A computation model which relies on quantum-mechanic phenomena, such as entanglement and superposition. This generalizes the probabilistic model of computation.

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Will the growth of calculation speed of personal computer end after that of classical computer will end? [closed]

According to the answer of Andrew Yeats in this link, quantum computer's advantage is so narrow that personal computer is not likely to benefit from the development of quantum computer. I think this ...
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28 views

Question about the Simon's algorithm

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

How many inputs does the Hadamard gate have?

Look at the diagram in the middle of page 6-3 here, http://stellar.mit.edu/S/course/6/fa14/6.845/courseMaterial/topics/topic3/lectureNotes/qctlec6/qctlec6.pdf I am confused as to how should one think ...
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How is quantum function $f(x) = a^x \mod N$ constructed in Shor's algorithm?

I can't see how I can apply quantum function $a^x\mod N$ to initial states. Explanations of Shor's algorithm often skips this part, and I do not see what unitary matrix this algorithm would correspond ...
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43 views

How would a for loop differ in quantum computing? [closed]

Consider for example the following code: Array A = {a, b, c, d}; for ( int i = 0, i < A.length, i++){ if A[i]=="c" print["1"]; else print["0"] } and ...
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103 views

Evaluating Grover's algorithm on 3-SAT

I recently asked this very similar question on how Grovers algorithm must be modified in order to solve 3-SAT and learned that it actually needs no modification at all. However, what I still don't ...
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How must Grovers algorithm be modified in order to solve 3-SAT?

Grover's algorithm was designed for a database with exactly one item that matches a given search criterion, and can be used to find that very item. However, when checking whether a given formula is ...
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173 views

What type of algorithms are faster with a quantum computer?

I am a beginning CS student and I am learning algorithms. I heard that even with quantum computers, that general sorting algorithms can never have better than $n\log n$ time. However, I also know that ...
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89 views

Creating bigger controlled nots from single qubit, Toffoli, and CNOT gates, without workspace

Exercise 4.29 from Quantum Computation and Quantum Information by Nielsen and Chuang has me stumped. Find a circuit containing $O(n^2)$ Toffoli, CNOT and single qubit gates which implements a ...
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17 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 ...
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Quantum multi valued decision diagrams

I recently came across the paper "QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits" by Thornton and Miller. It deals with a way of compactly representing transformation matrix ...
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159 views

Can a quantum computer (theoretically) do things a classical computer (literally) can't?

I've been searching the net for an answer to this question, but it's guetting quite confusing. I want to know if there are some undecidable problems for a classical computer that a quantum computer ...
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55 views

Is $BQP$ in $P^{NP}$?

I read in the introduction of this paper http://www.scottaaronson.com/papers/uncompute.pdf that there is a problem $B$ such that $BQP^B \not\subset P^{NP^B}$, and that $B$ is in $BPP$. But, using ...
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1answer
28 views

Quantum state probabilities and amplitudes - absolute value squared?

It has just appeared to me that I've overlooked a possibly important fact. When we want to calculate probability $p_x$ of measuring the state $X$ and we know the amplitude of $X$ is $\alpha$, we know ...
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Multi-qubit gates matrix representation

Consider the gate used in Simon's Algorithm. It operates on a control register and target register, changing state like: $|\textbf{x}\rangle|\textbf{y}\rangle->|\textbf{x}\rangle|\textbf{y}\oplus ...
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273 views

What happens to multi-qubit quantum state after one of qubits is measured?

If we have a quantum state consisting of (let's say) 3 entangled qubits and we read the value of one of them, what happens to the probabilities of the remaining possible states? For example, if we ...
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298 views

Quantum computers and computable functions

A quantum computer can possibly calcluate computable functions faster, but it can't calculate functions which a normal computer can't calculate? If a function is not computable? Does this mean it ...
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1answer
80 views

Trying to understand how the first Hadamard gate in Deutsch–Jozsa algorithm works

I'm still a beginner in the quantum aspect of computer science (self-studying). So please bear with me if this may sound like a stupid question. I know Hadamard gate transforms qubit into a ...
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64 views

Measure two qubits, one from entangled pair, in Bell basis?

In quantum teleportation we require both sender (Alice) and receiver (Bob) to share an entangled pair of qubits in the $|\beta_{00}\rangle$ Bell state. Then, if Alice wants to teleport a quibt ...
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79 views

How to apply a 1-qubit gate to a single qubit from an entangled pair?

Reading about superdense coding I came upon a calculation I can not understand. We have an EPR entangled pair of qubits $\frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and we want to apply a Pauli X gate ...
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37 views

Why $\theta/2$ in common qubit representation?

If we take angle names as shown on the Bloch sphere below and a typical qubit representation written as $\cos(\theta/2)|0\rangle + \mathrm{e}^{-\mathrm{i}\phi}\sin(\theta/2)|1\rangle$, why do we ...
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58 views

Can a CS grad student work on quantum field theory and string theory problems? [closed]

The mathematical aspect of particle physics theory are interesting and there seems to be a lot more connections being made to computation and information (like with complexity theory having some ...
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116 views

A Black Box Algorithm

I'm taking an introductory quantum computations class and I am attempting to solve the following question(s), but we haven't touched on black box algorithms like this in class, and I honestly don't ...
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578 views

Will the future quantum computers use the binary, ternary or quaternary numeral system?

Our current computers use bits, so they use the binary numeral system. But I heard that the future quantum computers will use qubits instead of simple bits. Since in the word "qubit" there is the ...
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Are there specific rules for programming languages applicable to Quantum Computers?

What would be the requirements for programming languages that are used for quantum computers? Do standard procedural languages with their constructs be sufficient, and succinctly capture the computing ...
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What difference does it make when universal classical gates in quantum computation are reversible but not unitary?

