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27 views

Pure State Entanglement and Private Communication [on hold]

My question is about the relation between two protocols of transmitting a quantum message through a Quantum channel using entanglement (entanglement Transmission or generation for this question) and ...
1
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0answers
19 views

Temperature influence in Optical Quantum Computing

I've recently been looking into the (perhaps a bit outdated but still very interesting) field of linear optical quantum computing. Using photons as information carriers, and using objects like ...
1
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0answers
14 views

Efficient ways to solve complicated kinematics problems

I'm curious about the range of approaches one can take to perform motion/kinematic simulations on many 3D objects. Currently I am familiar with the iterative process of doing such a simulation, that ...
1
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0answers
39 views

How does one arrive at the two qubit matrix that represents a gate? [closed]

The two qubit CNOT gate is represented by a 2x2 matrix. However, it is also represented pictorally. How does one arrive at that matrix representation? I am not looking for "take a diagonal matrix and ...
1
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1answer
87 views

Quantum computing, NP complexity [closed]

Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing. I want understand how a qubit can return usable data faster then a regular bit, how ...
3
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0answers
75 views

Quantum computing with biological matter? [closed]

As a biologist with physics background I wonder whether there is a way to use biological matter to create quantum computers or at least to advance the field somewhat. Usually, my first feeling would ...
1
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1answer
381 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 ...
1
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1answer
42 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 ...
2
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0answers
45 views

How to calculate quantum cost of a reversible logic circuit?

I am trying to develop new reversible logic synthesis algorithm. But I need a good quantum cost measure for a synthesized circuit to compare my results with existing ones. For now I'm using RCViewer+ ...
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1answer
272 views

Quantum and classical scaling of memory

In the literature of Quantum Computation (QC), when discussing the simulation of quantum systems, one usually comes across comparisons with the classical digital analog such as: "Classically the size ...
4
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3answers
224 views

Quantum circuit equivalent of quantum pseudo-telepathy game

I'm trying to understand the wikipedia article on quantum pseudotelepathy. I've been trying to figure out the quantum circuits the players can use to win the game from the wiki article. (Level of ...
0
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1answer
51 views

How do we imagine a Hadamard gate acting on the Bloch Sphere? [closed]

We can rewrite the Hadamard gate as $R_x(-\pi/2)R_z(-\pi/2)R_x(-\pi/2)$. I am trying to visualize the effect of applying the Hadamard gate to $|+\rangle$ on the Bloch sphere. The X gate takes ...
2
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1answer
36 views

Quantum circuit and Witness preserving amplification for QMA

My question is about the witness preserving amplification scheme for QMA proposed by Marriott and Watrous in 2005 (see http://arxiv.org/abs/cs/0506068 and ...
2
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1answer
282 views

Quantum algorithm for checking if element exists

I am currently having hard times while facing an interesting idea, which could speed up many present quantum algorithms, but I am not sure whether my thought is not misleading, or more precisely, ...
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1answer
40 views

Burden of proof for a quantum mechanical or classical mind [closed]

The only valid answer to the question “how does an intelligent mind work?” is currently “don’t know”. I'd like to avoid discussing how the mind could actually work as part of this question; the topic ...
2
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1answer
113 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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1answer
85 views

Which information is “destroyed” when a qubit is read?

A quantum bit is a unit vector in $C^2$. That is, a four dimensional unit vector. A computational basis is a pair of orthogonal vectors in $C^2$ that you choose - say, [0, 1] and [1, 0]. So the ...
5
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0answers
78 views

are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is the ...
6
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1answer
467 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 ...
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1answer
191 views

What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Nielsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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3answers
89 views

How much can we compute with one single qubit?

This might be a little stupid question, but I was just talking with some friends who are working in neuroscience and I tried to explain them quantum computing. When I explained them the bloch sphere ...
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2answers
96 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 ...
3
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1answer
79 views

Infinite bits to describe a qubit

In the Quantum Computation book by Nielsen and Chuang, the authors write in the context of quantum teleportation "Even if she (Alice) did know the state |w> , describing it precisely takes an ...
12
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1answer
483 views

Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
0
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1answer
37 views

What determines the anyon fusion outcome (if several are possible)?

Given the fusion rule (for anyons) "A x B = 1 + C" it is possible for the anyons A and B to fuse to the vacuum "1" or to fuse to the anyon C. What determines what will happen if they fuse? Is the ...
1
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1answer
58 views

Proof of inversion about the mean (Grover's) [closed]

I just have an probably trivial question, but i got stuck when deriving the inversion of the mean as used in Grover's search: I simply want to show that the application of $(2 \left| \psi ...
0
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1answer
55 views

Why are simulated qubits less effective?

