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1answer
37 views

Relationship between Toffoli gate and Deutsch gate

I am reading a book called "Quantum Computing for computer scientists" and stuck at this exercise for a day. Bellow is the description of Deutsch gate: And here is the description of Toffoli ...
-3
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2answers
63 views

Quantum computers for string theory? [on hold]

I read something about that locating our space in the multitude of multidimensional spaces of M-theory (and so identifying particular particles which we can measure with particular strings) is a too ...
1
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1answer
39 views

Controlled Phase Gates

The Quantum Fourier Transform consists of 2 gates. Controlled Phase Gates, and Hadamard gates. I'm assuming the Controlled Phase Gate is a combination of a Control Gate, and a Phase Gate. But what ...
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3answers
288 views

Is entanglement necessary for quantum computation?

Is entanglement necessary for quantum computation? If there was no error in the computation,superposition of states would be sufficient for quantum computation to be carried out.Is this right?
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0answers
27 views

How is this circuit equivalent to a Bell measurement?

The circuit elements are : CNOT gate, first qubit is the control bit Hadamard gate (H) The dials represent measurements made in the computational basis Therefore, the circuit (without the ...
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0answers
25 views

How to find a single coefficient of quantum Fourier transform reliably

Quantum Fourier transform transform $X \in \mathbb{C}^{2^n}$ to $Y \in \mathbb{C}^{2^n}$. Suppose one wishes to find $y_0$, the first coefficient of "vector" $Y$. However, as this is quantum process, ...
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1answer
34 views

Can a classical 50/50 probability be distinguished from a quantum superposition with a single measurement?

$\renewcommand{\ket}[1]{|#1\rangle}$ 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. ...
2
votes
1answer
335 views

Hamiltonian reduction having constant of the motion

I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin. I know that I can have only one excited spin in my configuration a time. (eg: 0110 nor 0101 ar not permitted, but ...
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4answers
9k views

Quantum entanglement faster than speed of light?

recently i was watching a video on quantum computing where the narrators describes that quantum entanglement information travels faster than light! Is it really possible for anything to move faster ...
3
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1answer
850 views

Do quantum computers manufactured by D-Wave Systems, Inc. work? [duplicate]

D-wave claims to have built 128 qbit quantum computers which are commercially available? What I don't understand is that have they really been able to do this given that the scientific community is ...
4
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1answer
129 views

How is classical information put into and retrieved from a quantum computer?

How, if you had to find the factors of say a 256 digit number, would you go about inputting the data and how do the proper answers "drop out" of a quantum computer. Other than terms such as qubits, ...
0
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2answers
57 views

Is a universal quantum computer expected to be able to shed any light on the measurement problem? - Part B [closed]

Following up on Part A. Suppose we build a universal quantum computer and it functions as we currently expect it to. Is there any reason to suggest that, beyond its uses for things like ...
2
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0answers
74 views

Is a universal quantum computer expected to be able to shed any light on the measurement problem? - Part A [closed]

Suppose we build a universal quantum computer and it functions as we currently expect it to. Is there any reason to suggest that, beyond its uses for things like cryptography and quantum system ...
0
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1answer
64 views

Classical Computation without NOT [closed]

Is it possible to do universal classical computation using bits and 2-bit gates when you cannot perform a NOT operation on a single bit (hence cant do CNOT and so on). If yes, what are the possible ...
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7answers
6k views

Could quantum computers break any cipher? [closed]

I've been told that physicists and computer scientists are working on computers that could use quantum physics to increase significantly computation capabilities and break any cipher so cryptography ...
0
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0answers
23 views

Generallized Controlled-$U$ gates

Let $U$ be a quantum gate that acts on $n$ qubits represented by the $2^n \times 2^n$ matrix: $$U = [u_{ij}] \qquad \text{where} \qquad i,j \in \{ 1,2,3,\dots, 2^n \}$$ Can I state that the ...
0
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1answer
62 views

What are typical error rates of quantum computers?

I read in an article that in order to perform error correction on a quantum computer there can only be one error per 10.000 calculations (=unitary transformations). This sounds pretty high but how ...
0
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1answer
37 views

Why does a measurement on one qubit force another one into a given state in Simon's algorithm?

This comes from trying to understand the "Simon's algorithm". So we have a set of $2^n$ kets $|x_i >$ one each for $i \in \{0,1\}^n$. Each $x_j \in \{0,1\}^n$. And we have the further constraint ...
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3answers
88 views

The $n$-th root of the NOT gate

I simply can not find material containing facts about the $n$-th root of the NOT gate and it's realization in Q.M. and also in C.M.. Does anyone have material? A comparison of the $n$-th root NOT ...
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1answer
61 views

What causes continuous errors in a qubit?

I read that due to decoherence a qubit in a superpositon gets destroyed or put into one definite eigenstate. This kind of error seems to occur due to interactions with other stuff like the environment ...
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1answer
63 views

Quantum computing can be done via measurement alone, why is this significant?

I read in the Afterword section of Nielsen and Chuang's book Quantum Computation and Quantum Information that A second area of progress has been in understanding of what physical resources are ...
3
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1answer
132 views

Approximating a target operator

I was wondering if anyone knew how the author got to equation 12 on page four of this paper, I will attempt to explain the situation below. Given $C$, a target operator, we wish to create an ...
2
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1answer
59 views

Continued Fraction Algorithm in Shor's Algorithm

I am just trying to make the final link of Shor's algorithm clear. Here $r$ is the order of $x$ modulo $N$. We have a number $\psi$, which for a rational number $\dfrac{s}{r}$ satisfies ...
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1answer
40 views

Why do Transformations on Qubits for Quantum Computation have to be Unitary?

