Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
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Considering a spin-1/2 qubit, which is the ground state, |0⟩ or |1⟩?
Considering a spin-1/2 qubit, which is the ground state, |0⟩ or |1⟩? I apologize for the simplicity of the question.
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Understanding notation regarding phase oracle
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 ...
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How to implement the Circuit of Steane's code for Quantum Error Correction?
I have referred this same question here 'Circuit for implementing Steane's code for Quantum Error Correction' . But the answer discusses the circuit to compute the syndrome and not clearly the ...
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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,...
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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:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
glS♦
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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 ...
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Are projective measurements the only optimal measurements to discriminate between two states?
Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one.
There is an optimal measurement to ...
glS♦
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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
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glS♦
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Question about entanglement forging
For circuit knitting (entanglement forging), do anyone understand the mechanism behind equation (3) which halves the amount of qubits required for a circuit ?
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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 ...
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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}...
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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 $...
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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
$$
\hat{M} = |1\rangle \...
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Transformation of 0 state to superposition of 0 and + state with only using single qubit gates
How to transform a qubit from state $|0\rangle$ to $(|0\rangle+|+\rangle)/N$ by only using an additional qubit, a controlled Hadamard gate, a Hadamard gate and a $Y$ or $Z$ gate? Sequence of the gates ...
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How to perform the measurements on a quantum circuit in W state basis?
I need to perform the measurements on a quantum circuit in the basis $\{ \eta^\pm,\zeta^\pm \} $. Where $ \eta^\pm,\zeta^\pm $ are given as follows:
$$\eta^\pm = \frac{1}{2}|001\rangle + \frac{1}{2}|...
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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=...
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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 ...
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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{...
glS♦
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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 ...
glS♦
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Google Colab - ImportError: The class MatplotlibDrawer needs pylatexenc
When I run the following command
qc.draw(output='mpl')
for my circuit qc, I get this error:
...
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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 $L$?
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get statevector from bloch coordinates for one 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 ...
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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 $\lvert 0\rangle \otimes \lvert \psi \rangle$.
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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 ...
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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
$$
F_N(a,b) \cdot r/|r| = G \cdot \...
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Rotation of qubit - Pauli Gates XYZ
I don't understand how to apply a Pauli Gate on a qubit.
Lets say 8 got a qubit with in state:
$$|\psi\rangle = 0.891 |0\rangle+ 0.454i |1\rangle$$
How would I compute e.g. rotating it 90 degrees ...
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Calculate the product state/quantum register back into its tensor product
So let's asume I have a product state/quantum register as a result of a tensor product of two qubits.
Lets take a "hard" product state matrix like:
$$\frac{1}{\sqrt{2}}
\begin{bmatrix}
\...
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How does grid or ring (coupling map topology) affect the depth of the circuit?
Why does different grid maps have different depths, i.e why does a 10x10 grid has more depth than 10x3. Also how does topology affect the depth?
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QRAM and amplitude encoding
I'm still confused about what a QRAM should be.
Is amplitude encoding a form of performing QRAM ? Or are they related in a way ?
What is today's state of the art about QRAM ?
CommunityBot
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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 ...
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How do we achieve mathematically that the probability that Eve learns $x$ is $\cos^{2}\left ( \frac{\pi }{8} \right )$?
I'm trying to understand this problem.
Alice I attempting to send a 2 classical bit message to Bob using 1 qubit such that there are 4 states $\varphi_{00}$ $\varphi_{01}$ $\varphi_{10}$ $\varphi_{11}$...
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Upper bounding the trace distance between a noisy and noiseless quantum state
Consider a quantum state
$$ \rho = \begin{pmatrix}
\rho_{00} & \rho_{01} \\
\rho_{10} & \rho_{11} \\
\end{pmatrix}. $$
Now, consider the effect of the amplitude damping noise $\mathcal{N}$ of ...
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Holevo bound and indistinguishability of non-orthogonal quantum states
I was trying to understand the fact that non-orthogonal quantum states cannot be reliably distinguished and I came across this link.
The explanation finishes with the result that the probability of ...
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circuit for quantum simulation?
What would be the circuit for operation exp(iθZ⊗Z⊗Z⊗X) by only using CNOTs and single-qubit gates. And How we can improve the circuit to implement the operation exp(iφZ⊗Z⊗X⊗Z ).exp(iθZ⊗Z⊗Z⊗X).Are ...
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How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?
Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...
CommunityBot
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When does CNOT entangle?
Let $|\psi_1\rangle$ and $|\psi_2\rangle$ be qubit states such that $\text{CNOT}|\psi_1\rangle \otimes |\psi_2\rangle$ is entangled. I'm interested in if there is a simple condition that this imposes ...
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Expressibility and Entanglement Capability of the Parameterized Quantum Circuits
I am trying to calculate the expressibility and entangling capability of a quantum state resulting from a circuit as defined in reference I.
One of my attempts was to follow reference II which gives ...
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Initialize data qubits in the first step of syndrome measurement
I saw many papers that say that in syndrome measurement of the stabilizer codes, such as surface codes and color codes, firstly, all data qubits are initialized to $|0\rangle$. What is the reason? I ...
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