"We could map the whole Universe — all of the information that has existed since the Big Bang — onto 300 qubits" I've seen statements like this over the years coupled with the same explanation ...
0
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1answer
63 views

State evolution for Dot product of quantum states (Llyod et al. 2013) [closed]

I was reading the paper by Lloyd et al. which is concerned with quantum machine learning algorithms. In the algorithm they use the evolution of the following kind (i use a reduced formula, which is ...
35
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11answers
2k views

Examples of number theory showing up in physics [duplicate]

Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the trivial to ask but often unhelpful ...
0
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1answer
38 views

Clarification on paper: “Information Flow in Entangled Quantum Systems” - David Deutsch and Patrick Hayden

Referencing paper "Information Flow in Entangled Quantum Systems" by David Deutsch and Patrick Hayden, specifically the section concerning Quantum Teleportation: ...
4
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1answer
386 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
0
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0answers
23 views

Are quantum computers just massively parallel computers? [duplicate]

I am a computer engineering major so I do not understand a lot of quantum science but from what I hear about quantum computers, it sounds like they are just massively parallel computers. In quantum ...
2
votes
3answers
96 views

Are quantum computers at least build able?

Assuming a highly unrealistic where you basically have unlimited money to burn. Is it possible to a build a size scalable quantum computer? My premise is that I often read tha people have a made a ...
6
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1answer
386 views

Is it possible to construct a quantum “computer” using laser light similar to the double-slit experiment?

Is it possible to construct an arrangement of optical devices (lasers, mirrors, slits, splitters) such that the construction could carry out a single quantum "computation"? I understand that such a ...
5
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2answers
179 views

Nobel Prize challenge: Could neutrinos be used for quantum information processing?

We know that two scientists, Takaaki Kajita and Arthur B. McDonald, working on Neutrinos have just been awarded the 2015 Nobel Prize in Physics. My question as a Nobel Prize Challenge Question is: ...
2
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1answer
91 views

Understanding measurement based quantum computing

I am currently reading M. A. Nielsen's review on Cluster-state Quantum Computation (Nielsen, Michael A. "Cluster-state quantum computation." Reports on Mathematical Physics 57.1 (2006): 147-161.). ...
2
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2answers
601 views

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

I'm looking through Nielsen & Chuang'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 ...
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3answers
185 views

Question about orthonormal decompositions over unitary operators

I'm teaching myself quantum information theory using Nielsen and Chuang's "Quantum Computation and Quantum Information" and I'm at a point in the book where the formalism is starting to make my eyes ...
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0answers
12 views

Is the truncated Wigner method efficiently classical simulatable?

The continuous-variable Gottesman-knill theorem says that the operation which varying the initial state described as the gaussian function (such as vacuum) to the final state described as the gaussian ...
4
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3answers
365 views

If quantum computing requires hundreds of digits of accuracy, how will it be possible?

Leonid Levin said, "Exponential summations used in QC require hundreds if not millions of decimal places accuracy. I wonder who would expect any physical theory to make sense in this realm." See ...
3
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1answer
100 views

How can I derive Fusion-Rules for Anyons?

I am reading Pachos "Introduction to Topological Quantum Computation". Pachos writes that a model for anyons consists of a list of all anyons and a fusion rule for them. Given a model with anyonic ...
2
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2answers
205 views

How could memory be organized in quantum computers?

A classical computer has a memory made up of bits, where each bit represents either a one or a zero and its implemented by two-state transistor logic. However, a quantum computer maintains a sequence ...
0
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1answer
63 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. ...
0
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2answers
107 views

How Much Computing Power would be Required to Fully Simulate a Cubic Meter? [closed]

Imagine you want to simulate a cubic meter down to the particle. By following the Standard Model and other basic physical equations, how much computing power would be required to do this, in say, a ...
11
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1answer
343 views

Which qubit states are accessible with linear optics operations?

Given a quantum state of $n$ qubits, and being restricted to linear optics (that is, the output annihilation operators are linear combinations of the input annihilation operators): Which states are ...
5
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1answer
346 views

Output of a beamsplitter with photon number (Fock) state inputs

Given a beamsplitter drawn below, where $\hat{a}$ and $\hat{b}$ are input modal annihilation operators, transmissivity is $\tau\in[0,1]$, and output modal annihilation operators are ...
2
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1answer
74 views

Eigenvalues of density operator under quantum channel

Consider a 2x2 density operator $\rho$ with eigenvalues $\lambda_{1},\lambda_{2}$ (where $\lambda_{1}\geq\lambda_{2}$) evolving into a 4x4 density operator $\rho'$ (with eigenvalues ...
-1
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2answers
59 views

Rotation Operators [closed]

How can I rotate a state $|\psi>=\alpha|0>+\beta|1>$ to $|\psi'>=\delta|0>+\gamma|1>$ using a unitary U, where the values of $\alpha, \beta, \gamma, \delta$ are known?
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2answers
44 views

Is this model of a finite quantum coprocessor violating physical principles?

I want to consider a classical computer without any artificial restrictions, which has a single quantum coprocessor with a fixed finite number of qubits. It can perform the following three types of ...
0
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1answer
68 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 ...