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2
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1answer
250 views

How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
1
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0answers
62 views

Usage example of stabilizer codes QEC

This question directly follows the previous one about $X$ stabilizers and phase-flip errors: Practical example of stabilizer codes Let's now consider a second part of the quantum circuit that is ...
1
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0answers
39 views

Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above ...
1
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0answers
52 views

Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
1
vote
1answer
92 views

Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
1
vote
1answer
64 views

Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
2
votes
1answer
49 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
101 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
votes
0answers
60 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
104 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
80 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
157 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
84 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
90 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
119 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
2answers
128 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 ...
3
votes
3answers
617 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 ...
4
votes
2answers
215 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
680 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
91 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
214 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 ...
1
vote
2answers
127 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
votes
1answer
76 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
383 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
218 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
votes
0answers
118 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
votes
1answer
263 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
242 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
votes
0answers
43 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
240 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
vote
1answer
361 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
664 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
124 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 ...
2
votes
0answers
69 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
233 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
95 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 ...
7
votes
1answer
773 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 ...
1
vote
2answers
120 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
345 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
103 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
votes
0answers
204 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 ...
14
votes
3answers
738 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. ...
-2
votes
1answer
88 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
152 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
169 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
374 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 $\rho$ ...
13
votes
2answers
2k 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
votes
2answers
309 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
483 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
85 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 ...