# Questions tagged [pauli-gates]

For questions about Pauli matrices in general or Pauli gates in particular, as relevant to quantum computing and/or quantum information theory. The Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. The three Pauli gates are: Pauli-X gate, Pauli-Y gate & Pauli-Z gate. X = {{0,1},{1,0}}; Y = {{0,-i},{i,0}}; Z = {{1,0},{0,-1}}.

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### Dimension reduction to subsystem in Pauli-Liouville basis: How to implement partial trace of Pauli-Transfer Matrices?

I have a complementary question to my previous (thankfully answered, but I can't verify for larger systems) question: Multi-qubit quantum channels in Pauli-Liouville basis: Tensor product of Pauli-...
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### scaling of error of sum of Pauli strings with number of shots

I have a question which I suppose is quite basic. Let's say I want to measure the average of an obersvable which is the sum of non-commuting Pauli strings on $N_q$ qubits:  \langle O\rangle =\sum_i^{...
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• 597
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### How is Quantum Computing expressed in the language of abstract algebra?

I've lately been taking further coursework in abstract algebra, and it has struck me as fairly reminiscent of quantum computing. Of course, Pauli matrices, etc. have relevant roots within abstract ...
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### Expectation value of a given observable computed manually using qiskit.Sampler is different as with qiskit.Estimator

I am trying to calculate the expectation value of a given observable for a certain state $\psi$ using qiskit primitives Sampler (using Sampler requires some further calculations) and Estimator. I ...
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### Physical description of trace of ancilla state yields a depolarising channel

Let's start with $Tr_{\Omega}[|0,\Omega_{0}\rangle\langle0,\Omega_{0}|U^{\dagger}] = \sum_{\alpha}E_{\alpha}|0\rangle\langle0|E_{\alpha}^{\dagger}$ where $U$ be a unitary operator. The trace operator ...
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### Coupling map in QISKIT transpile

I have a 3-qubit unitary represented by a circuit with the following dictionary: {'cx': 30, 'h': 22, 'rz': 15, 's': 4, 'sdg': 4}. I want to use this circuit on IBM ...
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### How to interpret the encoding circuit for the 5-qubit QECC

I have a question on circuit which constitutes the sydnrome measurement for the 5-qubit error correcting code. If I focus on just a portion of the circuit: Reference for image. The full circuit can ...
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### How can I implement a Hamiltonian which is sum of tensored pauli operators on qiskit?

I am working with a Tight Binding Hamiltonian with N sites and one orbital at each site in a closed chain. I have converted the fermionic expression to a spin expression using Jordan Wigner ...
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### The Output of Transversal Bell Measurement in Knill's Method of Fault-Tolerant Error Correction (FTEC)

On page 26 of arXiv:quant-ph/0504218, it is written that in Knill's method of fault-tolerant error correction (FTEC), the output of the transversal bell measurement becomes \$(P_m \otimes I) | \Phi_0 \...
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