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# Questions tagged [quantum-state]

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

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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 ...
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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 ...
1 vote
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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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### 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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### 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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### 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 vote
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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 vote
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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. ...
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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 ...
1 vote
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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)...
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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 with NOT. Second, I want ...
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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 ...
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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.
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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)
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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 ...
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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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### 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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### 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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### 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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### Truncating the bond dimension of an MPS -- how good is the approximation?

$\newcommand{\complex}{\mathbb{C}}\newcommand{\ket}{|#1\rangle}$ 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 ...
1 vote
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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, ...
1 vote
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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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### 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 ...
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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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### 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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### 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 ...
1 vote
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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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### 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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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 ...