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}}.
Questions tagged [pauli-gates]
232 questions
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Fast way to check if two state vectors are equivalent up to Pauli operations
I'm looking for fast code, or a fast algorithm, for checking if a given state vector $A$ can be transformed into another state vector $B$ using only the Pauli operations $X$, $Y$, $Z$.
The naive strategy is to simply iterate through all $4^n$ ways…
Craig Gidney
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Can there be multiple energy eigenstates corresponding to the same eigenvalue of a Hamiltonian (Pauli-X)?
all. I am a high-school student who has recently familiarized himself with linear algebra and is looking to understand quantum computing. So, I bought the classic textbook "Quantum Computation and Quantum Information" by Nielsen and Chuang.
In the…
QFTUNIverse
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Why do we have only 3 Pauli gates X, Y and Z
This question is out of curiosity thus might not be of much importance.
We have Pauli X, Y, Z gate which rotate the phase by π along X, Y and Z basis. Just wondering why not do we have these 3 gates why not more since there are vectors with more…
Vinay Sharma
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What is the procedure of finding z-y decomposition of unitary matrices?
The title explains it all. Suppose one needs to find z-y decomposition of unitary matrix H or T. What is the step by step process to find it?
user27286
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Similarity Transformations on Pauli Operators in 2-qubit states (eq. 11 - Farhi's QNN Paper)
Again, I am new to quantum computing and have a CS background, so apologies if this seems like an obvious question or if I seem unclear. $\newcommand{\braket}[1]{\langle #1 \rangle}\newcommand{\bra}[1]{\langle #1 |}\newcommand{\ket}[1]{| #1…
Skyris
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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:
$$
\langle O\rangle =\sum_i^{N_p}\langle P_i\rangle,
$$
where each $P_i$ is a…
Lior
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Calculate $\sqrt[4]{X}$ for the Pauli $X$ gate
I was trying to build a $cccx$ gate. According to this paper by Berenco et al., it requires a $\sqrt[4]{X}$ gate. Furthermore, I found another paper by Muradian and Frias with this formula:
$$\sqrt A=\frac{1}{\sqrt{2i}}(iI+A).$$
From this I…
Syed Emad Uddin
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