Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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Does Controlled-U gate entangle qubits?

I've read C-NOT gate entangles qubits, but is it only for C-NOT or any arbitrary CU gate (apart from the likes if CI) entangles qubits?
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Represent a pure state in terms of 2 antipodal points on the Bloch sphere

I recently had an assignment where the question is based on the assumption that we can write any pure state qubit $|\phi \rangle$ as: $$|\phi \rangle = \gamma |\psi\rangle + \delta |\psi^\perp ...
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It two unitaries are delta apart in trace norm, then what is the trace norm of outputs states when the same input state is applied to two unitaries?

Suppose we are given two unitary matrices $U$ and $V$, with the following guarantee, $$||U - V||_1 \geqslant \delta$$ for some $\delta \geqslant 0$. We apply an input density state $\rho$ ...
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Find local state and compute Bloch coordinates, like Quirk

In a multi-qubit system I can find the amplitudes of a state and compute probabilities, $\theta$, and $\varphi$. This falls out from simulation with simple numpy arrays. For example, after application ...
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Need some help with Purity calculation

maybe you could help me a little about my calculation of a quantum pure state with purification. I have this density matrix: \begin{equation} \rho= \begin{pmatrix} 0.4489 & 0.2304 & 0.2162 &...
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How to switch bit in the quantum state?

I want to transform binary representation from one to other. Here, I have 2 registers one act as control register and another is target register with the same number of qubits $n$. Consider $n = 3$ ...
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Gate corresponding to $-I$

I am implementing a quantum circuit in Qiskit. I create the equal superposition state $$ -|00\rangle + |01\rangle + |10\rangle +|11\rangle $$ but I want to obtain the quantum state $$ |00\rangle - |...
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What exactly does it mean to embed classical data into a quantum state?

As the title states. I am a Machine Learning Engineer with a background in physics & engineering (post-secondary degrees). I am reading the Tensorflow Quantum paper. They say the following within ...
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What is the precise definition of the environment a qubit lives in?

The book An Introduction to Quantum Computing (section 10.4.1 Error Models for Quantum Computing) by Phillip Kaye, Raymond Laflamme and Michele Mosca states the following: Errors occur on a qubit ...
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Creating Bell states (a question from tutorial)

I was going through a Quantum Computation lecture series on YouTube given by Umesh Vazirani. There in Lecture 6.3 he talks about creating a Bell state using a Hadamard and CNOT gate. He seems to be ...
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Bloch sphere, where are magnitude and phase of a qbit?

Where are magnitude and phase of a qbit on Bloch sphere? Phase is angle φ. What do you mean by magnitude? Amplitudes? They are given by angle θ - amplitude of |0⟩ is cos(θ/2) and amplitude of |1⟩ ...
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What is the probability to get all qubits equal zero after QFT

Question from exam: Bob built a quantum computer wiht 10 qubits. All qubits are set to zeroes. Bob performed a quantum Fourier transform on the system and then measured the system. what is the ...
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Uniform superposition of states with one qubit set to $|1\rangle$ and others to $|0\rangle$

I am wondering what a circuit should look like if I want to prepare the state of the following form: $$ |0\rangle^{\otimes n} \mapsto \dfrac{ |1000\ldots0\rangle + |0100\ldots0\rangle + |0010\ldots0\...
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Why is Hilbert space considered especially large?

In Nielsen & Chuang section 1.2 introduces multiple qubits and Hilbert spaces. More generally, we may consider a system of n qubits. The computational basis states of this system are of the ...
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How is a qubit represented on a bloch sphere?

A quantum state can be represented as linear combination of 2 states: In Chuang and Nielsens book, it states that because the squared amplitudes sum to 1: That the combination can be rewritten as: ...
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Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
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How can I calculate the probability of a quantum system in superposition to be in the “up” state?

I've got this question to answer and from what I can tell, I need to take the square of the absolute value for the probability amplitude. In this case I think the answer should be the square of $e^{i\...
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Can we use the process of recursion in predicting the future process?

Because while recursion we tend to find the possible result of a current problem by going into its future state through recursion and sometimes by means of through memorization. Then why can't we use ...
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How does the teleportation circuit work after the initial entanglement?

I'm trying to understand why we do what we do when we teleport a state from Alice's first qubit to Bob's qubit. I understand the initial entanglement, but could use help walking through the program. ...
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How to calculate state fidelity in Qiskit?

I have a circuit with different structures, now I'm trying to calculate the fidelity between those with the original one. How do I calculate the fidelity? I want also to initialize the state vector by ...
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Half of Standard Basis Measurement

I know that we can measure a state in standard basis (Z) where the post measurement state is either $|0\rangle$ or $|1\rangle$. But can you do a 'half-Z' basis measurement? I mean, you only measure ...
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Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
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Is Quantum Entanglement the one-dimensional spatial relationship between two particles as described by mathematics?

