Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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Two-way quantum computers (like in Ising model) - are they possible? Could solve general NP problems? [closed]

Standard one-way quantum computers (1WQC) allow for e.g. Shor, Grover algorithms, however, general NP problems seem too difficult for them(?) - bringing an open question if they could be somehow ...
Jarek Duda's user avatar
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General structure of the state with $I(A:B|C)_{\rho}{=}2 \log_2 \{\min (d_A, d_B)\}$

The conditional quantum mutual information (CQMI) of a state $\rho^{ABC}$ respects the dimension bound $I(A:B|C)_{\rho}{\leq}2 \log_2 \{\min (d_A, d_B)\}$ (Mark Wilde's book, exercise 11.7.9). One ...
Abir's user avatar
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How to tell if an $n$-qubit state is entangled? [duplicate]

Given a state of n qubits, how can I find if it is entangled? Specifically, I want to find all qubits (if any) that can be separated from a state. I have seen many answers for two-qubit states but how ...
HumbleLearner's user avatar
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Proper way to represent anti-matter in a 3D model?

I'm trying to create a simple 3D model to represent the basic atomic structures involved in matter (i.e., Matter, Molecules, Atoms, Electrons, Protons, Neutrons, Quarks, Anti-Matter, Forces, etc.). I ...
Roger A. Grimes's user avatar
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2 answers
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Qiskit, Statevector.from_label

I apply Grover's on an eigh qubits circuit I just want to amplify the states whose qubits 6 and 7 are |1> The following test works (the state 11011001 is correctly amplified) ...
Maurice Clerc's user avatar
5 votes
2 answers
342 views

What is the expectation value of $|\langle \psi|U|\psi \rangle|$ over Haar random states $|\psi\rangle$?

We know the average unitary fidelity, $\int |\langle \psi|U|\psi \rangle|^2 d\psi$, has a nice closed-form solution: $\frac{1+\frac{1}{d}|Tr (U)|^2}{1+d}$, thanks to Horodecki and Nielsen. However, I ...
Abir's user avatar
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Global vs local: global density matrix and all the reduced density matrix

I prepare a $n$-qubit quantum state $\sigma$ whose ideal state is $\rho$, then perform state tomography on all the $m$- qubit reduced states. Ideally, I find that all the $m$- qubit reduced states are ...
Michael.Andy's user avatar
3 votes
1 answer
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Cirq seems to output 0 instead of |2> with qutrits

I am experimenting a bit with qutrits on Cirq and came across a problem: my output is 0 when it should be |2>. I defined my qutrit as follows: ...
Q.Ask's user avatar
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Change of basis on a per vector component level

Suppose we have an $n$-qubit quantum state in the computational basis encoded in a classical blackbox function $f(x)$. That is, with $x \in \{0,1\}^n$ we can query $f$ and get the respective ...
MonteNero's user avatar
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Random variable as tensor product of its components

Consider a finite random variable $X: \Omega \rightarrow \mathbb{R}^d$ on a probability space $(\Omega, 2^{\Omega}, P)$. Let $H_{\Omega}$ and $H_E$ be two Hilbert spaces with basis states $ \{| \omega ...
Simon's user avatar
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What is the density matrix of a pure state?

By definition of the density matrix for example the density matrix of $|0\rangle$ state (pure state) is: $$\rho=|0\rangle \langle 0| = \begin{pmatrix} 1 & 0 \\ ...
Curious's user avatar
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Given a unitary $U_p:|0\rangle\to\sum_\omega\sqrt{P(\omega)}|\omega\rangle$, what does $|0\rangle$ represent exactly?

Consider a random variable $X$ on a probability space $(\Omega, 2^\Omega, P)$. Let $H_\Omega$ be a Hilbert space with basis states ${| \omega \rangle}_{\omega \in \Omega}$, and fix a unitary $U_P$ ...
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Is there a method to implement qutrit using qubits?

