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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.

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Non-layperson explanation of why a qubit is more useful than a bit?

I have a computer science and mathematics degree and am trying to wrap my head around quantum computing and it just doesn't seem to make sense from the very beginning. I think the problem is the ...
0
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0answers
79 views

FPGA qubit simulation

This question is regarding the simulation of qubits, using FPGAs. My question is: how does using FPGAs to simulate qubits help us understand or give us an insight into how quantum computers could be ...
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0answers
61 views

How to encode a qubit in standard basis?

I wonder what the steps for encoding a qubit in a certain basis are (you can give your answer in terms of the standard basis for simplicity). Example and a little explanation about steps would be ...
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1answer
68 views

How to measure in the standard basis?

I saw some related topics, but none of them give step by step instructions on measuring in standard basis (or some other basis). Could you please give such instructions? Giving an example would be ...
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3answers
284 views

Why is the state of multiple qubits given by their tensor product?

How did we derive that the state we get by $n$ qubits is their tensor product? You can use $n=2$ in the explanation for simplicity.
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2answers
61 views

Why do $n$ inputs to a ket give a vector of dimension $(2^n,1)$?

NB - notation from Octave. I understand that ket([0]) is the $(1,0)$ in a $(x,y)$ plane. But when I try a ket with three numbers I get a column vector of dimension $(8,1)$. I assume that comes ...
7
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2answers
382 views

Transformation of a Bell state

I am relatively new and interested in quantum computing. Specifically, I am interested in transforming an equation that I found on Wikipedia. But I did not quite understand the transformation. $ \...
3
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1answer
51 views

Could we use varying voltage with programmable gates?

One of the benefits I'm reading about qubits is that they can be in an infinite number of states. I'm aware of Holevo's bound (even though I don't fully understand it). However, it made me think of ...
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3answers
82 views

Imperfect Quantum Copying

It is known by the no-cloning theorem that constructing a machine that is able to clone an arbitrary quantum state is impossible. However, if the copying is assumed not to be perfect, then universal ...
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3answers
111 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(|...
2
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2answers
280 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.
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1answer
136 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: ...
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3answers
151 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 ...
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4answers
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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
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1answer
57 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 ...
4
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1answer
53 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?
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4answers
450 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
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1answer
573 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? ...
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2answers
762 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 ...
5
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1answer
81 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 ...
3
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1answer
77 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 ...
8
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3answers
369 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 ...
4
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1answer
124 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 ...
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3answers
283 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 ...
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2answers
604 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, ...
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2answers
437 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&#...
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1answer
243 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?
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2answers
453 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?
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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 $4$ ...
7
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2answers
436 views

Measuring in standard basis meaning

What does it mean to measure a qubit (or multiple qubits) in standard basis?
5
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1answer
110 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?
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2answers
400 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 ...
7
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2answers
1k 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 ...
6
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1answer
278 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 ...
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1answer
182 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 ...
7
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1answer
180 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 ...
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2answers
565 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 ...
7
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1answer
122 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 ...
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0answers
65 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 ...
4
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1answer
117 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. ...
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2answers
480 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 ...
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2answers
235 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 ...
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5answers
520 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 ...
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2answers
226 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 ...
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4answers
659 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\...
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4answers
889 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 ...
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3answers
2k 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 ...
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2answers
62 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 ...
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269 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 ...
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2answers
237 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 ...