Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,383
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Can we determine the inner product using a single pair of states?
I got a review from a journal that
The problem with their proposal is that they wrongly assume that the
inner product between a pair of quantum states can be determined
exactly even when one is given ...
- 289
2
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1
answer
234
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Pennylane: take qml.state of one function and use it as the initialization for another
In Pennylane, I created a function to set the initial parameters of my qubit, and then called qml.state() to return the output. I now want to feed this initialization into another circuit, but I'm not ...
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0
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43
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Calculate the single qubit unitary (U) created by the sequence of gates: U=XZH
I don't know how are we going to proof this by using tensor product of XZH
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1
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80
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When do qubits get entangled?
I was just curious; when do the qubits get entangled? Do the qubits get entangled right after initialization or do they get entangled when we apply Hadamard Gates to the qubits?
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How to perform a basis change on a 2x2 density operator?
I have an ensemble described by following density operator:
$$
P=3/8 |+\rangle\langle+| + 5/8 |-\rangle\langle-|
$$
I am trying to write this operator in $\{|0\rangle, |1\rangle\}$ basis.
I know that ...
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1
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165
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Prove that uniformly random states have moments ${\bf E}_\psi|\langle x|\psi\rangle|^{2t}\sim1/\binom d t$
Im looking for the moments of Haar random states. Is it true that
$\textbf{E}_{\psi\sim \text{Haar}}|\langle x| \psi\rangle|^{2t}\sim \frac{1}{\binom{d}{t}}?$ How does one prove this?
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48
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Move the phase in Controlled-Controlled-Phased-Gate
I wonder how we can move the phase in CCZ gate onto different diagonal element
$$
\left(\begin{array}{ccc}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & ...
3
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1
answer
69
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Symbolic library for qubit states
Is there any symbolic package (in Python or Julia, for example) that can represent qubit state coefficients symbolically?
For example, let's assume we have an initial two-qubit state:
$$ | \psi \...
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3
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97
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Can you construct a quantum circuit where all qubits are initially in a superposition, but there is still entanglement?
The most basic example of entanglement is when we have 2 qubits, where q0 is in the |+> state and connects to q1 (which is in the |0> state) with a cnot gate:
The state is entangled, as the ...
1
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1
answer
47
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How $X\otimes X^{1/2}$ propagates through $CZ$
I am trying to find out how the $X\otimes X^{1/2}$ operator propagates through a $CZ$ one.
Below a circuit example.
- 1,300
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1
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34
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Store/load superposition state of a qubit into/from classical register
I know this question looks ridiculous.
But I simply want to know if possible to store/load a superposition state into classical register from qubit. Specifically two bit of classical register.
...
2
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0
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94
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Measure or Amplify the least probable state
Qubits can be represented by a state vector $\psi \in \mathbb{C}^{2^N}$, where $N$ is the number of qubits.
The higher $| \psi_i |$ is, for any index $i$, the more likely it is to be measured. But is ...
- 383
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1
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58
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Qubit reset using Grover iteration
Suppose I’m building a long circuit and I need to reuse a qubit from a previous step but I don’t want to use the reset operation (or I’m not using an IBM computer so I don’t even have the reset option)...
- 21
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1
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122
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How to copy value from classical register to quantum register?
I have 1-qubit of quantum register and 2-bit of classical register.
I have this simple algorithm:
First, I'm doing simple process for q[0] with NOT.
Second, I want ...
2
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4
answers
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Why do computer scientists care about the phase of qubits?
When I design some classical register, flip-flop, binary counter, small byte of RAM, etc from scratch with classical logic gate, I never deal with such binary direction because classical bit doesn't ...
0
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2
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63
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How $X$ noise propagates through controlled-$S$ gate
I am struggling to find how an $X$ noise propagates through a controlled-$S$ gate.
Here`s the circuit.
- 1,300
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1
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How to calculate the meauring probabilities of quantum states $\vert 0\rangle$ and $\vert 1 \rangle$ in $R_x$ gate?
In the below code snippet, what is the probability of measuring $|1\rangle$?
qc = QuantumCircuit(1)
qc.rx(3*math.pi/4, 0)
2
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2
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If measurement collapses the information and we lose information, what's the point of using a qubit?
It's a basic question, I'm new to the domain and still studying qubit.
