Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,726
questions
2
votes
1
answer
71
views
Density Matrices for states $|+\rangle$ and state represented by $\rho = \frac{|0\rangle \langle0| + |1\rangle \langle1|}{2}$
As per my understanding, the first one is a "pure state" and represents a system with one qubit having equal probability of being measured as $|0\rangle$ or $|1\rangle$ (standard basis ...
- 1,311
0
votes
0
answers
23
views
How does counting in classical 32-bit systems compare to quantum systems with 32 qubits in superposition?
I'm trying to understand how counting in a classical 32-bit system compares to a 32-qubit quantum system.
In a classical 32-bit system, we can count from 0 to the maximum value (i.e., ) using a CPU ...
1
vote
2
answers
684
views
Find a unitary to prepare state $|0\rangle$ to a specific vector
I am working with Variational Quantum Linear Solver (VQLS) algorithm, where it needs to prepare a control_b circuit.
Given a vector $\bf b$ with $ 2^n $ elements in it I need to find a unitary $U$ ...
- 3,003
4
votes
1
answer
366
views
Why are orthogonal spins $(1,0)$ and $(0,1)$ represented as collinear vectors in the Bloch sphere?
I'm reading the book "Quantum Computing for Everyone" by Chris Bernhardt and I have a question about the following phrase on page 39 (Chapter 3) which says that
As we mentioned in the ...
- 3,003
1
vote
1
answer
43
views
Build a query circuit that set the first bit to 0
This is a question from Chapter 2, 8(c) in Quantum Computing: Lecture notes by Ronald de Wolf.
Suppose we can make queries of the type $|i, b\rangle→ |i, b\oplus x_i\rangle$ to input $x\in\{0, 1\}^N, ...
0
votes
0
answers
51
views
Find inner product or coefficient from a quantum state in quantum circuit and qiskit [closed]
From a 4 qubit circuit, I prepared state $|w \rangle = a|1000\rangle + b|1010\rangle +c|1110\rangle$. Now I need to find 'a' with sign(+/-), that is I want to find $\langle 1000|w\rangle$. How do I ...
- 898
0
votes
1
answer
60
views
Modify a quantum state prepared with HHL [closed]
I can prepare a state $|1\rangle|x\rangle|0\rangle$ using HHL. How do I prepare $|1\rangle|x\rangle|0\rangle+|0\rangle|y\rangle|0\rangle$ or simply $|1\rangle|x\rangle|0\rangle+|0\rangle|0\rangle|0\...
- 13.6k
0
votes
1
answer
54
views
Custom Quantum Gate equivalence to backend basis gate set
Hello I am using Qiskit and I have defined a custom gate which implements the array shown in the image:
This array is unitary and the function R(theta) works by tuning a continious variable into 0 of ...
CommunityBot
- 1
2
votes
0
answers
30
views
Bloch representation of a quantum channel acting on a 2-qubit density-matrix
A previous answer nicely show the relationship between the Pauli transfer matrix (PTM) and the Bloch representation of a quantum channel that acts on single-qubit density matrix.
In short, given a ...
- 268
4
votes
1
answer
189
views
Is the closest diagonal state to a given state always the dephased original state?
This question is about the following optimization problem:
Given some density matrix $\rho\in\mathbb C^{n\times n}$ find the diagonal state which is closest to it in trace norm. More precisely, find
$...
- 3,003
0
votes
1
answer
82
views
IBM quantum composer possible bug?(state amplitudes of quantum circuit)
I have this quantum circuit:
and from the IBM quantum composer I get this state amplitudes:
I wanted to flip the target qubit and keep only its pure state however this is not what I am getting.I am ...
CommunityBot
- 1
21
votes
6
answers
1k
views
Counterexamples in quantum information theory
As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "...
- 3,003
7
votes
1
answer
168
views
Prove that $|(\langle \psi|_{A} \otimes \langle \phi|_{B})|\theta\rangle_{AB}|^{2}<1$ for entangled $|\theta\rangle_{AB}$
I am trying to show that $|\langle \psi|_{A} \otimes \langle \phi|_{B}|\theta\rangle_{AB}|^{2}<1$ given $|\theta\rangle$ is an entangled state, and as such has Schmidt rank $>1$. Decomposing it, ...
- 3,003
4
votes
3
answers
1k
views
Are complex amplitudes really needed?
Qubit amplitudes are defined as complex numbers. But in all tutorials I have recently read, only real numbers are used and everything works. So, if I completely forget the official 'complex' ...
- 3,003
0
votes
0
answers
53
views
Observables vs. bases-right mathematical structure
Throughout my encounter with the mathematics of QM, I got used to the idea that observables are represented as self-adjoint operators in Hilbert spaces. Since self-adjoint operators have a real ...
glS♦
- 26.4k
3
votes
1
answer
121
views
Expectation value of an observable containing a single projector vs Born rule for the projector
Suppose I have a state $|\psi\rangle$ and I want to estimate the probability of obtaining a computational basis state $|x\rangle$. Then by the Born rule:
$$
p(x) = |\langle x|\psi\rangle|^2 = {\rm tr}[...