Is Quantum Entanglement the one-dimensional spatial relationship between two particles as described by mathematics? By one dimensional I mean, when they travel at opposite directions their spin is ...
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2 qubit gate operation on multi qubit systems

Considering a 3 qubit system, what does the matrix operation will look like if I apply CNOT on qubit 1 and qubit 2 and then apply CNOT on qubit 1 and qubit 3?
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Cirq - Print state of qubit

Seeing a state of qubit is too complicated in Cirq I don't want to simulate, I would be happy for debugging, to see the probability/ amplitude of the state of a qubit, without measure and simulate ...
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How should I understand the change of qubit's basis as a rotation?

I have a little difficulty with understanding. How do I properly visualize the change of qubit's basis as a rotation? Let's say that we have classical basis vectors, $|0\rangle$ and $|1\rangle$. Now, ...
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How to decompose a multi-target controlled gate?

I'm trying to replicate with qiskit the results of this paper in which basically they implement a quantum version of the Principal Component Analysis applying Quantum Phase Estimation algorithm in ...
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Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
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Computation of a reduced density matrix

On wikipedia, the article on quantum entanglement gives an example of the computation of a reduced density matrix. I would like to understand precisely what's going on with the computation. First the ...
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How to get Bloch sphere angles given arbitrary qbit as linear combination of basis vectors?

I understand that given a pure state $ |\psi\rangle$, we can express it in terms of two angles $\theta$ and $\varphi$ such that $|\psi\rangle = \cos(\theta/2)|0\rangle + \mathrm{e}^{i\varphi}\sin(\...
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Negative of a qubit state

I have a quick question: Is the qubit state $|\psi\rangle$ the same as $-|\psi\rangle$?
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What is the implementation of the state in superdense coding?

What is the implementation of quantum superdense coding protocol if the sender and receiver share the entangled state $ \frac{1}{\sqrt{2}} (\left| 01 \right> - \left| 10\right>) $?
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Viewing two-qubit measurement as a projective measurement

I am following Nielsen and Chuang, section 2.2.5: A projective measurement is described by an observable, $M$, a Hermitian operator on the state space of the system being observed. The ...
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Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?

My understanding is the Helstrom measurement distinguishes between 2 pure quantum states. Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
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How can I find the fidelity of preparation?

I want to know the fidelity (or error rate) of the preparation ($|0\rangle$) How can I have it?
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How do I explain qubits to my cousin who is 8 year old?

How do I explain qubits to my cousin who is 8 years old?
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Magnitudes and phases of coefficients of a qubit

Quantum mechanics is based on the idea of waves, and waves have both a magnitude and a phase? $$|\psi\rangle = i\alpha|0\rangle + \beta|1\rangle.$$ Does $\alpha$ and $\beta$ represent magnitude and $...
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How to prepare mixed states on a quantum computer?

I am a little bit confused by density matrix notation in quantum algorithms. While I am pretty confident with working with pure states, I never had the need to work with algorithm using density ...
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How long can a qubit exist without decoherence?

In 2020, practically speaking, how long (time-wise) will a qubit function normally before decoherence kicks in?
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Can I generate 4 entangled states (each 5 qubits) on a 5 qubit quantum computer?

Suppose that I have a 5 qubit quantum computer and want to generate 4 entangled states (each of 5 qubits) Single 6 qubit entangled state. Are these 2 cases possible? I am a beginner please help!
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How to find measurement probabilities of a single qbit in a tensored state

Given a tensored state of qbits such as $$ \frac{1}{\sqrt{3}}|0\rangle_1|1\rangle_2 + \sqrt{\frac{2}{3}}|1\rangle_1|0\rangle_2 $$ or $$ \frac{1}{\sqrt{2}}(|0\rangle_1|+\rangle_2 + |+\rangle_1|-\...
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Affine Map of the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture of single ...
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How to set initial state on IBM Q?

For my undergraduate final project I am working on a Quantum Inspired Genetic Algorithm. For this I am using IBM Q real devices and I need to set a custom initial state on qubits. Using the ...
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Does quantum computing already possess the level of abstraction to be explicable even without knowledge of physics?

Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only ...
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Can I compute the fidelity between two states without having to diagonalise them?

So I have been given the following quantum states: $$\rho = \frac{I}{2} + \frac{\bar{s}.\bar{\sigma}}{2}$$ $$\pi = \frac{I}{2} + \frac{\bar{r}.\bar{\sigma}}{2}$$ How do I calculate the fidelity ...
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Why do we need different basis vectors?

There is a basis consisting of $|0\rangle$ and $|1\rangle$ states, i.e. z-basis. Why do we need different basis (in quantum computation), like polar basis and others ($|+\rangle$ and $|-\rangle$)?
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The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?

I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
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What are $|+\rangle$ and $|-\rangle$?

On a view places, I've seen kets that look like this $\left|+\right>$ or this $\left|-\right>$ but I don't seem to find any explanation of this base online. Is it just a different notation for $...
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Quantum algorithm for binary assignment problem

Based on the properties of the qubit, how could I solve this problem: I have 3 person A B C and 2 taxis T1 and T2 A and B are friends B and C hate each other A and C hate each other How could I ...
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Quantum PCA State Preparation

In Quantum Algorithm Implementations for Beginners is an example of the Quantum PCA with an given 2 x 2 covariance matrix $\sum$. The steps for state preparation are given in the paper. The steps are: ...

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