I want to implement 3 level system on a qubit quantum computer. Currently I feel I can use 2 qubits and encode the states of a 3-level system as such |0>=|00>, |1>=|01>, |2>=|10> The ...
Chetan Waghela's user avatar
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Understanding notation regarding phase oracle continued

Since I am not able to comment on my post, I had to register an account and start a new post. Maybe my old post can be deleted, which is found : here I am new to quantum computing. I cannot get my ...
Simon's user avatar
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Understanding notation regarding phase oracle [duplicate]

I am new to quantum computing. I cannot get my head around the following: Consider a finite random variable $X : \Omega \rightarrow E$ on a probability space $(\Omega, 2^{\Omega}, P)$. Let $H_{\Omega}$...
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What is an initial state of a qubit in PennyLane?

I just started trying to use the PennyLane Python package. It seems like the default.qubit device initializes each wire as an up-spin qubit. However, I am not ...
Silly Goose's user avatar
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3 answers
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Considering a spin-$\frac{1}{2}$ qubit, which is the ground state, $|0\rangle$ or $|1\rangle$?

Considering a spin-$\frac{1}{2}$ qubit, which is the ground state, $|0\rangle$ or $|1\rangle$? I apologize for the simplicity of the question.
Student's user avatar
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Representation of maximally entangled states of $2n$ qubits with Pauli matrices?

I'm reading this paper while the author states in the eq(A1) that, for a $2n$ qubits maximally entangled state $|\Psi ^+\rangle \langle \Psi ^+|$, we can write it with Pauli operators $P_u\in\left\{ I,...
Sherlock's user avatar
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What is the mistake in this Qutip implementation of the classical shadows protocol (Huang et. al. 2020)?

So I'm trying to replicate the results from Huang's paper, following Pennylane's tutorial. But instead of using Pennylane (in particular their recently implemented ClassicalShadow class), I'm trying ...
EdwardGHPhy's user avatar
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1 answer
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How to estimate the qubit frequency from a two-frequency Ramsey experiment?

In a two-frequency Ramsey experiment, we obtain two Ramsey sequences from $f_d-\delta$ and $f_d+\delta$, where $f_d$ is the current drive frequency and $\delta$ is some detuning. We then estimate ...
Ziyuan's user avatar
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Why are we only interested in the linear combination $|\phi\rangle = a |0\rangle + b |1\rangle$?

They say superposition enables qubit to live in linear superposition of two states. I.e. \begin{equation} |\phi\rangle = a|0\rangle + b |1\rangle \end{equation} Why are we interested only in linear ...
QuanTUM's user avatar
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Can we say what happens to phases after a reset?

Take a simple state-vector of a 2 qubit system: $$ |\psi\rangle = \frac{1}{3\sqrt{2}}\pmatrix{1 \\ 2i\\ -3 i \\-2} $$ Suppose we now reset the last (second) qubit. This forces the state space to ...
Craig's user avatar
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Confusion regarding the definition of state of a qubit

I am currently reading the "The Mathematics of Quantum Coin-Flipping" by Carl A. Miller. On page 1909 (the second page in the pdf linked above) the author defines the state of a qubit as a ...
3nondatur's user avatar
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Quantum algorithms and binomial distributions and probabilities

Qubits in a quantum computer are mostly spins of quantum particles.But since spin can take up to 2 values does this mean quantum algorithms are applied mathematics which make use of binomial ...
Volpina's user avatar
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The operator of the composite system given the operator of the single system

Define the operator on a qudit system as \begin{align} o &= \sum_{s, s^\prime=1}^d o_{s,s^\prime}\vert s\rangle\langle s \vert \otimes \vert s^\prime\rangle \langle s^\prime \vert. \tag{1} \end{...
Michael.Andy's user avatar
3 votes
2 answers
229 views

Can you distinguish between $|0\rangle, |1\rangle$, and $\frac{1}{\sqrt 2} (|0\rangle + |1\rangle)$?