- 3,003
1
vote
3
answers
172
views
Prove an identity related to the quantum Fourier transform
I'm reading Ronald de Wolf's lecture notes, and in Chapter 4.5 he writes that
$$
\frac{1}{\sqrt N}\sum\limits_{j=0}^{N-1}\prod\limits_{l=1}^{n}e^{2\pi i j_l k / 2^l}|j_1...j_n\rangle =
\bigotimes\...
- 3,003
0
votes
2
answers
263
views
Is the 4x4 matrix $|00\rangle\!\langle00|+|11\rangle\!\langle11|$ of product form?
Can the diagonal matrix $$\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0& 0 \\0&0&0&0 \\ 0&0&0&1 \end{pmatrix}$$ be written as a tensor product $A\otimes B$...
- 3,003
4
votes
2
answers
149
views
Prove ${\rm tr}(\rho^2)={\rm tr}((\rho \otimes \rho')S)$ with $S$ the swap operator
I'm trying to prove $P(\rho)={\rm tr}((\rho \otimes \rho')S)$, where $P(\rho)={\rm tr}(\rho^2)$ is the purity and $S$ is the swap operator. My question is that since ${\rm tr}(AB)={\rm tr}(BA)$, do we ...
- 482
2
votes
4
answers
144
views
How to realize the index shift operation in quantum circuit?
Can we realize the index shift in a quantum circuit as we do in a classic circuit?
$\forall$ $a,b,c \in \{0,1\}$, $\left|abc\right>\mapsto\left|bca\right>$
e.g. $\left|001\right>\mapsto \left|...
- 13.6k
2
votes
1
answer
106
views
What are non-standard ways to describe the distance between states?
I understand that when comparing two arbitrary quantum states, one may use various measures to encapsulate the difference between states such as trace distance, fidelity or relative quantum entropy. I ...
- 2,309
4
votes
1
answer
327
views
Defining a discrete quantum walk on a 3D hypercube
I am trying to implement at a discrete-time quantum walk on a 3D hypercube using cirq.
I have three qubits for the position register: the $|x\rangle$ qubit, $|y\rangle$ qubit and $|z\rangle$ qubit, ...
- 13.6k
0
votes
1
answer
54
views
Does tensor product of mixed states produce a product, correlated, or entangled state? [closed]
I am trying to understand the difference between correlated and entangled states; from what I gather, a correlated state is to a product state what a mixed state is to a pure state — the former is a ...
- 6,226
-1
votes
1
answer
55
views
How to prepare a cluster state $\frac12(|0000\rangle+|0110\rangle+|1001\rangle-|1111\rangle)$ in Qiskit?
Build the circuit in Qiskit, cluster state.
- 24.2k
1
vote
1
answer
18
views
Visualizing the Effect of a Parameterized Gate on a Qubit Using the Bloch Sphere in Qiskit 1.0
I am seeking assistance with visualizing the effect of a parameterized gate on a qubit using the Bloch Sphere representation. I have a preliminary code snippet as follows:
...
- 1,311
3
votes
1
answer
61
views
Can you store $2(2^n -1)$ classical bits of information in $n$ qubits?
I just had a lecture where my professor said that the relation in the title of the post was valid. He even told us that we could for example store 1TB of data, in just 35 qubits. But does this mean ...
- 665
1
vote
1
answer
82
views
Can we find the quantum state using the Bloch vector in the Bloch sphere?
I had a question about qft. When we apply QFT in a circuit, we can display the qubits separately in the bloch sphere with the plot_bloch_multivector function. I realized that the bloch vectors do not ...
2
votes
1
answer
194
views
How to prepare a superposed state?
Given two arbitrary states, $|\psi\rangle\ \text{and}\ |\phi\rangle$ that are possibly unknown to the preparer, is there a way to prepare the superposition $|\psi\rangle+|\phi\rangle$ of them? (If it'...
- 60.8k
-1
votes
1
answer
88
views
In Qiskit, no state vector after measure and reset
The code below doesn't work. I am looking for a workaround.
OK, I can save the state vector as numpy array, recreate the whole circuit and initialize it thanks to this array. It works, but any simpler ...
CommunityBot
- 1
3
votes
2
answers
130
views
Effecient creation of a sudoku/permutatation state
I have $n^2$ qubits indexed $|x_{i,j}\rangle\, i,j \in \{0,...,n-1\} $ and want to create the state $|\psi\rangle = \frac{1}{\sqrt{n!}}\sum _{x\in S} |x\rangle$ where $x\in S \iff \forall i\, \sum_{j}...
