Qubits

    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...
  4. K

    I Can Quantum Entanglement Enhance Atomic Measurement Accuracy?

    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...
  5. Arne

    I Z2 symmetry in the hydrogen molecule when mapping to qubits

    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...
  6. Danny Boy

    A Quantum Ising model correlation function query

    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...
  7. tomdodd4598

    I Number of qubits required for Shor's algorithm to factor a number < 2^n

    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...
  8. E

    How Do Measurements Affect GHZ States?

    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...
  9. S

    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?
  10. jedishrfu

    Who needs qubits? Factoring algorithm run on a probabilistic computer

  11. P

    I Measurement with respect to the observable Y

    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...
  12. Haorong Wu

    Prove that the product of two n qubits Hadamard gates is identity

    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...
  13. J

    A Shor's algorithm - need to uncompute auxiliary qubits?

    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...
  14. F

    I Two quantum states and qubits....

    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...
  15. B

    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...
  16. I

    B Understanding the difference between |01>+|10> and |01>-|01>

    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>...
  17. I

    B How does a Bell State lead to a probability in the CHSH game

    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...
  18. .Scott

    "Quantum Supremacy" expected at 50 qubits

    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"...
  19. C

    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?
  20. Raptor112

    High-Fidelity Qubit Readouts: Definition & Overview

    What does one mean when one says "high-fidelity qubit readouts"?
  21. T S Bailey

    Retrieving information from qubits

    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...
  22. T

    Understanding Qubits: How Superposition Powers Quantum Computers

    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...
  23. K

    Understanding Qubits and Complex Scalars: The Role of Imaginary Numbers

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

    Spins and Qubits: Exploring Determinism in Measurements

    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...
  25. Julian Blair

    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...
  26. Erwin

    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...
  27. ant0n

    How would observation of the state of qubits affect them?

    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...
  28. M

    How can I calculate the exponential of a non-diagonal matrix?

    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 &...
  29. Julian Blair

    Creating superimposed states in an Hydrogen Atom

    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...
  30. Elroy

    Visually representing entangled qubits (i.e., Bell state)

    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...
  31. Elroy

    Qubits, 2 complex numbers, forcing one to real

    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...
  32. A

    Qubits Entanglement: Calculate & Interpret

    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...
  33. lfqm

    Qubits and angular momentum-like operators

    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...
  34. Strilanc

    Superdense coding for sending 2 qubits at a time?

    [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...
  35. G

    Calculating Matrix Representation of 11><11 for 2 Qubits

    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...
  36. M

    Could packet round-trip times be an analog to qubits?

    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...
  37. O

    How can we measure the reality in quBits?

    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...
  38. E

    Qubits and common calculations

    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?
  39. F

    Difference and benefits of qubits compared to regular bits?

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

    Logic gates in excitonic single-quantum-dot qubits

    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...
  41. S

    Logic gates in excitonic single quantum dot qubits

    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...
  42. D

    Possible States of n Qubits as opposed to classical bits

    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...
  43. C

    Question About Qubits and the Representation of the Bloch Sphere

    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...
  44. Y

    Quantum optics, 2 qubit gates acting on 2 qubits - cannot be factorized?

    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.
  45. J

    How Many Qubits Are Needed to Accurately Simulate Hydrogen Molecules?

    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...
  46. 1

    What is a Qubit in Quantum Computing?

    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?
  47. W

    Solving the State of 2 Qubits from a General Werner State

    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...
  48. A

    Understanding Quantum Qubits: Up, Down, and Beyond

    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)?
  49. LaserMind

    Exploring Quantum Computers: Understanding Qubits and Entangled Particles

    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?
  50. D

    Find Min Copies Needed for Certainty of Permuted Qubits w/ General State

    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...