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2
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2answers
66 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 qubits, ...
0
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1answer
63 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 ...
0
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0answers
21 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 ...
20
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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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1answer
57 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 ...
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0answers
21 views

Quantum error correcting codes for X and Z error

There are various examples of quantum error correcting codes, which encode $k$ qubits in $n$ qubits, correct all $X,Z$ and $Y$ errors, assuming errors act on at most $t$ qubits. In ...
0
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1answer
36 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 ...
0
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3answers
64 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 ...
1
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1answer
60 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 ...
1
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1answer
61 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
votes
1answer
131 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 ...
0
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1answer
39 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
56 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 ...
1
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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} ...
1
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2answers
46 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 ...
0
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0answers
57 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 ...
0
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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 ...
1
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1answer
78 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 ...
3
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0answers
67 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 ...
1
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0answers
24 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 ...
1
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0answers
72 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
29 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
votes
1answer
73 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 ...
2
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2answers
101 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 ...
3
votes
1answer
90 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
83 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 ...
1
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1answer
61 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 ...
0
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2answers
64 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 ...
2
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1answer
64 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 ...
0
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1answer
74 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 ...
5
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0answers
56 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 ...
1
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1answer
49 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 ...
0
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0answers
49 views

Difference between apply quantum gate and measure a qubit?

When you apply a quantum gate, why does the superposition state not collapse? Does this in any way intervene with the qubit as in the measurement?
1
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2answers
80 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, ...
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
77 views

What type of Quantum Gate is this

I'm trying to work out if this is a certain type of 'known' Quantum Gate $|1\rangle|1\rangle $ goes to $|1\rangle|1\rangle $ $|1\rangle|0\rangle $ goes to $|1\rangle|0\rangle $ $|0\rangle|1\rangle ...
0
votes
1answer
70 views

Hadamard Gate application help

I need to prove that if you apply Hadamard gates on the input/output before and after a CNOT gate that you get the same answer as flipping the target and control qbits of a CNOT. So for example I'm ...
2
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1answer
57 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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0answers
47 views

In Grover and Shor Algorithms 2 registers of qubits are handled at books, but it's really just one seen as 2?

I found in the literature that we require at least two quantum registers for arithmetics operation. Example: The function $f(x)=x^2$ is then a unitary evolution of the two registers, in this ...
1
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1answer
60 views

Quantum computer simulators [closed]

What are good, free, open source, GUI-based quantum computer simulators? I remember there used to be a Java-based one that was very good, but it doesn't seem to be online anymore, or it's relocated.
0
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1answer
28 views

Condition for quantum error correction based on encoded states

I am trying to understand the properties of quantum error correcting codes. Consider a quantum code on a lattice, with the property that a given region $R$ is correctable (for any error localized to ...
5
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0answers
170 views

Quantum Error Correction: Surface code vs. color code

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit ...
1
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0answers
40 views

Have there been any experiments that have demonstrated a quantum error correcting code?

Has quantum error correction been demonstrated? I know that classical error correction has been demonstrated by [1], they correct a single bit flip error, but has anyone been able to detect and ...
0
votes
1answer
44 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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0answers
67 views

QFT Perturbative analysis of multiple atom-level quantum computers close to each other

Following up on this question, I'm wondering about electromagnetic interactions perturbation expansions close to a "black-box" quantum computer and modularity of Feynman diagrams in general. Let me ...
5
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2answers
114 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 ...
2
votes
3answers
381 views

Can existing quantum computers be considered evidence for parallel universes?

In this video ( http://www.youtube.com/watch?v=bJpIclDmi2M ) Max Tegmark , a MIT cosmologist says that if we build a quantum computing successfully it will be a evidence that Parallel Universes ...
2
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2answers
293 views

What is the difference between a bit and a qubit?

I am Computer Science student and learning about quantum computing. But, I have a problem in understanding Bit and Qubit relationship. A bit with 2 bits = 4 states 00,01,10,11--- 1 state at a time. ...
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0answers
45 views

How does one devise a Grover quantum oracle despite the no-cloning theorem?

I think I have misunderstood Grover's quantum search algorithm, and would appreciate clarification. From what I understand, the Oracle operator takes an index register of qubits $|x\rangle$ (that ...
3
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1answer
81 views

Deutsch's Algorithm. Unitary Transform $U_f$

I'm studying Deutsch's algorithm and I keep coming across the phrase along the lines of "There is a unitary transform (a sequence of quantum gates) $U_f$ that transforms the state $|x\rangle |y\rangle ...