# Questions tagged [pauli-group]

Questions about or related to the Pauli group.

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### Can an $n$-qubit observable be constructed from single-qubit Pauli X and Z observables? [duplicate]

Any $2\times2$ matrix can be expressed as the sum and product of the identity, Pauli $X$ and Pauli $Z$ matrices. This is often used to express a singe-qubit state using just Pauli matrices. One can ...
1 vote
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### Higher spin Clifford gates

We're familiar with Clifford gates for qubits, which have attracted a lot of attention and research effort. Clifford circuits normalize Pauli strings, i.e., under conjugation, Clifford circuits map ...
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### Complexity of Variational Quantum Eigensolvers

I am doing research surrounding VQE and am a bit confused about the complexity and its comparison to classical systems. My brief research has yielded me that classical eigenvalue solving is $O(n^3)$. ...
1 vote
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### Calculating Nested Commutator using a program

The $\tilde\alpha_{\text{comm}}$ mentioned in Theory of Trotter Error paper is calculated via the nested commutators. For a Hamiltonian $H = \sum_\gamma H_\gamma$, the formula for pth order is as ...
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### Under what conditions are two sets of Pauli operators Clifford-equivalent?

Suppose I have two set of $N$-qubit Pauli operators $\mathcal{S} = \{P_1,\ldots,P_K\}$ and $\mathcal{T} = \{Q_1,\ldots,Q_K\}$. In this context, a Pauli operator is a Hermitian element of the Pauli ...
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### What unitary commutes with all local Pauli operators?

I was thinking about this problem of identifying a set of unitary operations (other than the identity operation) that commute with local pauli $\sigma_X$ and $\sigma_Z$ matrices, i.e. find $U$ such ...
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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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### Simulating stabilizer groups

Can any existing software be used (either directly or with a bit of persuading) to work with general stabilizer groups? From what I can see, tableau-based options like Stim and Qiskit can be used to ...
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1 vote