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Questions tagged [qubit-state]

For questions on the manipulation and creation of 'qubits' and the state they represent. These actions may be either from theory or practice, use other tags to indicate this.

17
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3answers
223 views

How does measurement of one qubit affect the others?

To represent a quantum computer's state, all the qubits contribute to one state vector (this is one of the major differences between quantum and classical computing as I understand it). My ...
15
votes
4answers
583 views

Alternative to Bloch sphere to represent a single qubit

In order to represent the single qubit $|\psi\rangle$ we use an unitary vector in a $\mathbb{C}^2$ Hilbert space whose (one of the) orthonormal base is $(|0\rangle, |1\rangle)$. We can draw $|\psi\...
14
votes
2answers
203 views

Representation of real numbers in quantum computers

In classical binary computers, real numbers are often represented using the IEEE 754 standard. With quantum computers you can of course do this as well - and for measurements this (or a similar ...
13
votes
2answers
546 views

Is it true to say that one qubit in an entangled state can instantaneously affect all others?

When a qubit is measured, there is a ‘collapse of the wave-function’ as a result is randomly chosen. If the qubit is entangled with others, this collapse will also effect them. And the way it affects ...
12
votes
2answers
205 views

What makes quantum computations different from randomized classical computations?

One of the many thing that confuse me in the field of QC is what makes the measurement of a qubit in a quantum computer any different than just choosing at random (in a classical computer) (that's not ...
11
votes
3answers
1k views

How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...
11
votes
2answers
161 views

State produced by spontaneous parametric down-conversion (SPDC)

I'm researching SPDC's efficacy for use in an optical quantum computing model and I've been trying to figure out exactly what state the photons are in when they come out (as represented by a vector, ...
10
votes
5answers
440 views

What is the difference between a qudit system with d=4 and a two-qubit system?

I understand that a qudit is a quantum $d$-state system. If $d=4$, is this exactly the same as a two-qubit system, which also presents $4$ quantum states? The Hilbert space is the same, right? Are ...
9
votes
2answers
563 views

CNOT Gate on Entangled Qubits

I was trying to generate Greenberger-Horne-Zeilinger (GHZ) state for $N$ states using quantum computing, starting with $|000...000\rangle$ (N times) The proposed solution is to first apply Hadamard ...
8
votes
2answers
572 views

How to show that an n-level system is entangled?

"How do I show that a two-qubit state is an entangled state?" includes an answer which references the Peres–Horodecki criterion. This works for $2\times 2$ and $2\times3$ dimensional cases; however, ...
7
votes
3answers
805 views

What's the difference between a pure and mixed quantum state?

As per my limited understanding, a pure state is the quantum state where we have exact information about the quantum system. And the mixed state is the combination of probabilities of the information ...
7
votes
3answers
241 views

Why does the “Phase Kickback” mechanism work in the Quantum phase estimation algorithm?

I've probably read the chapter The quantum Fourier transform and its applications from Nielsen and Chuang (10 th anniversary edition) a couple of times before and this took this thing for granted, but ...
7
votes
2answers
819 views

How to input 2 qubits in 2 Hadamard gates?

Let's say we have a circuit with $2$ Hadamard gates: Let's take the $|00\rangle$ state as input. The vector representation of $|00\rangle$ state is $[1 \ 0 \ 0 \ 0]$, but this is the representation ...
7
votes
2answers
390 views

How to check if a matrix is a valid density matrix?

What conditions must a matrix hold to be considered a valid density matrix?
7
votes
2answers
333 views

Measuring in standard basis meaning

What does it mean to measure a qubit (or multiple qubits) in standard basis?
7
votes
3answers
52 views

General construction of $W_n$-state

Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|...
7
votes
2answers
233 views

Density matrices for pure states and mixed states

What is the motivation behind density matrices? And, what is the difference between the density matrices of pure states and density matrices of mixed states? This is a self-answered sequel to What&#...
7
votes
1answer
139 views

Embedding classical information into norm of a quantum state

According to An introduction to quantum machine learning (Schuld, Sinayskiy & Petruccione, 2014), Seth Lloyd et al. say in their paper: Quantum algorithms for supervised and unsupervised machine ...
6
votes
2answers
58 views

Symmetry of tensor product in QC wrt Vazirani 2-qubit video

Quantum Computing (QC) pioneer Vazirani has graciously long provided some nice videos on an intro to QC. E.g. in "2 qubit gates + tensor product" (2014) he introduces the tensor product w.r.t. QC ...
6
votes
1answer
110 views

Does superdense coding allow to double the information capacity of a set of qubits?

I read the basic introductory information about qubits on Wikipedia: There are two possible outcomes for the measurement of a qubit—usually 0 and 1, like a bit. The difference is that whereas the ...
6
votes
1answer
157 views

How to find a density matrix of a qubit?

If we are given a state of a qubit, how do we construct its density matrix?
6
votes
1answer
234 views

How to calculate the state given by two qubits?

Let's say two qubits are both in $|+\rangle$ state. We need to find $a_1$, $a_2$, $a_3$, and $a_4$ in $|\phi\rangle = a_1|00\rangle + a_2|01\rangle + a_3|10\rangle + a_4|11\rangle$, how do we find ...
6
votes
2answers
212 views

Are there measuring standards (and units) for the identification of qubits?