(A beginner here; possibly a stupid question. Please be gentle. Sorry if I used a wrong tag.) Suppose that I receive a (classically) random number, which is either $1$ or $2$ or $3$. Depending on this ...
Viliam Búr's user avatar
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Simple proof that entangled pure states are not separable

I am trying to understand more about the notion of separable states. For clarity, I will only use the word entangled for pure states, even if a non-separable state is sometimes called entangled too. ...
user8622655's user avatar
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1 answer
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Nonsensical projection of initialized qubits in Qiskit

I wanted to try Qiskit by setting up two qubits initialized to $ | 11 \rangle $ or $ | 01 \rangle $ and two classical bits to measure those two initialized qubits. For this simple demonstration, I ...
Blackwidow's user avatar
1 vote
1 answer
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How is the depth of a circuit creating "Constant size vector states" $O(\log b)$

In Prakash's thesis - (link to PDF), section 2.2.2 Constant size vector states: We show that the vector state $|x\rangle$ for $x\in R^b$ can be created in time $\widetilde{O}(\log(b))$ using a ...
bubakazouba's user avatar
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0 answers
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Half-wave plate (HWP) Hadamard gate implementation

The transformation of a qubit encoded in the polarization state from $|H\rangle$ to the state $|+\rangle$ is theoretically achievable with an HWP@π/8. However, I rarely see this solution in ...
Francesco Sisini's user avatar
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0 answers
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Uncorrectable error due to error on ancilla qubit

Consider a controlled-NOT (CX) gate between the two qubits, implemented with an interaction of the form $ \widehat{H}_{\mathrm{CX}}=V\left[\left(\frac{\hat{I}_1+\widehat{Z}_1}{2}\right) \otimes \hat{I}...
Aubrey Sharansky's user avatar
1 vote
0 answers
103 views

Superposition of states, finding the "maximum" one

I designed a circuit (under Anaconda/Jupyter/Qiskit) whose output is a superposition of states of n qubits, q(0), ...q(n-1). For most of them q(n-1) is |0>, and for a few |1>. I'd like to ...
Maurice Clerc's user avatar
0 votes
1 answer
19 views

Is there a polynomial time mapping from 'Grover States' to an orthonormal set of vectors

Grover's algorithm solves the problem of 'Quantum Search' which I will describe below: Given some oracle, $O_f$, such that $O_f | x \rangle = (-1)^{f(x)} | x \rangle$, find a value of $x$ such that $...
Andrew Baker's user avatar
3 votes
3 answers
132 views

What is the conditional min-entropy of a pure bipartite state?

In this paper, it is stated that the conditional min-entropy $H(A|B)_{\rho_{AB}}$ of $A$ conditioned on $B$ for any $\textbf{pure}$ quantum system $\rho_{AB}=|\psi_{AB} \rangle \langle \psi_{AB} |$ is ...
quantum_theo's user avatar
-1 votes
2 answers
73 views

Is a quantum state with coefficient 0 still there?

Potentially stupid question but is a quantum state with a zero coefficient still there? I didn't think it was but then I saw in the answer to a problem that when we measure $$ \hat{M} = |1\rangle \...
redpanda2236's user avatar
3 votes
2 answers
135 views

Transformation of 0 state to superposition of 0 and + state with only using single qubit gates

How to transform a qubit from state $|0\rangle$ to $(|0\rangle+|+\rangle)/N$ by only using an additional qubit, a controlled Hadamard gate, a Hadamard gate and a $Y$ or $Z$ gate? Sequence of the gates ...
Jack's user avatar
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1 vote
1 answer
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Why are the basis unit vectors |0⟩ and |1⟩ written as column vectors [1, 0] and [0, 1], respectively?

I am starting to learning quantum computing and am currently reading Quantum Computing: A Gentle Introduction. As I started reading into the first section after the Introduction, it talks about basis ...
Jayex_Code01's user avatar
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0 answers
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Understanding the meaning of [2, 2] for input_register and target_register in a custom Cirq gate

I'm learning a custom gate implementation from google Cirq official tutorial of shor algorithm(https://colab.research.google.com/github/quantumlib/Cirq/blob/master/docs/experiments/shor.ipynb#scrollTo=...
Tonight223's user avatar
1 vote
0 answers
29 views

Tighter upper bound of $\operatorname{tr}[ (\mathcal{H}[L]\rho )^2] \leq \delta$

I am wondering about an upper bound of the trace function $\operatorname{tr}[ (\mathcal{H}[L]\rho )^2] \leq \delta$ (we assume that $\rho$ is the $N\times N$ density matrix representing the quantum ...
Kochan's user avatar
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2 votes
1 answer
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Can a quantum gate send $|a,b\rangle$ to $|0,a\rangle+|1,b\rangle$?