- 11.5k
1
vote
0
answers
52
views
How to mathematically determine the final state of a system after some Gaussian microwave pulse?
I'm trying to figure out the final state of a system after some arbitrary microwave pulse; let's say some physical Gaussian pulse with a duration $d$, amp $a$ and width $\sigma$. I’m looking for how ...
- 3,003
9
votes
3
answers
1k
views
Are quantum states like the W, Bell, GHZ, and Dicke state actually used in quantum computing research?
I recently started studying quantum computing and learned about several well-known quantum states such as the W state, GHZ state, and Dicke state. I noticed that there are also some questions here on ...
- 3,003
0
votes
0
answers
63
views
Is there a general parametric Bloch sphere transformation matrix corresponding to qutrit unitaries?
I've been looking into the structure of the Bloch sphere for qudits, and I am wondering if there is a transformation matrix (or rotation matrix) formula corresponding to high-dimensional quantum ...
- 3,003
1
vote
1
answer
47
views
Is entanglement distillation possible between states of different fidelities?
I am looking for an algorithm that allows me to perform distillation from a pair of W-states of different fidelities. All the algorithms I found so far are focused on distilling identical states, ...
- 40.8k
6
votes
5
answers
134
views
Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?
There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum ...
- 476
3
votes
2
answers
382
views
How to represent a qubyte?
I was not able to locate any visuals online. The visual I have in my head is a cube w/ bloch spheres as the eight vertices.
I am also curious about a matrix representation, although I am not sure ...
- 1
0
votes
0
answers
20
views
Encoding electron-phonon interactions in a quantum computer
I am trying to encode superposition of coherent-like states, that represent electron-phonon couplings on a chain, in a quantum computer.
Specifically, I would like to (approximately) generate states ...
- 221
0
votes
2
answers
389
views
How to perform a basis change on a $2\times 2$ density operator?
I have an ensemble described by following density operator:
$$
P=\frac38 |+\rangle\langle+| + \frac58 |-\rangle\langle-|.
$$
I am trying to write this operator in the computational basis.
I know that ...
- 3,003
1
vote
1
answer
150
views
Are the preparations of a logical state in a surface code random and do we need to update the stabilizers after preparation?
Reading Fowler et al, there is something in regards to the intialisation of the surface code in a logical state (ie a state of a logical operator) that is confusing me.
I can think of two examples ...
- 24.2k
1
vote
0
answers
80
views
State tomography in Qiskit on a subset of qubits of real QPU
Could anyone please explain how should I carry out a state tomography on a real device in Qiskit (version 0.43.2)?
I have access to devices with 127 qubits, but I want to perform a simulation using ...
1
vote
1
answer
110
views
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
- 1
3
votes
1
answer
138
views
Clarification defining/finding the relative phase of a qubit
Let the vector $ |V\rangle = r_0 e^{i\theta_0} |0\rangle + r_1 e^{i\theta_1} |1\rangle $ correspond to the state of a qubit where $r_0,r_1,\theta_0,\theta_1 \in \mathbb{R}$.
According to p. 22 of ...
- 3,003
1
vote
1
answer
50
views
Transformation between the canonical basis and the degraded Bell basis
I would like to know if the following results of mine made are correct.
My goal is to express the canonical basis $ \{ |00\rangle , |01\rangle , |10\rangle , |11\rangle \} $ using a degraded Bell ...
- 193
3
votes
1
answer
203
views
What's the intuition behind the definition of maximally entangled states?
I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
glS♦
- 26.4k
6
votes
1
answer
3k
views
What is the difference between "maximally entangled" and "entangled" states?
when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
glS♦
- 26.4k
0
votes
1
answer
37
views
Does an MCZ gate flip the phase of the target qubit if it is in the 0 state?
I am trying to flip the phase of the solution state in an oracle for Grover's algorithm. I am wondering if an MCZ gate will flip the target qubit of |0> if the control qubits are in their correct ...
- 5,849
3
votes
1
answer
223
views
Why does Schur's lemma imply that $\int \sigma^{\otimes n}_{HK} d(\sigma)$ must be a multiple of the identity on the symmetric subspace?
I am trying to understand Lemma 2 in this paper.
Consider a state $\tau_{H^n}=\int \sigma^{\otimes n}_{H} \mu(\sigma)$ where $\mu(\sigma)$ is the measure on the space of density operators on a single ...
glS♦
- 26.4k
1
vote
3
answers
68
views
GHZ Definition - Does it all have to be $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\rangle$
Trying to dig a bit into GHZ States and the proper definition.
Trying to determine if GHZ state is strictly $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\...
- 116
7
votes
0
answers
188
views
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
...
- 3,003
0
votes
1
answer
61
views
Where am I going wrong in my understanding of qubit associativity?
I am studying the basics of quantum computing math and am confused about qubit associativity. As I understand it, multiple qubits are represented as the tensor product of the qubits and the tensor ...
- 3,003