The representation of bits in different technological areas: Normal digital bits are mere abstractions of the underlying electric current through wires. Different standards, like CMOS or TTL, assign ...
6
votes
0answers
57 views

Threshold and practical requirements for initial state preparation?

At the beginning of a quantum computational process we generally want to start in a perfectly known initial state, and evolve from there. This cannot be done perfectly, for fundamental reasons, but I ...
5
votes
4answers
407 views

Why do Bloch sphere wavefunctions have half angles?

Suppose we have a single qubit with state $| \psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$. We know that $|\alpha|^2 + |\beta|^2 = 1$, so we can write $| \alpha | = \cos(\theta)$, $| \beta | ...
5
votes
2answers
200 views

Compute average value of two-qubit system

Show that the average value of the observable $X_1Z_2$ in a two-qubit system measured in the state $(|00\rangle + |11\rangle)/\sqrt{2}$ is zero. How would we approach this question? I understand ...
5
votes
3answers
248 views

How is a single qubit fundamentally different from a classical coin spinning in the air?

I had asked this question earlier in the comment section of the post: What is a qubit? but none of the answers there seem to address it at a satisfactory level. The question basically is: How is a ...
5
votes
1answer
568 views

Solving linear systems represented by NxN matrices with N not power of 2

As far as I have seen, when it comes to solving linear systems of equations it is assumed to have a matrix with a number of rows and columns equal to a power of two, but what if it is not the case? ...
5
votes
1answer
106 views

What is the $\left| 22\right>$ state?

I came across with a problem that involves $2$ quantum trits in state $\left| 22 \right>.$ What is it's tensor product interpretation and a matrix interpretation?
5
votes
1answer
132 views

No-cloning theorem and distinguishing between two non-orthogonal quantum states

I'm currently reading Quantum Computation and Quantum Information and I'm not sure if I correctly understand this exercise (on page 57) : Exercise 1.2: Explain how a device which, upon input of one ...
5
votes
2answers
370 views

How does using a superposition of 0 and 1 improve the processing capabilities of a quantum computer compared to classical computers? [closed]

Whenever I learn about quantum computing and qubits, it always talks about the superposition principle and that the qubits can be in both states 0 and 1 simultaneously, thus claiming that quantum ...
5
votes
1answer
77 views

Compact encoding of Boolean formula as oracle

As in the title, I have a doubt regarding the implementation of a boolean formula used as an oracle for a quantum algorithm. The problem is that so far I could reproduce the formula as a quantum ...
4
votes
4answers
485 views

What is the Computational Basis?

What is the computational basis of a quantum computer or for a quantum algorithm? Is it special? Note: I think this question is well-formed and complete, but apparently it lacks length in the view of ...
4
votes
2answers
256 views

How to check if 2 qubits are entangled? [duplicate]

I know that 2 qubits are entangled if it is impossible to represent their joint state as a tensor product. But when we are given a joint state, how can we tell if it is possible to represent it as a ...
4
votes
1answer
44 views

What is the significance of recent demonstration of a passive photon–atom qubit swap operation?

In reference to this recent nature article: https://www.nature.com/articles/s41567-018-0241-6 Specifically, does this warrant a new type of gate?
4
votes
1answer
119 views

What are the standard eigenvalues in $\mathbb{C^2}\otimes\mathbb{C^2}$?

In $\mathbb{C^2}$, we generally take $+1$ and $-1$ as the standard eigenvalues, that's what Pauli-X, Pauli-Z measurements, etc will give us. Is there a similar standard while measuring in the Bell ...
4
votes
1answer
94 views

What do we mean by the notation $\lvert \mathbf{x}, 0\rangle$?

In quantum computation, a common operation performed between two quantum states is the tensor product, which allows us to create a new and higher-dimensional state from two lower-dimensional states. ...
4
votes
3answers
87 views

How do we physically initialize qubits in a Quantum register?

In quantum algorithms we need to initialize the qubits at the start of our algorithm in some quantum register. Suppose that if we are working with a four qubit quantum register we can initialize the ...
3
votes
4answers
1k views

What's the physical significance of |0⟩ and |1⟩?

The word 'state' makes sense in Quantum Mechanics. In classical computers, numbers are represented in binary as a series of 0s and 1s. It seems that the word 'state' extracted from QM and the 0s and ...
3
votes
1answer
55 views

How is Quantum Mechanics (a Physics Concept) used in computing?

I've been taking a course on Quantum Mechanics in which, right now, I'm learning about its application in Computing to give Quantum Computing. Quantum Mechanics is a concept that is applied to ...
3
votes
1answer
72 views

How the joint state of these qubits is derived?

Can someone show to me the steps to derive the joint state at the bottom of this image, please? I tried to follow his explanation but I didn't get the same results… This is taken from the lecture ...
2
votes
2answers
149 views

How do I construct a Density Matrix corresponding to a Hamiltonian?

I have a Hamiltonian and I want to know the corresponding density matrix. The matrix I'm interested in is the one in this question.
1
vote
1answer
125 views

Why is this Hamiltonian matrix diagonal?

I've only recently started using density matrices in my work but I am confused with the following code that I have whether I am getting the right matrix: ...