Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,488
questions
0
votes
2
answers
109
views
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)
...
5
votes
2
answers
306
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 ...
- 135
2
votes
1
answer
55
views
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 ...
- 505
2
votes
1
answer
48
views
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 ...
- 2,359
0
votes
0
answers
44
views
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 ...
- 41
2
votes
2
answers
498
views
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 \\
...
- 249
2
votes
0
answers
47
views
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$ ...
- 41
2
votes
1
answer
57
views
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 ...
- 332
0
votes
0
answers
52
views
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 ...
- 41
2
votes
0
answers
44
views
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}$...
- 41
1
vote
0
answers
72
views
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 ...
- 199
1
vote
3
answers
201
views
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.
- 63
2
votes
1
answer
103
views
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,...
- 613
2
votes
0
answers
80
views
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 ...
- 21
0
votes
1
answer
66
views
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 ...
- 133
0
votes
1
answer
76
views
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 ...
- 1
1
vote
1
answer
122
views
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 ...
- 177
0
votes
1
answer
60
views
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 ...
- 173
0
votes
1
answer
40
views
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 ...
- 103
3
votes
2
answers
195
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 ...
- 133
0
votes
1
answer
30
views
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 ...
- 569
1
vote
1
answer
78
views
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 ...
- 271
0
votes
0
answers
105
views
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 ...
0
votes
0
answers
30
views
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}...
- 219
1
vote
0
answers
91
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 ...
0
votes
1
answer
17
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 $...
- 237
3
votes
3
answers
111
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
...
- 55
-1
votes
2
answers
70
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 \...
- 129
3
votes
2
answers
108
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 ...
- 31
1
vote
1
answer
96
views
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 ...
- 13
0
votes
0
answers
47
views
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=...
1
vote
0
answers
28
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 ...
- 31
2
votes
1
answer
122
views
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{...
- 379
1
vote
1
answer
86
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 ...
- 469
2
votes
2
answers
89
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 $L$?
- 31
9
votes
2
answers
360
views
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 $\lvert 0\rangle \otimes \lvert \psi \rangle$.
...
- 193
2
votes
1
answer
72
views
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 ...
- 161
1
vote
1
answer
124
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:
...
- 209
0
votes
0
answers
48
views
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
$$
F_N(a,b) \cdot r/|r| = G \cdot \...
1
vote
1
answer
40
views
Calculate the product state/quantum register back into its tensor product
So let's asume I have a product state/quantum register as a result of a tensor product of two qubits.
Lets take a "hard" product state matrix like:
$$\frac{1}{\sqrt{2}}
\begin{bmatrix}
\...
1
vote
2
answers
112
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 ...
- 275
2
votes
1
answer
170
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 ...
1
vote
1
answer
38
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 ...
2
votes
1
answer
72
views
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 ...
- 1,251
4
votes
0
answers
111
views
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 ...
- 53
0
votes
2
answers
112
views
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 ...
- 31
3
votes
3
answers
491
views
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 ...
- 429
1
vote
1
answer
141
views
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 ...
- 35
4
votes
0
answers
52
views
Is circuit cutting equivalent in anyway to quantum teleportation?
I've been introduced recently to circuit cutting, and after seeing the 4 orthogonal measurements with their 8 corresponding initializations but no initial transfer of classical info, the first thing ...
0
votes
0
answers
42
views
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 ...
- 51