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...
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...
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...
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...
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...
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]...
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>...
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...
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...
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...
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...
Following these links:
https://people.cs.umass.edu/~strubell/doc/quantum_tutorial.pdf
https://www.codeproject.com/Articles/1131573/Grovers-Search-Algorithm-explained
I have these questions:
The Oracle "knows" the correct bits in the first invocation itself. So why do sqrt(N) invocations where...
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?
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...
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...
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...
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...
Jpmcke
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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...
quantumheels
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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:
https://drive.google.com/open?id=0B5JsDLKoUSA5emk5Qk9nUHVIelE
Each photon...
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...
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...
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...
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...
I'm in a proyect to simulate quantum circuits in robots like in this paper
( http://ieeexplore.ieee.org/document/4215941/ ) ,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"...
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...
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...
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 &...
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...