As I've come across Grovers algorithm I dont understand why when computing F(X), which is an oracle function people use classical reversible circuits(toffoli, fredkin) to evaluate the circuit. Why ...
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84 views

What happens to quantum algorithms such as BB84 if P=NP

Under the hypothesis that P=NP, many cryptographic protocols are no longer secure (i.e. attacks are feasible). The BB84 algorithm (http://en.wikipedia.org/wiki/BB84) is based on the idea that by ...
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Quantum Computing - Relationship between Hamiltonian and Unitary model

When developing algorithms in quantum computing, I've noticed that there are two primary models in which this is done. Some algorithms - such as for the Hamiltonian NAND tree problem (Farhi, ...
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36 views

Finding the private key in BB84 quantum cryptography

I'm trying to teach myself Quantum Cryptography for an exam I have soon, and I came across the following question: To establish a common key, Alice and Bob analyse a sequence of 20 photon pairs. ...
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Grover algorithm for known number of solutions

I am reading Computational Complexity book and specifically Grovers search algorithm. I am aware that if we knew in advance exact number of solutions $K$, then the basic algorithm can be tweaked to ...
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1answer
44 views

Is Simon's problem a good NP-intermediate candidate?

We know that $BPP \subseteq BQP$ but we have no proof $BPP \subset BQP$ (Though we have the proof that BQP $!=$ BPP with an oracle) Since Simon's problem (as factoring) it's easily solvable by a ...
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177 views

Quantum algorithms and quantum computation

Is my (very high-level) understanding correct here regarding quantum algorithms — Quantum computers can process a massive amount of operations in parallel to the nature of qubits and their ...
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169 views

How to do Tensor product of two qubits using gates [closed]

I want to do tensor product of two qubits which are passed through two Hadamard gates. I understand feeding the control bit of CN gate the output of Hadamard gate and target bit |0> gives me the Bell ...
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999 views

Quantum Computing and Turing Machines: Are Turing Machines still an Accurate Measure?

In class last week, my professor commented and said that Turing machines are used as a standard measure/model of what is computable and are a helpful basis of discussion for that subject. She also ...
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237 views

Is Quantum Computer analog?

We used to have analog computers several decades ago. Modern days computers are Digital. What about Quantum computers? Is it analog or digital? I am asking this since qubit can be many things at the ...
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What languages does a (1-way) quantum finite state automata recognize?

Sorry if this is well known, but most of the research is paywalled. So far I know that it is a subset of the regular languages, but I cannot seem to find any (available) research which pins it down. ...
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Qubits Related to RAM?

I read in this article that the amount of bits that can be emulated by a certain number of qubits is 2^(number of qubits). This is because each qubit can be in one of 2 states after it collapses, and ...
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Why and how is a quantum computer faster than a regular computer?

I'm currently reading a book (and alot of wikipedia) about quantum physics and I'm yet to understand how is a quantum computer can be faster than the computers we have today? what causes the ...
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135 views

Quantum computer code cracking

everyone! I don't know a whole lot about the fields of encryption or quantum computing, but I've read a lot of articles on the subjects and that is prescisley what caused this question. I've been a ...
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105 views

How to measure processing power of a quantum computer?

Is there any way to get an equivalent of computing power of quantum computers in terms of computing power of common computers? I mean, how many teraflops (or so) can a quantum computer compute? How ...
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246 views

Simple explanation of Simon's Problem

I just read the Wiki article for Simon's Problem but I don't fully understand it because I don't follow the symbolic notation used to describe functions (I am not a computer scientist). Can someone ...
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415 views

Shor's Algorithm speed

I'm a fledgling computer science scholar, and I'm being asked to write a paper which involves integer factorization. As a result, I'm having to look into Shor's algorithm on quantum computers. For ...
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265 views

How does Grover's Quantum Sorting avoid reading the list?

It is well known now that Grover's quantum algorithm can SORT a database of $N$ entries in $O(\sqrt{N})$ time. How can an algorithm work without reading through the list of entries which needs $O(N)$ ...
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Quantum Algorithms and CT vs Classical counterparts

How is Quantum Algorithms and Complexity Theory essentially different from Classical Counterparts? Also how are non-deterministic Turing Machines(NTM) different from Quantum Turing Machines(QTM)? ...
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455 views

What is meant by an oracle separation between classes $\mathsf{BPP}$ and $\mathsf{BQP}$?

In these notes about quantum computation by Scott Aronson, he explains that the computation classes $\mathsf{BPP}$ is contained in $\mathsf{BQP}$, but that they are not equal, and So, the bottom ...
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154 views

Finding all marked elements using Grover's algorithm

Grover's algorithm uses an oracle function $f(x) \to \{0,1\}$ to find the location of a single marked element from an unordered database of $2^n$ elements with high probability. As part of an ...
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(Slightly) faster simulation of quantum Fourier transform

Suppose I want to write a classical software simulator of a quantum circuit with $N$ qubits. When it comes time to simulate the quantum Fourier transform I can evaluate all $2^N$ states to determine ...
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Quantum computers, parallel computing and exponential time

I've read that quantum computers can solve 'certain problems' exponentially better than classical computers. As I think I understand it, it's NOT the same to say that quantum computers take any ...
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356 views

Quantum computing roadmap

I have to create a roadmap for the quantum computing technology. Looking around I found the timeline on wikipedia that is pretty wide but does not highlight the key events in quantum computing ...
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The difference between a bit and a Qubit

Ok, I have done a lot of research on Quantum computers. I understand that they are possibly the future of computers and may be commonplace in approximately 30-50 years time. I know that a Binary is ...