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2
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1answer
53 views

Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
0
votes
2answers
113 views

Question on quantum computation, entanglement and speed of information propagation

Imagine a following thought experiment. Suppose we have a large amount of entangled particle pairs, several million or billion. Now suppose there are two observers, each carrying one member of ...
2
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0answers
77 views

How to obtain stabilizer's generators of a QEC code

The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators. To understand better what I am concerning about, let's consider the 7-qubit ...
2
votes
0answers
110 views

Can we “safely” assume that quantum computing systems will be finite-dimensional?

This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space. According ...
1
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0answers
102 views

Beginner projects in NMR quantum computing [closed]

I have applied for a summer project in NMR quantum computing as I want to learn this field, but my professor wants me to tell him the project title. I have no idea about the field and what projects ...
4
votes
1answer
161 views

Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( ...
5
votes
1answer
100 views

When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
2
votes
1answer
103 views

Coefficients of the vectors in a tensor product

The postulate says that if we want to build the compound state of two sub-systems, we just take the tensor product $\otimes$ of the respective state vectors. This means that if one of the vectors has ...
3
votes
0answers
120 views

Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system ...
4
votes
3answers
175 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 ...
4
votes
3answers
916 views

What is the next step beyond quantum computation?

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...
5
votes
2answers
253 views

Is entanglement necessary for quantum computation?

Is entanglement necessary for quantum computation? If there was no error in the computation,superposition of states would be sufficient for quantum computation to be carried out.Is this right?
14
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2answers
1k views

Why doesn't the no-cloning theorem make lasers impossible?

As I understand lasers, you start off with a few photons that are in an identical state, and other photons that are created later tend to have the same quantum numbers due to Einstein-Bose statistics. ...
2
votes
0answers
102 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
5
votes
2answers
237 views

Classically efficient universal quantum computation (P=BQP) with magic and bound states

$\text P$ vs $\text {BQP}$ is an open question. That is, "can systems which require a polynomial number of qubits in the size of an input be described with only a polynomial number of bits?" If the ...
2
votes
2answers
207 views

Why does the classical equivalent to a quantum computer take so many bits?

A quantum computer with 10 qubits is classically equivalent to $2^{10}$ bits. How is this equivalence worked out? I understand that a single qubit is a vector in a 2-dimensional hilbert space, whose ...
0
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1answer
77 views

Adiabatic quantum Hamiltonian of variable dimension

Is adiabatic quantum Hamiltonian of variable dimension possible? This is very hypothetical and I am afraid may not have enough merit to belong to this forum. I would still like to elaborate. Here is ...
2
votes
1answer
665 views

Help on applying a Hadamard gate and CNOT to two single q-bits

I am stuck on a few issues in this video. (Note: It is at the frame concerning this question.) In it, from what I understand (which could be wrong) we first apply the Hadamard gate to a qbit in the ...
1
vote
2answers
319 views

Quantum XOR: How do you generalize it?

Consider the classical XOR Gate: Given a 2 bit system: $G = [u_1, u_2]$ $$XOR(G) = (u_1 + u_2) \ mod \ 2$$ Is the following a good generalizaiton of a Quantum XOR Gate: Given a 2-qubit system: ...
2
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0answers
127 views

Quantum annealing computing

What is Quantum Annealing and quantum annealing computing and what are its advantages and disadvantages with respect to quantum circuit quantum computing/computers?
3
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1answer
479 views

Measuring Entangled Qubits

Suppose we have a pair of entangled qubits. $$ |\psi\rangle = \frac{1}{ \sqrt{2} } ( |00\rangle + |11\rangle ) $$ Now we give one qubit to Alice and other to Bob. Alice measure the her qubit to ...
1
vote
1answer
382 views

CNOT gate output with both inputs in superposition

What is the output of a CNOT gate if both inputs are in superposition? For example, what happens if: $\left|x\right>=\alpha_x\left|0\right>+\beta_x\left|1\right>$ and ...
2
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0answers
53 views

