# 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 $H_{\Omega}$...
1 vote
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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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### 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 ...
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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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### What it is represent if my density_matrix is mixed matrix and it's a diagonal matrix，Can i get the state vector from it?

i have a pqc: ...
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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 ?
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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 ...