Read about quantum computation | 32 Discussions | Page 1

  1. ubergewehr273

    I Extraction of a particular quantum state from a quantum circuit

    Hello everyone! I'm trying to implement a quantum circuit that yields a superposition state $$\frac{1}{\sqrt{2}} (|01 \rangle + |10 \rangle)$$ I'm using parameterized gates to achieve this. I have been able to create the state $$\frac{1}{\sqrt{2}}(|01\rangle + e^{i\phi} |10 \rangle)$$ Is there...
  2. B

    A Quantum Period is Compression Robust The paper finds that one can reduce the number of qubits to a constant (just one works) used in the last, modular exponential register of the variants of Shor's algorithm, used to factor integers and find discrete logarithms, by applying a universal hash...
  3. 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...
  4. ngrunenberg

    B How do quantum computers find a solution?

    Apologies in advance if this is a stupid question, I'm not the brightest. I recently listened to Scott Aaronson's conversation with Lex Fridman, and an interview he did for Scientific American, regarding quantum computing (QC from now on) and have a question regarding how a QC finds a solution...
  5. Quantum Alchemy

    I How does Classical Physics explain Quantum Entanglement?

    As a Computer Programmer, it's hard to wrap my head around Quantum Entanglement and non locality being explained in the context of Classical Physics. In other words, if the universe at it's core is physical where does Quantum Entanglement fit within a physical picture of reality? There's been...
  6. Auto-Didact

    Google: Demonstrating Quantum Supremacy

    Here is the paper, published today in Nature: Arute et al. 2019, Quantum supremacy using a programmable superconducting processor
  7. E

    Quantum gravity and quantum cosmology books

    At the risk of annoying some people but hopefully also interesting others I would like to mention my new book on the periodic table, which has just been named as one of 7 "outstdanding academic books of the year 2007" in the category for chemistry But the book is as much about physics as it...
  8. P

    I Quantum Computing - projection operators

    Assume ##P_1## and ##P_2## are two projection operators. I want to show that if their commutator ##[P_1,P_2]=0##, then their product ##P_1P_2## is also a projection operator. My first idea was: $$P_1=|u_1\rangle\langle u_1|, P_2=|u_2\rangle\langle u_2|$$ $$P_1P_2= |u_1\rangle\langle...
  9. Haorong Wu

    [Quantum Computing] Verify a circuit implementing and operation

    This is an exercise from "Quantum search as a quantum simulation " in Chapter "Quantum search algorithms". The circuit is shown as the following picture. For small time interval, the effect of the operation in the problem statement could be written as ## exp \left ( -i \left | \psi \right >...
  10. I

    Programs Topics at the junction of AdS/CFT and quantum information

    I have been asked to draft a (informal) research proposal for a PhD thesis. I have some background in quantum information and my interests are leaning towards the AdS/CFT correspondence. I was wondering if you could suggest a few (preferably recent) theory papers at the junction of quantum...
  11. Haorong Wu

    I Is there a procedure for designing some quantum circuits?

    In Nielsen's book, the chapter of quantum circuits does not describe explicitly any procedures to design a circuit. For example, given the matrix of Fredkin gate, ##\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1...
  12. Haorong Wu

    I The Schmidt decomposition in QC

    Hi, there. I have some problems when learning Schmidt decomposition in Nielsen's QC. The statement of Schmidt decomposition is simple and clear, however, the book doesn't give a clear procedure to do the Schmidt decomposition. I don't know whether the proof under the theorem is the the one I...
  13. D

    I HHL Algorithm for Solving Linear Equations

    I have a question about HHL algorithm for solving linear equations of the form: A x = b Where A, x and b are matrices Take for example 4x1 + 2x2 =14 5x1 + 3x2 = 19 HHL apply the momentum operator eiAτto/T on the state, do a Fourier Transform on |b> and...
  14. meyol99

    A Atomic state that is a coherent superposition?

