Read about quantum computing | 132 Discussions | Page 1

  1. porton

    I Are electrons universal problem solvers?

    Existence of an universal problem solver, a polynomial-time NP-complete algorithm is a $1000000 prize question. But suppose that we were able to know something "simple", e.g. an electron state or electron wave function exactly. Would we be able to solve complex mathematical problems (like...
  2. E

    Measurements of GHZ state

    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...
  3. E

    Constructing the GHZ state

    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...
  4. E

    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...
  5. E

    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...
  6. E

    Qubit Operations

    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]...
  7. Quantum computing & chill

    Quantum computing & chill

    A thing doing its own thingy thing could compute faster than a computer can compute.
  8. M

    A Tensor and vector product for Quantum

    Hello, I am calculating the krauss operators to find the new density matrix after the interaction between environment and the qubit. My question is: Is there an operational order between matrix multiplication and tensor product? Because apparently author is first applying I on |0> and X on |0>...
  9. F

    A Random Quantum Walk

    I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
  10. Q

    I "Basic" question about Grover's Quantum Computing algorithm

    Hi everyone, I'm a computer scientist (not a physicist), so I will ask a computer scientist's question. In all the descriptions I found of Grover's algorithm, there is an element that is puzzling the computer scientist in me: it seems that you need to tell the Oracle about the position of the...
  11. R

    Can random, unguided processes produce a rational brain?

    I am fascinated by Einstein’s quote that the most unbelievable aspect of the universe was that it was intelligible. So my question is does anyone know whether it is so unlikely as to be absurd to suppose that random unguided processes could produce a rational brain in man in as little as 3...
  12. F

    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...
  13. D

    I Oracle questions in Grover's Algorithm

    Following these links: I have these questions: The Oracle "knows" the correct bits in the first invocation itself. So why do sqrt(N) invocations where...
  14. E

    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?
  15. E

    I Quantum Computing and Superposition of states

    I'm watching a lecture on the intro to quantum computing. See the attached image which will be useful as I describe my question. So the professor says that we have this single photon and it's in this state, ## | 0 > ##. He states that when we send this photon through a beam splitter that it...
  16. D

    What is Leakage in terms of quantum computing?

    I am doing a project on stabilizer code, and I keep running into a term about qubits and leakage. What does leakage mean?
  17. R

    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...
  18. 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...
  19. J

    New member thread (Interested in Quantum Computing, AI)

    Hey all, I'm a student in university who wants to Double Major in Computer Engineering and Physics or Mathematics. Ideally I want to get some time in working on quantum computers and some time in working on advanced AI, so one of the big things I want to do is pick the community's brain on...
  20. Q

    Physics Orienting myself toward quantum computing or a related field

    I am well aware that QC-related graduate programs are competitive so I am preparing myself for a rejection. Not because I'm unconfident. But because everyone should have a backup plan just in case. I haven't applied yet because I'm about to take the GRE. I really do enjoy both quantum physics...
  21. C

    A Simple way to create entangled photon pairs?

    Two photons arrive at a hypothetical 50:50 Beam-Splitter with no phase shift between reflected and transmitted modes. One enters the Left side and the other the Bottom side of the BS as shown in Fig.1 of the link below: Each photon...
  22. R

    I Arithmetic Block in Shor Algorithm

    Hello everyone! So I was looking at Shor Algorithm for prime factorization and I have some doubts in the arithmetic part. Let's define a function f that : f(x) = ax mod N. The middle step in shor algorithm is to calculate, simultaneously, all values of f. In some papers and books, I saw some...
  23. S

    A What's the best quantum simulator?

    Hello. What is the best quantum simulator till now? We could select two categories: a) Best full simulator able to solve the equations describing a system in 3D and watching its temporal evolution. b) Best digital simulator, algorithm analyzer. For the second options I have some candidates...
  24. S

    Books on quantum computing?

    Hello. What is a good book to learn Quantum Computing? I've being looking for the most common ones and reading some reviews at Amazon, and created this list: A Short Introduction to Quantum Information and Quantum Computation, Le Bellac, 2006 An Introduction to Quantum Computing Algorithms...
  25. Q

    Physics Simulation and model science or quantum computing

    I am a computer science under graduate,I am more interested in scientific research, so I am preparing to enrol myself masters in quantum computing or simulation sciences. before i join i want to research what are the scope and job opportunities are available for simulation sciences(like...
  26. victor94

    I Help in understanding a quantum circuit

    I'm in a proyect to simulate quantum circuits in robots like in this paper ( ) ,the first thing that i need to do is to simulated the circuit that is in that paper: But i'm having trouble understanding how the hadamard gate affects the "C"...
  27. Luis Obis

    Programs Choosing a Master's degree in Physics

    I am a physics student from Spain and hopefully I will be finishing my degree in physics (4y) by next June. I am trying to decide on a Master's program to study but I am finding very difficult to decide since there are so many oportunities and so diverse specially when looking for programs...
  28. A

    I Simon's Algorithm

    Hi all, I am sure some of you have heard of Simon's algorithm that calculates a secret string s when given a black box. Basically, let's say we have a qubit x that is n digits long. Now the black box contains a function f that outputs f(x+s) where s is the mystery string and + is bit-wise modulo...
  29. munirah

    I How reduced density matrix obtained from the matrix.

    Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...
  30. Abhishek Sethi

    Research in Quantum Computing

    Hi, I am an undergraduate student from India. Pursuing double major in Physics and Mechanical Engineering. I have completed 4 semesters(2 years) of my college. I had taken a class titled "Quantum information and computing" and it interested me a lot. I really love math and computations...