The role of state space composition in quantum computation

In a paper by Richard Josza and Noah Linden they argue that the way state spaces of composite systems are formed is a key aspect in the benefits of quantum computers. In (classical) phase space, two ...
2
votes
1answer
307 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
490 views

Ising spin vs Pauli spin matrices

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
3
votes
1answer
735 views

Do quantum computers manufactured by D-Wave Systems, Inc. work? [duplicate]

D-wave claims to have built 128 qbit quantum computers which are commercially available? What I don't understand is that have they really been able to do this given that the scientific community is ...
0
votes
1answer
148 views

how many qubit do we need to store “16”?

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 so how this ...
3
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0answers
77 views

What is three-photon interference?

Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
8
votes
1answer
260 views

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 $$ x_k = {\rm Tr}(\rho \sigma_k), $$ ...
2
votes
0answers
101 views

Creating matrix Hamiltonian for Feynman's CCNOT [closed]

I'm trying to read Quantum Mechanical Computer and to implement the CCNOT logical gate with Mathematica. Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized that i need to ...
10
votes
1answer
1k views

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 ...
2
votes
2answers
143 views

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 ...
2
votes
1answer
406 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 ...
2
votes
1answer
107 views

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 ...
3
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0answers
217 views

Studying Feynman articles nowadays

I'm curious to know if it's useful to study Feynman article "Quantum Mechanical Computer" nowadays. I'm a computer scientist, and i don't know any of the literature in quantum computers. Since long ...
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3answers
887 views

Does quantum computing rely on particular interpretations of quantum mechanics?

It is my understanding that quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed. ...
-1
votes
1answer
100 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 ...
1
vote
1answer
184 views

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 ...
6
votes
1answer
188 views

fixed input qubit state to an arbirary pure state using two variable rotations and one fixed rotation

It is a theorem that any arbitrary unitary transformation in SU(2) can be factored into the following form: $ O = U_X(\theta) U_Y(\phi) U_X(\delta) $ Where $U_X$ is a Bloch sphere rotation. I ...
9
votes
2answers
379 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 $\rho$ ...
17
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2answers
3k views

Basic questions in Majorana fermions

Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
0
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2answers
444 views

Quantum gate: Phase shift

I dont undestand how to apply a phase shift gate to a qubit. By example how to map $|\psi_0\rangle = \cos (30^\circ) |0\rangle + \sin (30^\circ) |1\rangle$ to $|\psi_1\rangle = \cos(-15^\circ) ...
1
vote
1answer
609 views

Hadamard gates and constructing them

Can anyone explain the process required to make a Hadamard gate that acts on 1st, 2nd and 3rd qbits? For Hgates acting on the first qubit i realise the matrix is $H=\begin{pmatrix} ...
5
votes
1answer
100 views

Scaling of quantum error correction

I'm having a question regarding quantum error correction. Using a large number of imperfect (but already very good) quantum gates, it is in theory possible to build an equivalent, error-corrected ...
4
votes
7answers
856 views

Quantum computers: are they possible or impossible?

I know quantum computers are very complicated and my question is is there any way in "Principle" to create one? Are there already quantum computers being created?
4
votes
2answers
2k views

How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
0
votes
2answers
326 views

Help on controlled quantum gates?

Obviusly a controlled-not gate is possible, is a not-controlled gate possible? I need a gate to flip the first qbit and leave the second unchanged, but in literature I have never seen such a gate. ...
3
votes
2answers
545 views

Quantum Teleportation Fidelity

I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
3
votes
1answer
76 views

Reversible gates

Is it possible to make any gate reversible merely by retaining the input bits in the output and introducing ancilla bits as necessary? That is, given an irreversible gate with $k$ inputs and $l$ ...
11
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1answer
307 views

Computability of physics

As far as I understand a Universal Quantum Simulator can simulate any quantum system and thus anything that exists in the universe. Also, a quantum computer can implement such a quantum simulator. ...