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Questions tagged [quantum-state]

In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. A mixture of quantum states is again a quantum state. (Wikipedia)

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How to represent $|+\rangle$ in Python?

I am using state vectors and operator matrices to test out my knowledge in a Python program. How would I represent the state $|+\rangle$ in Python? I want to then perform several operations in a ...
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$n$ qubit vs. a $d=2^n$ qudit states and measurements

The pure states of a qudit inhabit the $\mathbb{CP}(d-1)$ manifold. Is it true that the pure states of $n$ qubits live on the $\mathbb{CP}(2^n-1)$ manifold? If the answer to the first question is yes,...
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CX gate with Hadamard

Let's say we got a CX with a Hadamard gate on the control gate and any state at the target gate, will the target necessarily become a superposition of two states? Best.
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GHZ - measuring particles

I'm referring to an earlier question. It involves secret sharing based on the different measurement directions 3 people i.e Alice Bob and Charlie do. Now there is a block in the referred paper which ...
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How to find a common eigenstate of commuting operators?

I have multiple different operators in matrix form and I need to find their common eigenstates. The challenge is that the common eigenstate is in a superposition of multiple states and isn't just a ...
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44 views

Eliminating a term of a superposition state

Is there a way of eliminating a term of a superposition state? Let's say I have the state $$\frac{1}{\sqrt 2}|00\rangle + \frac{1}{2}|01\rangle + \frac{1}{2}|10\rangle$$ What operation would I do to ...
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Quantum fidelity simplified formula while both of the density matrices are single qubit states

I have a question while reading the quantum fidelity definition in Wikipedia Fidelity of quantum states, at the end of the Definition section of quantum fidelity formula, it says Explicit expression ...
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85 views

Quantum secret Sharing using GHZ state paper

I am reading a paper on Quantum Secret Sharing Quantum Secret Sharing using GHZ states I have doubts regarding the initial phase of the paper, which are: Let me state what things I read and ...
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What does “an $n$-qubit array can represent $2^n$ possible array elements” mean?

I read "...an $n$ qubit array can represent $2^n$ possible array elements.." on this post. A classical $n$-bit array can represent $2^n$ possible array elements as well, so I'm confused about the ...
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Measuring first qubit of Bell state

Let's consider the following Bell state: $$\lvert \Phi^+\rangle = \frac{1}{\sqrt{2}} (\lvert00\rangle + \lvert11\rangle)$$ What would happen if I measure the first qubit in the standard basis and ...
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Weeding out qubit states with leftmost qubit as 1

Need help! I was working on a project when I required to use a projection operator. For an example case, I have the Bell state, $$|\psi\rangle = \frac1{\sqrt2}\left(\color{blue}{|0}0\rangle+|11\rangle\...
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How can I write the maximally mixed state on m qubits as a linear combination of basis vectors?

The maximally mixed state on m qubits is defined to be the quantum state with associated density operator $\rho_m = \frac{1}{2^m} I$. Examples are On one qubit this is $\rho_1 = \frac{1}{2}(|0\...
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How to tell if the ground states of two Hamiltonians are solutions of the same optimization problem?

Let's say, that we have an optimization problem in the form: $$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p, $$ where $f(x)$ is an objective function, $g_i(x)$ are ...
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Question on state distinguishability

Consider the following protocol. We are given either $|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ or $|\phi\rangle = \alpha_{0} |0\rangle + \alpha_{1}|1\rangle$ where $\alpha_{0}^{2}$ ...
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Complex number in the representation of a qubit

I do not know if the question is not too easy, but I'll put it here, because I'm interested in it. So the state of a qubit is often stated in this form: $$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$...
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222 views

Understanding a quantum algorithm to estimate inner products

While reading the paper "Compiling basic linear algebra subroutines for quantum computers", here, in the Appendix, the author/s have included a section on quantum inner product estimation. Consider ...
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Can entangled qubits be disentangled without using code or software?

Is there a way to revert two entangled qubits to a separate state without using code...like restarting a quantum computer? Note: By "restarting a quantum computer", I do not mean restarting a virtual ...
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Converting a Qubits state to a binary value in Q#

In Q#, How do I store a Qubits state in a binary-based disk / hard drive for use by regular digital programs? Is this even possible?
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Restoring an initial state after computation

Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\...
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What “states” can a qubit have if it doesn't have values?

I was told that qubits don't have a value, they have a "state". What does that mean? What are the different "states" that a qubit can have (like bits can be either 1 or 0)?
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Quantum operation in blocks

I have $n$ states in superposition $|A\rangle=\dfrac{1}{2^{l/2}}\sum_{i=0}^{2^l-1}\sum_{j=0}^{2^l-1}|0\rangle^{\otimes q}|i\rangle^{\otimes l}|j\rangle^{\otimes l}$. Now I have to apply the transform ...
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How to interpret $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle$?

I'm having trouble accepting, intuitively, that $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle = \rvert1\rangle \otimes -\rvert1\rangle$. It's my understanding that $ -\rvert1\rangle$ ...
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How do physical implementations of Z gate selectively affect $\lvert1\rangle $ basis vector?

The Pauli Z gate inverts the phase of $\lvert1\rangle $ while leaving $\lvert0\rangle$ unaffected. When I think about how $\lvert1\rangle $ and $\lvert0\rangle$ are physically realized, however, as ...
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What happens when an operator is applied only to some bits of a mixed state?

