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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Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not
In Exercise 10.40 of Nielsen and Chunang's textbook, the reader is supposed to construct an inductive proof of Theorem 10.6 that any Clifford gate can be made of Hadamard, phase and c-not. There it is ...
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What does it mean that a qubit is a triple $(H,X,Z)$ with $H$ Hilbert space and $X,Z$ Pauli operators?
In this paper, http://users.cms.caltech.edu/~vidick/teaching/fsmp/fsmp.pdf, it gives the definition of a qubit as follows:
A qubit is a triple $(H, X, Z)$ consisting of a separable Hilbert space H and
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Is there an efficient algorithm for decomposing an arbitrary Hamiltonian into Pauli strings?
Basically the title. If I have a $2^N\times 2^N$ Hamiltonian $H$ of random numbers (we can take the Hamiltonian as normalized if we want) and $N$ is an integer, is there an efficient way of writing
$$
...
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What is the correct name of this quantum gate? Possibly state control gate
Let $\vec v \in \mathbb{C}^2 $ be the following quantum state:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
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How does Spin Measurement correspond to quantum NOT gate?
Newbie in quantum computing (and stack overflow) here. I am confused regarding the relation between spin measurement in quantum mechanics and the quantum NOT gate.
I have a Bloch sphere picture of a ...
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Efficient quantum algorithms to decompose Hessian matrices into sums of unitaries
Are there efficient quantum algorithms that given a d-sparse hessian $H \in \mathbb{C}^{N \times N}$ decompose it into a sum of unitaries (e.g. Pauli matrices)?
$$H = \sum_i^q a_i U_i$$
If an ...
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Is decomposing high-dimensional states in terms of Pauli matrices impossible?
I've been trying to decompose a 3x3 density matrix with 3-dimensional Pauli matrices but it doesn't work for all matrices.
For example, the density matrix of the state $|0\rangle + |1\rangle + |2\...
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Measurement on a specific basis and proof of circuit output
I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
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Is it possible to receive the optimal commuting partitioning of pauli strings (MIN-COMMUTING-PARTITION)
In this paper the authors describe that the MIN-COMMUTING-PARTITION problem is NP-hard. This problem is about finding sets of Pauli strings (of length $n$) in which the strings mutually commute - the ...
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Conjugating pairs of Paulis to each other with a non-entangling Clifford
This a follow-up question to Conjugating pairs of Paulis to each other with a Clifford
We call a Clifford gate local if it is a tensor product of single qubit Clifford gates.
We call a Clifford gate ...
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what is Pauli twirling approximation?
In this video, Artur Ekert shows that for a single qubit, 4 Kraus operators can be chosen such that the action on state $\rho$ is given as $\rho \rightarrow \sum_m p_m A_m \rho A_m^\dagger$. We can ...
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Expectation value of Pauli strings for VQE
I am studying VQE and have boiled it down to a matter of determining the expectation value of Pauli strings:
$$\langle H \rangle = \sum_i \alpha_i \langle\psi|\hat{P_i}|\psi\rangle.$$
I have been ...
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Understanding the EPR argument with a simple description using Pauli matrices
Can someone explain the EPR argument with a simple description using Pauli matrices?
Two non-commuting physical quantity are being discussed philosophically whether there is an element of reality ...
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Changing the Basis
I am attempting to use a VQE algorithm to find the ground state of a deuterium nucleus by applying a constructed hamiltonian to an ansatz state with one parameter created by a circuit. While I am ...
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Phase estimation of the Pauli-Y matrix
I'm trying to use the phase estimation algorithm to extract the eigen value for both eigen vectors of the Pauli-Y matrix using the ibm quantum experiance.
So far I have this for the possitive state |+&...
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Uncorrectable error due to error on ancilla qubit
Consider a controlled-NOT (CX) gate between the two qubits, implemented with an interaction of the form
$
\widehat{H}_{\mathrm{CX}}=V\left[\left(\frac{\hat{I}_1+\widehat{Z}_1}{2}\right) \otimes \hat{I}...
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Pauli decomposed Hamiltonian as Diagonal U gate
While trying to implement a quantum circuit, I had to apply Hadamard gates to all qubits to achieve equal superposition. Done.
The next operation is decomposing the Hamiltonian into a sum of tensor ...
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Equivalence check between rotational gates and Pauli gates
My question is highly related to this one.
I am trying to understand the relationship between rotational gates $R_P(\theta)$, where $P \in \{X,Y,Z\}$.
As stated here, $\exp(iPx)=\cos(x)I+i\sin(x)P$. ...
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Does anybody know what a low-degree Markov field is?
In the paper Fast Estimation of Sparse Quantum Noise I saw the following description:
quantum devices approaching the fault-tolerant regime will have very
few significant errors (and therefore are ...
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Convert Coherent Noise to Clifford Errors with Probability on Surface Codes
Following my question about the equivalence of coherent and no coherent error, in surface codes.
Now I understand, it is not equivalent. I tried to read some articles about it, and I couldn't find a ...
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