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2
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2answers
516 views

Constructing a Toffoli gate with 2-and 1-qubit gates?

I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
3
votes
1answer
360 views

Quantum computing problem [closed]

Suppose that a qubit is in the state $|\varphi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle$, where $a\in[-1,1]$. If we first perform a standard basis measurement on this qubit and then perform a ...
1
vote
1answer
86 views

Uneven Quantum Measurement

$\newcommand{\ket}[1]{\left| {#1} \right> }$ I have no academic background in physics, but I'm attempting to study quantum computation. I have read that a quantum system of two qubits is ...
1
vote
0answers
59 views

Finding all marked element by Grover search(not in superposition)

Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, ...
6
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2answers
3k views

Quantum Computing Power Advantages

Currently, the world's fastest supercomputer runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some ...
2
votes
2answers
225 views

Non-destructive measurement of qbits

Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says: "The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
5
votes
3answers
130 views

Controlled-measurement of a quantum register

Given a state vector $\left[\alpha,\beta,\gamma,\delta\right]$ which is not known a priori, does there exist an operation, which I will call "controlled-measurement", which results in the ensemble ...
8
votes
4answers
494 views

If quantum computation is reversible, what is the point of Grover's search algorithm?

Wikipedia et al say the following about Grover's algorithm: Although the purpose of Grover's algorithm is usually described as “searching a database”, it may be more accurate to describe it as ...
16
votes
1answer
583 views

If the ground states of interacting QFTs are so complicated, how did Nature find them?

My question was inspired by trying to understand the paper Quantum Algorithms for Quantum Field Theories, by Jordan, Lee, and Preskill. The main result of that paper is that scattering experiments in ...
3
votes
1answer
228 views

Qubit, one or two complex numbers?

I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent qubits. It is often stated that a qubit is represented as $a|0\rangle + ...
1
vote
1answer
156 views

NOT Universal Operator and Computational basis

This is the relationship between density operator and Bloch vector: $$\rho= \frac{1}{2}({\bf{\hat{1}}}+{\bf{b}}.\boldsymbol{\hat{\sigma}})$$ We define the NOT Universal Operator in the following way: ...
1
vote
1answer
693 views

How is a Qubit in two states under Superposition?

I have read a little about Quantum computing. From what I understand, Quantum Superposition is when a qubit is in a state $\alpha|0\rangle$ + $\beta|1\rangle$, where $\alpha$ and $\beta$ are ...
3
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4answers
750 views

Why is quantum entanglement so important?

Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
0
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1answer
156 views

Latest advances in experimental quantum processors?

I'm and undergraduate student and I'm doing a report on Quantum computing. As a conclusion of my report I'd like to highlight the latest experimental advances in Quantum Computing, especially in ...
3
votes
1answer
202 views

What is the basic idea behind how quantum computation is supposed to work?

As far as I know that QM is probability-based and Feynman proposed a quantum computer (QC) as an emulator for fast computation. Reading the introductory articles, I just do not get the essence of the ...
6
votes
1answer
767 views

Why do we want to entangle qubits?

The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
1
vote
1answer
100 views

Using wavepackets instead of photons in quantum computer

Why does a photonic quantum computer require photons? Why wouldn't wave packets work just as well, better in fact since it would get away from the use of fragile single photons? (Article)
6
votes
1answer
1k views

How many states can a n qubit quantum computer store?

A classical computer composed of '0' or '1' transistors stores $2^n$ states. Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
2
votes
4answers
277 views

Computer Science Modeling of Physical World

I am curious what efforts have been made to date to define virtual computer worlds based on the physics we know in the real world? I think it would be awesome to say start off with an atom defining ...
4
votes
1answer
74 views

Do error checking costs of quantum computing shrink BQP?

BQP is the set of problems solvable in polynomial time for a given error tolerance, and it is suspected to be larger than P (and BPP, which is probably equal to P). However, inability for the gates to ...
3
votes
1answer
358 views

No cloning theorem and exclusive-or (XOR) operator

According to IBM's website, [...]where we would [classically] have done an assignment (x=y), we instead initialize the target (x=0) and use exclusive or (x^=y). This sounds like x is a copy ...
1
vote
1answer
73 views

How is a qubit realized in a cavity?

Considering a single photon in a cavity, how is a qubit realized in this setup? How is the qubit $|0\rangle$ or $|1\rangle$ manipulated? I.e. how are the transitions $|0\rangle \to |1\rangle$ and ...
4
votes
2answers
545 views

Mathematically challenging areas in Quantum information theory and quantum cryptography

I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
0
votes
1answer
229 views

Will quantum computers ever work? [duplicate]

Possible Duplicate: Why do some physicists believe that scalable quantum computing is possible? The idea of a quantum computer is that a quantum system can be in a Quantum Superposition of ...
3
votes
1answer
118 views

Quantum computers and algorithm performance

I have a question. Gradually quantum computers will emerge someday. So, nowadays making algorithm efficient is important; I mean, making it optimal to run as fast as possible. But once quantum PC ...
4
votes
2answers
245 views

What is the most natural classical polynomial complexity class that includes all of BQP and NP?

Since we know that there are some oracle problems which can be solved on a quantum computer, but not on an NP machine with the same oracle, the idea of nondeterministic (i.e. infinitely parallel) ...
3
votes
3answers
210 views

How can quantum (Internet) network be possible?

According to the knowledge I have, there are routers, switches etc. Therefore, packets would have to be "measured" before continuing on. (If not, how will anyone know the damn IP address?) But this ...
1
vote
1answer
598 views

Does Heisenberg's energy-time uncertainty principle imply that quantum computing is no more efficient than classical computing?

