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Quantum Computing

Questions tagged [quantum-operation]

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For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.

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$\newcommand{\kket}[1]{|#1\rangle\!\rangle}\newcommand{\bbra}[1]{\langle\!\langle #1|}\newcommand{\hilbert}{\mathcal{H}}\newcommand{\ket}[1]{|#1\rangle}$I'm interested in an intrinsic notation ...
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3answers
191views

Why do we only need to account for Pauli X and Z errors for full QEC?The basis of quantum error correction is that we only need to correct for X and Z errors. We can choose Paulis as a basis set for ...
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QEC works on the basis of detecting and subsequently correcting Pauli errors. However, the general physical noise does not need to be a Pauli channel. Randomized Compiling (RC) / Pauli Twirling (PT) ...
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163views

Is there a result guaranteeing that if a CPTP quantum channel is sufficiently far from any unitary channel (in some norm), then, the channel is necessarily entanglement breaking ?Are there simple ...
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TLDR: Circuit Drawer function draws just the second half of the list of Pennylane operations.I am trying to create a “circuit drawer” function that takes in a list of Pennylane operations, and then ...
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I encountered one question when preparing for the exam.(b) Suppose each of the qubits of the state $|\phi^+\rangle_{AB}$ undergoes a decoherence process of the form$$\rho \mapsto e^{-t} \rho + (1 - ...
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Suppose we have an $n$-qubit stabilizer code with the logical state $\rho_L$, which goes through a quantum channel $\mathcal{E}(\rho_L)$. Here, I assume that the quantum channel is arbitrary, for ...
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287views

I am trying to prove the following submultiplicativity property of the diamond norm. Suppose\begin{align*}\mathcal{E}_1 : L(H_1) \to L(H_1') \quad \text{and} \quad \mathcal{E}_2 : L(H_2) \to L(H_2')...
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380views

In quantum maximum likelihood decoding (QMLD), the noise model is assumed to be the Pauli channel (or the depolarizing channel).Is it possible to perform QMLD with other noise models as well? For ...
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I have seen multiple definitions of the depolaring channel on $N$ qubits :$\varepsilon(\rho)=(1-p)\rho + \frac{pI}{2^N}Tr(\rho)$(Depolarizing channel for $n$ qubits: why is there a trace term?)$\...
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$\DeclareMathOperator\PSU{PSU}\DeclareMathOperator\U{U}\DeclareMathOperator\SU{SU}\DeclareMathOperator\O{O}\DeclareMathOperator\SO{SO}\DeclareMathOperator\GL{GL}\DeclareMathOperator\ASL{ASL}\...
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I know that the purity of a density matrix is calculated as the $tr (\rho^2)$.Is there anything equivalent for superoperators? And if there are what are some examples where finding the purity of a ...
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431views

Given a single-qubit state $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$, is it fine to calculate something like:$$\langle\Phi^+|\psi\rangle = \frac{1}{\sqrt{2}}(\alpha\langle0| + \beta\langle1|),$$...
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188views

In the quantum process formalism, we assume that we begin with a product state $$\rho \otimes |e_0\rangle \langle e_0|$$ where $\rho$ is a mixed state in a system of interest and where $|e_0\rangle$ ...
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Consider a Gaussian operator$^{1}$ $M=Ce^{i\sum_{n,m=1}^N a^\dagger_n L_{nm} a_m}\equiv e^{ia^\dagger La}$, with $a_n^\dagger,a_n$ fermionic creation and annihilation operators, $C\in\mathbb{C}$, and $...

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