To my knowledge, One of the most important advantages of a qubit over a classical bit is that it can store more information than ...
0
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1
answer
42
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Cannot derive probability graph for Hadamard gate given in Qiskit textbook
I am reading the Qiskit textbook(beta) and they have explained Hadamard gate using an amplitude tree. To show how two H-gates on a qubit give the output as 0 everytime they said to consider that it ...
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1
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268
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Prove that the trace distance is upper-bounded by the Hilbert-Schmidt distance
In (Haah et al. 2015), in the third page, second column, the authors use the following result: given a pair of states $\rho,\sigma$, we have
$$
\|\rho-\sigma\|_1 \le 2\sqrt{\min(\operatorname{rank}(\...
glS♦
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251
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About swap gate [closed]
As I was reading Qiskit textbook and there is this problem ... How can I swap a $|+\rangle$ to a $|-\rangle$
Qiskit textbook --> Basic Circuit Identities
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61
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Expectation values of non-local operators in Qiskit
Is there a convenient way in Qiskit to calculate the expectation value for a non-local operator, i.e. I would like to calculate:
$$ \langle \Psi|O|\Psi \rangle $$
More precisely, I would like to ...
- 143
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1
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132
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State tomography with Pauli basis measurements for a high number of qubits
My end goal is to recover the quantum state in its computational basis or reduced density matrix of a high number qubit circuit in a real QPU. Taking into account that the number of qubits will be ...
1
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1
answer
67
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Is there an alternative algorithm to extract a probability of states of qubit after measuring?
Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below.
The ...
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0
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134
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Entangling attack on BB84 protocol
I am trying to solve the exercise 5.3 from the book "A Gentle Introduction to Quantum Computing". The exercise reads as follows:
Suppose Eve attacks the BB84 quantum key distribution of ...
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0
answers
40
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Quantum measurement on Bloch Sphere
I'm reading the paper "Data re-uploading for a universal quantum classifier".
This paper proposes the classification process as follows
$x_i $ with different rotation angle $\theta_i$
...
- 101
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0
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27
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How to read data from multiple qubits and feed it to a MLP
Being new in the field of quantum computing, I tried with the implementation of "https://qiskit.org/textbook/ch-machine-learning/machine-learning-qiskit-pytorch.html" using a single qubit. ...
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338
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Why are orthogonal quantum states represented as collinear in the Bloch sphere?
We know that the angle between two orthogonal qubit states is 90 degrees. Why then, when we use the Bloch sphere, the angle becomes 180 degrees?
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0
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Construct the unitaries U by decomposition in TSP Qiskit? [duplicate]
I'm stuck in here and really don't understand this stuff. In order to construct the unitary matrices for Quantum Phase Estimation, Qiskit decomposes the diagonal unitary matrices U(j) by tensor ...
0
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1
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110
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Why is Dirac notation used for quantum states?
I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ ...
- 123
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1
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67
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How simulation of noisy quantum circuits is done in Qiskit using the statevector method
While performing VQE calculations of medium-sized molecules like H2O, using Qiskit AerSimulator with noise, I noticed that even for a large number of shots, the speed of simulation using statevector ...
- 218
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93
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Decomposing a projector in the computational basis in terms of Pauli matrices
I have a $x \in \mathbb{N}$, and I would like to decompose it in terms of the Pauli matrices $\sigma_x, \sigma_y, \sigma_z$ and the identity. My first steps are as follows:
$$
\begin{align}
|x \...
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2
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228
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How do I draw a multi control cz gate or do I have to make my own gate?
I want to build a diffuser and an oracle so that's why I wanted a multi control cz gate but I looked everywhere I didn't get any
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1
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224
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How to represent a statevector in Dirac notation form using Qiskit?
I am learning from qiskit textbook, and I was wondering how may I get a statevector of the following form:
$$ \frac{\sqrt{2}}{2}|00\rangle + \frac{\sqrt{2}}{2}|10\rangle $$
If I run code for this in ...
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2
answers
95
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Preparing a superposition state modulo $k$
Consider being given the description of a function $f: \{0, 1\}^n \rightarrow \{0, 1\}^m$ and the binary representation of an integer $k$. Is the state
\begin{equation}
|\psi_{f, k}\rangle = \frac{1}{\...
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1
answer
97
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Truncating the bond dimension of an MPS -- how good is the approximation?