I am looking for a quantum gate (or a circuit) that operates on two quantum registers of equal size and in states $|a \rangle$ and $| b \rangle$, respectively, and prepares the state: $\frac{1}{\sqrt{...
wavosa's user avatar
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1 vote
1 answer
94 views

Can we use purity for separable states?

Purity is a measure of how much a state is pure. Suppose $\rho$ is a density matrix. Then purity $p$ is defined as $$ p = \mathrm{tr}(\rho^2). $$ I wonder if we can use purity for separable states? Or ...
reza's user avatar
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2 votes
2 answers
92 views

Does the inequality $\mathrm{tr}(L^\dagger L \rho^2)-\mathrm{tr}(L^\dagger \rho L\rho )\geq 0$ hold generally?

Does the inequality $$\mathrm{tr}(L^\dagger L \rho^2)-\mathrm{tr}(L^\dagger \rho L\rho )\geq 0$$ hold for any density matrix $\rho$ and any non-Hermitian Lindblad operator $L$?
Kochan's user avatar
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9 votes
2 answers
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Does post selection of a qubit introduce non-linearity?

Problem I have a multi-qubit state $\lvert \psi \rangle$ and an ancilla qubit $\lvert 0 \rangle$ that I use to extend my state, getting the new state $\lvert 0\rangle \otimes \lvert \psi \rangle$. ...
Andrea's user avatar
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2 votes
1 answer
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Is the global phase of qubits important if qubits interact with each other?

I know that if we have two qubits in states differing by a global phase it does not matter that they are in the same state. But if we have a qubit in state_1 and another in state_2 does the global ...
Qubii's user avatar
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1 vote
1 answer
152 views

SX operator and superposition

I am running some tests using the probabilities we get from statevector to assert values in qiskit. For instance, with two qubits and a hadamard gate on the first one we have: ...
neilson's user avatar
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0 answers
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Analogies of a combination of Newton's and Coulomb's law interpreted in Hilbert sphere in quantum mechanics?

I wanted to share with you something I stumbled upon about Hilbert spaces and Newton's formula for gravitation. Newton's formula for gravitation is represented by $$ F_N(a,b) \cdot r/|r| = G \cdot \...
stackExchangeUser's user avatar
1 vote
1 answer
45 views

Calculate the product state/quantum register back into its tensor product

So let's asume I have a product state/quantum register as a result of a tensor product of two qubits. Lets take a "hard" product state matrix like: $$\frac{1}{\sqrt{2}} \begin{bmatrix} \...
Christian Bernhard's user avatar
1 vote
2 answers
191 views

How to get a state vector from bloch sphere coordinates for 1 qubit?

I need to get a state vector for one qubit from bloch coordinates no matter if there could be many states that describes the same bloch coordinates, and it does not have to be normalized, because the ...
Luis ALberto's user avatar
2 votes
1 answer
230 views

Rotation of qubit - Pauli Gates XYZ

I don't understand how to apply a Pauli Gate on a qubit. Lets say 8 got a qubit with in state: $$|\psi\rangle = 0.891 |0\rangle+ 0.454i |1\rangle$$ How would I compute e.g. rotating it 90 degrees ...
Christian Bernhard's user avatar
1 vote
1 answer
41 views

What is the Eigen Value corresponding to a Coin Toss when we make a measurement?

I am asking this question to all the Quantum Computing or Quantum Mechanics practitioners. I have studied that when you measure a state, then you will get an eigenvalue for sure corresponding to ...
Deb Prakash Chatterjee's user avatar

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