# Tagged Questions

1answer
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### Positivity in the Pauli/Bloch/coherence vector representation

Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is $$x_k = {\rm Tr}(\rho \sigma_k),$$ ...
0answers
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### Creating matrix Hamiltonian for Feynman's CNOT

I'm trying to read Quantum Mechanical Computer and to implement the CNOT logical gate with some analytical software. Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized ...
1answer
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### How are qubits better than classical bit?

WHAT I KNOW: classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states. Now ...
0answers
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### Deutsch-Jozsa algorithm [closed]

How many calls are required to determine is the function balanced or not on the classical computer with probability of error < 50%. Ref: Deutsch-Jozsa algorithm.
2answers
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### Qubit projections

Given the qubit: $$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$ What is the corresponding point on the extended complex plane and Bloch sphere? How to perform calculations and get the point representing ...
1answer
56 views

### Two qubits problem [closed]

Given the 2 qubit state: (a/b) |00> + (c/b) |01> + (c/b) |10> + (d/b) |11> What is the probability that 2 qubits are equal? Thanks much!
0answers
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### Constructing a Toffoli gate from CNOT and single-qubit gates [closed]

Toffoli gate in terms of CNOT and single-qubit gates. Thanks much!
1answer
153 views

### I am interested in learning Quantum Computing what should I do? [closed]

I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
1answer
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### Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$?

Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$, where $k$ is the number of "hits" in a total of $N$ possible values for $|\,x\rangle$? If we know $k$, and know ...
1answer
44 views

### 2 following gates, inverse circuit

I have a circuit that has 4 wires and 2 following each other Toffoli gates. The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below. What will look ...
1answer
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### 2 following gates, permutation matrix

I have a circuit that has 4 wires and 2 following each other Toffoli gates. I have permutation matrix for each Toffoli gate (A and B). Do I have to multiply that 2 matrices to get the entire ...
2answers
307 views

### Entropy of a state subject to the action of a set of random unitaries

Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
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1answer
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### 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 ...
1answer
252 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 ...
2answers
485 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 ...
1answer
119 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 ...
0answers
142 views

### Quantum Compting or DNA computing [closed]

My friend and me are working on DNA computing and on some improvements to it. Of course, we are working on computing aspects of this branch. So, we have insufficient knowledge about physics and ...
1answer
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### 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 ...
1answer
158 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 ...
0answers
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### 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. ...
1answer
129 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: ...
1answer
141 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 $B$, ...
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### Is the universe a quantum computer - is light speed barrier a computational constraint [duplicate]

Possible Duplicate: Is the universe a quantum computer - is light speed barrier a computational constraint Cross-posting this question, since physics.stackexchange has not provided any ...
3answers
930 views

### Is the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
2answers
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### Quantum memories: What are they?

Searching the literature for the term "quantum memory" seems to bring up results from two different communities. On the one hand there are quantum opticians, who see a quantum memory as something ...
3answers
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### Depolarizing threshold for CSS codes

Many years ago, when CSS codes were first invented, the error threshold of p=0.11 was found when bit and phase flips are independent. Has a threshold yet been found for the case of depolarizing noise? ...
2answers
451 views

### Quantum Computing, Qubit Creation/Entanglement

I am currently a high school student researching quantum computing. I was referred to this site by Google and a friend. Currently I am researching the qubit part of quantum computing. My question is ...
3answers
3k 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 ...
3answers
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### What is the use of a Universal-NOT gate?

The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
1answer
472 views

### Can quantum annealing be used for factorization?

It is known that there is a famous quantum factorization algorithm by Peter Shor. The algorithm is thought to be suitable only for quantum gate computer. But can a an adiabatic quantum computer ...
1answer
1k views

### What is quantum discord?

What is quantum discord? I stumbled upon this term on Quantum Computing: The power of discord, but have never heard of it before. Can you give a bit more mathematical explanation of the term here?
2answers
3k views

### What can the D-Wave quantum computer do?

The media are reporting the commercially sold 128-bit quantum computer from D-Wave http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n which of course ...