See http://arxiv.org/abs/quant-ph/0006080v1 "On Non Efficiency of Quantum Computer", by Robert Alicki. In this paper, the author argues using Heisenberg's energy-time uncertainty principle, that ...
5
votes
1answer
366 views

If quantum mechanics is ultimately deterministic, would Shor's factorization algorithm still work for large integers?

Victor Stenger argues that the apparent randomness in quantum mechanics is a result of the randomness in the macroscopic detectors (similar to the randomness in the laws of thermodynamics) and is not ...
3
votes
1answer
131 views

Does quantum fingerprinting really argue for the exponential size of wavefunctions?

Does quantum fingerprinting really argue for the exponential size of wavefunctions? Quantum fingerprinting is the idea that an exponentially long classical string can be encoded in a linear number of ...
5
votes
1answer
149 views

Fast algorithm for maximizing the quantum fidelity

Consider the following optimization problem: Given a quantum state $\sigma$, a constant $b$ and a Hermitian operator $A$, find $\underset{\rho} \max F(\rho,\sigma)$ subject to $\text{Tr}(\rho ...
4
votes
6answers
922 views

Why do some physicists believe that scalable quantum computing is possible? [closed]

If you drop a glass cup on the ground, it will break and shatter into pieces. This happens all the time and is consistent with quantum mechanics. But it never happens that a shattered glass cup ...
3
votes
3answers
345 views

what breakthrough Physics needs to make quantum computers work?

I read some posts on this forum and some articles which repeatedly state that it is not impossible to build q-comps but to make it successful, physics needs a great breakthrough. I tried finding but ...
4
votes
2answers
604 views

Shor's algorithm and Bohmian Mechanics

Do quantum computer's tell us anything about the foundations of quantum theory? In particular Shor argued in the famous thread by 't Hooft Why do people categorically dismiss some simple quantum ...
1
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0answers
82 views

Efficiently distinguishing mixed quantum states?

Assume we know two different mixed states, p and q, and an efficient (quantum) algorithm for creating such two. Does it follow that there exists a computationally efficient method/measurement for ...
10
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3answers
2k views

Can a parallel computer simulate a quantum computer? Is BQP inside NP?

If you have an infinite memory infinite processor number classical computer, and you can fork arbitrarily many threads to solve a problem, you have what is called a "nondeterministic" machine. This ...
7
votes
2answers
372 views

What nonstandard theory forbids quantum computers?

What would a nonstandard model which reproduces all experimental quantum data so far but still cause quantum computers to fail when implementing Shor's algorithm look like? Would it have to be very ...
4
votes
1answer
696 views

Entanglement of qubits circuit- Bell states

I know that the quantum circuit $\text{CNOT}\; (H \otimes I)$, where $\text{CNOT}$ is the controlled-not gate and $H$ the Hadamard gate, takes the computational basis of two qubits ...
4
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3answers
2k views

Can I study Quantum Computing or Quantum Mechanics with an Engineering background?

I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue ...
7
votes
1answer
856 views

Areas of computer science required for quantum computing

What knowledge of computer science should I have, to be able to pursue research in quantum computing. I am a Physics undergrad and would take three core courses in QM, before the completion of my ...
0
votes
1answer
244 views

Existence of quantum computer

At time there are talks about quantum computers and lot of talks and discussion on its exponential speed. But studying in some more details it makes reference to "Heisenberg uncertainty principle", ...
6
votes
1answer
397 views

Ground state degeneracy of a variation of Toric Code model

We know that the ground state degeneracy of Toric Code model is 4. An easy way of seeing this is the following: Consider a 2D spin model where all the spins live on the links. The Hamiltonian is ...
7
votes
2answers
1k views

What is “code” in “toric code”?

When I first heard people talking about using Kitaev's toric code to do topological quantum computation, I was thinking how many lines does the toric code have. Then I was told that the "code" really ...
3
votes
1answer
142 views

How can you distinguish between projections of quantum states?

Consider this problem in quantum cryptography: We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which ...
1
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0answers
63 views

Commutating Annihilators with a beamsplitter

I am reading Nielsen and Chuang on P. 291, for anyone interested in the origin of my question. Given an annihilator $a$ and its corresponding creator $a^\dagger$ such that $[a,a^\dagger] = 1$ and ...
0
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1answer
54 views

Building some measurement appratus that distinguish between two mixtures

We have a measurement $M$ that distinguishs between $\rho_1$ and $\rho_0$, if it has three possible answers 1,2,3 and whenever it answers something different than 3 it's correct. $M$ succeeds with ...
6
votes
1answer
320 views

partial trace with sparse matrices

Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space. For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
2
votes
0answers
127 views

Looking for description of Helstrom's measurement

I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook Quantum Detection and Estimation Theory. ...
2
votes
1answer
153 views

Shor's Algorithm: Why throw away the f(x)?

I'm having a little trouble understanding Shor's algorithm - namely, why do we throw away the result f(x) that we get after applying the F gate? Isn't that the answer we need? My notation: ...
1
vote
1answer
191 views

Quantum Coin Flipping Protocol

$\newcommand{\ket}[1]{\left|#1\right>}$ I have the next protocol: $A$ tosses a fair coin $a\in \{0,1\}$, if $a=0$, $A$ sends to $B$ $\ket{\psi_0}=\ket0$, if $a=1$ $A$ sends to $B$, ...