# 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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### In Variational Quantum Eigensolvers, what does “grouping Pauli operators into tensor products requiring the same post-rotations” mean?

In this paper (nature version), the authors state We group the Pauli operators into tensor product basis sets that require the same post-rotations. As a result, they have the table S2 in the suppl. ...
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### CNOT expressed with CZ and H gates by taking into account HZH =X

From this link: Where equation 1 is: I can probably brute-force this by explicitly calculating this quantum circuit's effective 4x4 matrix and seeing that its equivalent to this teleportation ...
28 views

### Principal square root of Pauli Y gate in Qiskit?

I've seen a similar question asked (How do I compute the square root of the $Y$ gate?) but I'm trying to understand how I can use the gates $Y^{\frac{1}{2}}$ or $Y^{\frac{1}{4}}$ in Qiskit in terms of ...
68 views

### controlled-Z rotation gates in symmetrical fashion

I was going through the qiskit textbook and in this chapter, i came across a statement under the topic "Kickback with the T-gate" related to the Controlled-Z gate that "the controlled-...
51 views

### 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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### Is there a function in Qiskit to measure tensor products of Pauli operators?

Is there a function in Qiskit similar to this function in Q# which measures strings of Pauli operators applied to different qubits?
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### Can you take infinitely many square roots of Pauli-X?

I am trying to find the cost for a n-bit Toffoli gate based on the recurrent circuit presented on Barenco's Work in Lemma 7.5 (Elementary gates for quantum computation) The construction requires that ...
67 views

### Why do we transform a Boolean variable into a a Pauli Z matrix

Under Qiskit QAOA's tutorial (https://qiskit.org/textbook/ch-applications/qaoa.html), the authors specify that a cost function $C(x)$ representing the optimization objective of a Binary Combinatorial ...
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### VQE: Can I build a non-hermitian Hamiltonian with just Pauli matrices?

From the VQE paper they claim that a Hamiltonian can be expressed as a polynomial series of pauli operators (equation 1). While coding up VQE from scratch I made a function which would allow me to ...
18 views

### Iterative qubit coupled cluster (iQCC) ansatz (Efficient screening procedure)

The paper Iterative Qubit Coupled Cluster approach with efficient screening of generators describes a new screening procedure for generators of the QCC ansatz. The paper states: 'In the absence of ...
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### Confusion about the state of a system after a measurement

I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $|\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle$. From my understanding, if one ...
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### How to build a circuit for simulation of a simple Hamiltonian?

Consider very simple Hamiltonian $\mathcal{H} = Z = \begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$. It has eigenvalues 1 and -1 with coresponding eigenstates $|0\rangle$ and $|1\rangle$, ...
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### Cannot interpret transformations on the bloch sphere as matrix multiplications

I understand that X,Y and Z gates are rotations around the axes with the respective letters, but I cannot understand how can Y gate multiply the amplitude of 0 with unreal number and have it landing ...
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### What kind of transformation does the Y-gate do on the bloch sphere?

I'm going through "Quantum Computation & Quantum Information" by Michael A. Nielsen and Isaac L. Chuang, and as a high school student with no previous knowledge, I cannot understand some things ...
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### Effect of Pauli X gate on minus state using bloch sphere

As I understood, the X gate flips the state around : $X(|0\rangle) = |1\rangle$. It can also be visualized with a $\pi$ rotation around the $x$ axis in the Bloch sphere. I have no problem with that. ...
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### Example of Hamiltonian decomposition into Pauli matrices [closed]

I need to see an example of how Hamiltonian, i.e. any Hermitian matrix, can be decomposed into a linear combination of Pauli matrices. Please show me how this is written in Python. What I have tried ...
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### Why can I apply $HS^\dagger$ and then measure in the computational basis to measure $Y$?

I come from a CS background I was reading Neven and Farhi's paper ("Classification with Quantum Neural Networks on near Term Processors"), and I am trying to implement the subset parity problem using ...
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### Qiskit flipped representation of qubits in CNOT gate?

The conventional CNOT gate is shown on the right, and the Qiskit version is on the left. Since Qiskit defines it has a flipped representation kindly explain what is happening to the 11 position?
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### Question Regarding Simulating Hamiltonian With Quantum Circuit

There have been a few other questions about this section of Nielsen and Chuang, but when working through the output of the circuit, there are some inconsistencies that are probably due to some mistep/...
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### How is the ground state of a Hamiltonian defined?

I'm studying VQE, but there is something I don't get. We know (I think) that for a given Hamiltonian the minimum eigenvalue is associated with the ground state. But if we take the Hamiltonian to be ...
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### Gate Y returns wrong phase in IBM's circuit composer

One can check that, with IBM's circuit composer, $Y$ gate acted on $|0\rangle$ or on $|1\rangle$ returns the same phase of $\pi/2$. Is this a bug?
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### What does the notation $\sigma_j^z$ mean for Pauli matrices?

In multiples papers or online article on the QAOA algorithm (such as this one), I found notation for the Hamiltonian similar to this one : $$\sum_{ij} \frac{1}{2} (I-\sigma_i^z \sigma_j^z)$$ I don'...
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### Qubit in a mix sin/cosine state

The question is pretty simple. How can I get an input qubit $|0⟩$ in the state, say $$\cos{\frac{\pi}{10}}|0⟩ + \sin{\frac{\pi}{10}}|1⟩$$ Or any other sine/cosine mix state? Which gates do I need to ...
### How do physical implementations of Z gate selectively affect $\lvert1\rangle$ basis vector?
The Pauli Z gate inverts the phase of $\lvert1\rangle$ while leaving $\lvert0\rangle$ unaffected. When I think about how $\lvert1\rangle$ and $\lvert0\rangle$ are physically realized, however, as ...