$\newcommand{\complex}{\mathbb{C}}\newcommand{\ket}[1]{|#1\rangle}$ Let $\ket{\psi}\in(\complex^d)^{\otimes n}$ be a pure quantum state. It is well-known that $\ket{\psi}$ is a matrix product state ...
- 183
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1
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42
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Formal measurement of the probability of an outcome of a Qubit in the hadamard base
I am fairly new to Quantum Computing and have a question which might be trivial for all of you, but I am really struggling with it.
From Quantum Computation and Quantum Information I have learned, ...
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1
answer
109
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How to rewrite the quantum state to qubits?
I have a following state (indexing everything from 0 here)
$$
| \psi \rangle = \frac{1}{\sqrt{2}} \left( | \uparrow_0 \downarrow_1 \rangle - | \downarrow_0 \uparrow_1 \rangle \right)
$$
and I need to ...
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4
votes
1
answer
109
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Is the post-measurement state always pure after a partial measurement?
Imagine I have two potentially entangled qudits and measure the first one using some Hermitian operator $M$ that has only one eigenstate per eigenvalue and get some outcome $m$. Can I know for sure ...
- 43
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1
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71
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Barren plateaus in multi-qubit system
I'm looking on pennylane's tutorial
https://pennylane.ai/qml/demos/tutorial_barren_plateaus.html
In this link, to illustrate barren plateaus, author used example circuit and barren plateau plots. ...
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Does a fidelity of $\mathcal{F}(U_1|0\rangle, U_2|0\rangle)=1$ imply that $U_1=U_2$?
I'm now studying quantum ML and now studying about fidelity ($\mathcal{F}$).
To my knowledge, fidelity means the distance between two quantum states, $\textit{i.e.,}$ if $\mathcal{F} ==1$, then the ...
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2
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140
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Method and Meaning of Quantum Encoding in Quantum Machine Learning
I'm now studying quantum machine learning. While studying papers about quantum machine learning, I have a question about quantum embedding.
To my knowledge, some general embedding algorithms, such as ...
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2
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132
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What does the phase $\phi_1$ in a state $|\psi\rangle=a_1|0\rangle+a_2|1\rangle$ with $a_j=r_j e^{i\phi_j}$ say about state $|1\rangle$?
I'm a beginner in quantum computing and this question has been bugging me for quite some time. I have seen in various articles that a qubit is a device whose state can be represented by a unit vector ...
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1
answer
58
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How can you extract all the state probabilities in e.g. Grover's search?
In the Qiskit tutorial for e.g. Grover's algortihm, there is a 3-qubit implementation on a real quantum computer
https://qiskit.org/textbook/ch-algorithms/grover.html#3.1.2-Experiment-with-Real-...
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4
votes
2
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253
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Creating a uniform superposition of a subset of basis states
Assume we have an n qubit system and $K \subset \{1,...,2^n\}, K \neq \emptyset $
I want to describe a circuit that takes the input $|0\rangle....|0\rangle$ to the state $|\psi\rangle = \frac{1}{\sqrt{...
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1
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139
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Factoring some qubits with Kronecker product
I have this quantum state:
$$|\phi \rangle =\frac{1}{4\sqrt{2}}|000\rangle +\frac{3-\sqrt{5}i}{8}|001\rangle +\frac{1}{4\sqrt{2}}|010\rangle +\frac{3-\sqrt{5}i}{8}|011\rangle \\+\frac{1}{4\sqrt{2}}|...
- 27
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votes
3
answers
263
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CNOT entangling a third qubit and how measurement impacts entanglement
I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better.
About entanglement:
I know that the circuit below will entangle the two qubits:
...
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0
answers
43
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A path towards building quantum Computing graduation project for undergraduates
I need help. I'm a computer science student with a Data science major. I have a final graduation project this year. With that, I want to create a project in the Quantum computing field. I'm already ...
0
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0
answers
12
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How we can switch the digital multi-qubit gates to analog multi-qubit blocks?
What is the difference between the digital and Analog Quantum gate? and the multi-qubit gates involved in a VQE ansatz can be switched to analog multi-qubit blocks. so How we can switch the digital ...
0
votes
1
answer
156
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What is the rank of the pure state?
Consider pure or nearly pure quantum state, is it usually low-rank? Can you give a example of a concrete state and its rank?
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