    Can someone explain the meaning of the k vector and the general meaning of this equation?
  15. G

    2D subspace of a Hilbert space

    Homework Statement Have to read a paper and somewhere along the line it claims that for any distinct ## \ket{\phi_{0}}## and ##\ket{\phi_{1}}## we can choose a basis s.t. ## \ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}=...
  16. D

    Finding the magnetization in nuclear magnetic resonance

    Homework Statement J-coupling term between two spins is HJ = ħJ/4 σz(1) σz(2) In the measured magnetization spectrum of the spins, this leads to the splitting of the individual spin lines by frequency J, which we’ll now derive. We can write the magnetization of spin 1 as: <M1(t)> =...
  17. DrHix

    How do I construct a controlled Hadamard gate?

    Homework Statement I am supposed to construct a controlled Hadamard gate using only single qubit and CNOT gates. Homework Equations [/B] We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix) I've...
  18. J

    A Shor's algorithm and similar exploitation of QM?

    Shor's algorithm is rather the most interesting quantum algorithm as it shifts a problem which is believed to need exponential classical time, to polynomial time for quantum computer, additionally endangering asymmetric encryption like RSA and ECC. The real question is if there are other...
  19. C

    A Generalizing distinguishability of photons on HOM dip?

    Hello all. I am trying to determine what is the effect of having photons that are distinguishable undergoing a quantum interference process. To do that, I try to generalize the Hong-Ou-Mandel effect, and try to determine what are the terms that appear as a function of the product of the creation...
  20. Johny Boy

    A Using feedback in quantum measurements

    If we consider an efficient measurement performed on a system in a pure state. How would we use feedback (by applying to the system a unitary operator that depends upon the measurement result), to prepare the system in the same final state for every outcome of the measurement (this can be done...
  21. E

    Other Better Supervisor or preferred field?

    I am attempting to choose a field of study for my masters course following my undergraduate course however due to the circumstances of the researchers I have to choose between a better supervisor or a preferred field of study; my ideal field would be theoretical quantum computing, however the...
  22. S

    I Why must qbits be entangled?

    Hello I understand what entanglement is and also what superposition is. But I don't understand why qbits in a quantum computer must be entangled.
  23. D

    I They physics of phase inversion in Grover's algorithm

    How would this operator be implemented physically if we had a quantum computer? In Grover's algorithm this magical operator is often called "phase inversion". Here is the operator from wiki: It’s...
  24. Auto-Didact

    A Decoherence-free phononic BEC quantum devices?

    Howl et al. 2016, Quantum Decoherence of Phonons in Bose-Einstein Condensates Anyone in the field of quantum information/quantum computation wish to comment on such an approach for building a quantum computer?
  25. munirah

    How to differentiate GHZ state and W state?

    Good day, I try to differentiate GHZ-state and W-state using three tangle. Suppose The value three tangle for GHZ-state equal to 1 while W-state equal to 0. I used three tangle formula, $$\tau_{ABC}=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}=2(\lambda^{AB}.\lambda^{AB}+\lambda^{AC}.\lambda^{AC})$$...
  26. munirah

    How can I make singular matrix become nonsingular matrix?

    << Mentor Note -- thread moved from Homework Help forums to General Math >> Good day, I run coding in Mathematica. But, I get singular matrix A at certain loop. In theory, how can I make matrix A become orthogonal A=\begin{pmatrix} 0& 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0& 0 & 0 & 0 & 0 & 0 & 0 &...
  27. munirah

    Parameter of SU(4) and SU(2)

    Homework Statement Good day, From my reading, SU(4) have 15 parameter and SU(2) has 3 paramater that range differently with certain parameter(rotation angle). And all the parameter is linearly independent to each other. My question are: 1. What the characteristic of each of the parameter? 2...
  28. A

    Programs Where can I do a masters in Quantum Mechanics?

    I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...
  29. polyChron

    I Rotations in Bloch Sphere about an arbitrary axis

    Hey, (I have already asked the question at, I am not sure this forum's etiquette allows that!) I am trying to understand the following statement. "Suppose a single qubit has a state represented by the...
  30. youssef99

    Schools Quantum computing in college

    Hello I have recently taken intrest in physics and mostly Quantum computing and i was wondering what is the best way of tackling that field . Is it to have a major in Computer Science and possibly a major/minor in physics? or to aim for colleges that have specific classes of quantum computation...