What happens when an operator is applied only to some bits of a mixed state? For instance, assume $\vert x\rangle\vert f(x)\rangle$ is entangled. Then what is the result of $\vert Ux\rangle\vert f(x)\...
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Quantum operation involving permutation

Suppose I have the state $\frac{1}{2^l/2}\sum_{i=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |i\rangle^{\otimes}|0\rangle_i^{\otimes l}$. I perform some unitary transformation between the registers $|i\...
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Writing the notation when gates act on non successive registers

Suppose I have registers $|a\rangle^{l}|b\rangle^{l} |c\rangle^{l}$ and want an adder mod $l$ gate between the $a$ and $c$ registers. Let $R$ be the adder mod $l$ gate. So is this the correct ...
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Reinforcement learning with a quantum agent [closed]

Is it an open question whether we can do reinforcement learning where the quantum agent is not present in the environment, that is, doesn't contribute noise to the environment? In a classical ...
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75 views

Most efficient way for general state generation

Assume we are given an $n$-qubit system and complex numbers $a_0, \ldots, a_{m-1}$ with $m = 2^n$. Assume further we start with the initial state $|0 \ldots 0\rangle$ and want to make the ...
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Which is the correct depiction of a qubit before it collapses?

Which is the correct depiction of a qubit state showing the possibilities before it collapses? Is it like: MODEL 1: 1000 0100 0010 0001 MODEL 2: 1000 0100 0010 0001 0111 1011 1101 1110 MODEL 3: ...
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Permutation of initialized states

Suppose I have an initial state: $$|A\rangle=\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1} |x\rangle^{\otimes l}|y\rangle^{\otimes l}|z\rangle^{\otimes l}|0\rangle^{\otimes ...
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Circuit construction and Dirac notation of the following operation

I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\...
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How to prepare a statistical mixture of $|0,0\rangle $ and $ |1,1\rangle $ in QuTiP?

A QuTiP novice here. It's easy to prepare a pure state in QuTiP. For example, to prepare $\frac{1}{\sqrt{2}}(|0,0\rangle + |1,1\rangle)$: ...
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56 views

Trace distance of two classical-quantum states

I have these two classical-quantum states: $$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\ \mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$ Where $a$ are the classical ...
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1answer
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State of a system after the second qubit of a Bell state sent through a bit flip error channel

The second qubit of a two-qubit system in the Bell state $$|\beta_{01}\rangle= \frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$$ is sent through an error channel which introduces a bit flip error with ...
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Implementing conditional operators in a quantum circuit

I have 4 states say $|00\rangle, |01\rangle,|10\rangle, |11\rangle$. I want to add the states in a manner such that $|a\rangle=|00\rangle\otimes|01\rangle\to |00\rangle\otimes|01\rangle$ and $|b\...
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Does a 5-partite state with these entanglement properties exist?

Is there a 5-partite state such that if two parties each hold 2 shares of the state, without knowing what shares the other party holds, they can create a Bell pair between them and know which qubit in ...
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1answer
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How to pick number of simulation qubits for finding eigenvalue of fermionic Hamiltonian?

I am having some trouble understanding how the number of simulation qubits are chosen when finding the eigenvalue of a fermionic Hamiltonian. For the phase-estimation algorithm, is the number of ...
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CNOT's control qubit preceded by Hadamard: Why is sqrt also applied to target qubit?

I'm going through the Quantum computing for the very curious (Matuschak & Nielsen) tutorial. The example shows a $\operatorname{CNOT}$ gate where the input of the control bit is preceded by a ...
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1answer
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Default value for a state created by QuantumRegister

What's the default value for a state created by QuantumRegister(1,'name_of_the_register')? Is it a $|0\rangle$ or a $|1\rangle$?
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How to implement the mixed quantum state fidelity in a quantum circuit?

Suppose we use Uhlmann-Josza fidelity $F(\rho, \sigma):=(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$, can we construct a quantum circuit that help us to calculate the fidelity of two mixed ...
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Large size of matrices for little outcome [closed]

I am stuck in a dilemma about how to proceed with a quantum computing algorithm that changes the original state of a system to another. Say I have a superposition of all $8$ bit integer values that ...
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What interesting properties can I measure with a 1 qubit state?

I am playing with the IBM Q and I would like to know what interesting properties I can measure with only a 1 qubit state. This is because things like Bell's inequalities, concurrence, PPT criterion, ...
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Is $ |x,y,z\oplus f(x,y)\rangle$ entangled?

Let $f(x,y)$ be a random 2n- to 1-bit function. Consider the quantum circuit $|x,y,z\rangle \to |x,y,z\oplus f(x,y)\rangle$. Is the new state entangled in general? Is it entangled if $x,y$ are $...
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1answer
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Making a maximally mixed 2-qubit state in the IBM Q

I am trying to make a 2-qubit maximally mixed state $\mathbb{I}/4$ where $\mathbb{I}$ is the identity $4\times 4$ matrix. I know that, for a maximally mixed 1-qubit state I can use a Hadamard gate, ...
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Tips and tricks for constructing circuits to generate arbitrary quantum states

I see a question quite a lot in past exam papers that goes like propose a quantum circuit that generates the state $|\psi \rangle$ given the initial state $|\phi\rangle$ Here's an example: Given the ...
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Why do we need reversibility?

Suppose we have qubit $|a\rangle$ and we want to implement quantum addition say adding $|a\rangle$ and $|a\rangle$. When drawing the circuit for this operation one of the outputs that we get is ...
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1answer
84 views

Quantum representation of cube

Let's say I have a square matrix of size $2^n\times 2^n$ with entries being 8 bit integers, where $2^n\times 2^n=b\times b\times b=2^l\times 2^l\times 2^l$, then if I want to represent that matrix in ...
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Encoding bosonic degrees of freedom

A well-known way of encoding $N$ levels of a harmonic (bosonic) oscillator is as follows: \begin{equation} |n\rangle = |1\rangle^{\otimes n} \otimes |0\rangle^{\otimes N-n+1} \quad,\qquad ...
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Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
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How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the ...