In the quantum circuit model we prepare some inital state $|\psi\rangle$ and throw our algorithm in form of some unitary transformation(s) $U$ on it to get our result $|\Psi\rangle$: ...
0
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1answer
62 views

How to apply Controlled-NOT gate?

look at the figure below it is about an example to multiply two qubits by 3 Controlled gate to get the SWAP operation .. I'm trying to follow this step-by-step but I couldn't know how this is ...
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0answers
15 views

Creating an arbitrary state of the quantum simple harmonic oscillator [duplicate]

Suppose $\mathcal{B}=\{\lvert 0\rangle, \lvert 1\rangle, \lvert 2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} ...
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2answers
49 views

Do we have algorithms that are polynomial on a Q-Computer but not poly. on a classical Computer?

I am currently reading “Introduction to Topological Quantum Computation” by J.K. Pachos. In the book the author mentions that Shor’s factoring algorithm is polynomial (with regard to the complexity ...
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0answers
67 views

Limitations of Quantum Simulations on a Classical Computer

My question is on the simulation of a quantum computer on a classical machine. I understand that a classical computer to simulate any quantum algorithm--the problem is that the quantum computer does ...
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0answers
62 views

Proof that Quantum Computation cannot be simulated on classical computers

I have read , for example , in chapter 3, Computer-aided-design Methods for Emerging Quantum Computing Technologies By David Dov Yehuda Feinstein this statement several times, but I am not able to ...
2
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1answer
80 views

How powerful would a quantum computer need to be to break RSA encrytion codes?

First off, just to reassure everybody, I have no motive other than pure curiosity for asking this question. I don't want my bank account hacked any more than you want the same done to yours. My ...
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0answers
72 views

Anyonic Braiding and Conformal Field Theory

I am looking for resources (both pedagogical and newer research articles) on the connection between topological quantum computation and conformal field theory. In particular, a CFT description of ...
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0answers
25 views

Is the first excited state of a superconducting qubit a stationary state?

A superconducting qubit is essentially an anharmonic oscillator with uneven spacings of the eigenstates. These states are eigenstates of the overall hamiltonian, which should mean that it is an energy ...
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0answers
74 views

How useful is the study of entanglement entropy to quantum computing? [closed]

My question is somewhat conceptual: how, exactly, can we get closer to building a quantum computer by studying entanglement entropy? I've been reading all about the AdS/CFT correspondence and watching ...
0
votes
1answer
31 views

How does one measure the state probabilities of a 2 level Hydrogen atom qubit?

I have been struggling with trying to understand how one could measure the probabilities of a superimposed Hydrogen atom's two energy states. Say the atom is in a superimposed state: Psi = a|0> + ...
3
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1answer
81 views

Rigorous definition of superselection sector/quasiparticle type in anyon systems

The systems I have in mind are for example Kitaev's toric code model (arXiv:quant-ph/9707021) and Kitaev's honeycomb model (arXiv:cond-mat/0506438). What I'm looking for is a mathematically rigorous ...
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3answers
2k views

How are physics and computer science getting united? [closed]

How is theoretical computer science getting united with physics? Phenomena like Quantum Computing uses Quantum Mechanics to be able to compute things, how are computers helping not just to model our ...
2
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2answers
118 views

Why is a transmon a charge qubit?

The classic charge qubit is the cooper pair box which is a capacitor in series with a Josephson junction. In my understanding, by changing the gate voltage at the capacitor, one can create a ...
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2answers
86 views

Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...
3
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1answer
97 views

which are the non-abelian anyons for universal quantum computation

I am trying to get a list of non-abelian anyons that can be used for universal quantum computation by implementing gates via braiding. I found that Majorana fermions and para-fermions (not sure about ...
1
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1answer
98 views

Topological Quantum Computing beyond Anyonic Braiding

In materials such as those that exhibit fractional quantum hall states, the ground-state topological degeneracy is known to be robust against external perturbations. This ultimately tells us that we ...
0
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1answer
45 views

Properties of controlled z-rotations

Given n qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which will ...
1
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1answer
65 views

are there known fundamental limits of quantum computer scaling?

Quantum computers provide exponential speedup relative to classical computers. However, it is empirical fact that increasing of number of qubits makes the the computer harder and harder to keep ...
1
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1answer
56 views

CNOT gate application to separated qubits

In the case 1 in the picture, it is easy to perform matrix calculations concerning the circuit to obtain a final state. In case 2 however, I am wondering what is a general procedure to calculate it ...
0
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2answers
70 views

Why can't a classical bit behave like a qubit?

For example i have a 2 qubits which can have 4 possibilities i.e. 00, 01, 10, 11 so this shows that the 2 qubits can contain four bits of information as they are superpositioned but i think 2 ...
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1answer
53 views

Quantum Computer Implementation

Hey I recently finished my bachelor in nanotechnology and am rather interested in quantum computation. I've already looked at the recommendation threads for this topic but they tend to be about ...
2
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1answer
71 views

How does quantum superposition make calculation faster?

In every description of a quantum computer I've seen (that isn't extremely technical), they've been described as computers that use qubits, that use a superposition of 1 and 0 to make processing ...
6
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1answer
2k views

Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
0
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1answer
75 views

Dilemma: Fusion space from a direct sum of anyons or NOT

In Preskill's note, 9.1.2 in page 44, concerning the fusion space, it states that: The fusion rules of the model specify the possible values of the total charge $c$ when the constituents have ...
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2answers
120 views

How would a quantum computer receive input from a classical computer?

One of the potential applications of a quantum computer would be as a coprocessor to a classical computing system, much in the same way as a graphics processing unit (GPU) performs specialized ...
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0answers
58 views

Why do flux qubits have to be micrometer-sized?

Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them. My question is that I've seen ...