Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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Is the Clifford group a semidirect product?

This is from Is the Clifford group finite? "Define the Clifford group $ \mathrm{Cl}_n(p) $ of n qudits of prime dimension p as the unitary normaliser of the generalised Pauli group. Define the ...
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Decompose native gates using Qiskit framework [closed]

I've read the papers about quantum hardware. These papers [1] [2] mention that native gates of IBM quantum computer are $R_x(\pi/2), R_z(\lambda)\space and \space CR \space (Cross Resonance)$ My ...
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1 vote
1 answer
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Is pennylane free?

I was going through the basics of pennylane. I am able to understand that it is used for quantum neural networks. I am not sure whether it is using paid cloud computer or simulator of xandu or ibmq? ...
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2 votes
1 answer
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Why does application of Hadamard gate on $|0\rangle$ inverts the state on bloch sphere?

I am trying to understand what is the affect of Hadamard gate on qubit. So far, I understand that applying $H$ gate on qubit, puts the qubit into superposition state where the probability of the qubit ...
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Qiskit: Getting weird error on creating an operator acting on certain qubits

I have a system of N qubits and I want to construct a quantum operator ZZ...ZZ of length ...
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1 answer
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How to write the code for decomposing only a subset of gates in a quantum circuit via Qiskit?

I have a quantum circuit with a number of gates, and some of them are labeled by some letters without showing the details inside. I have known the quantumcircuit.decompose() would help, but it would ...
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1 vote
2 answers
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Is it possible to create a controlled initialize instruction in Qiskit?

I know it's possible to create custom controlled gates from a circuit, for example, ...
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1 answer
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Duration of single qubit gate in IBM

how can we calculate the duration of single qubit gate using Qiskit in IBM? In other words if I have to insert a delay in the place of the single qubit gate, how would I know how much delay in ...
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Redundant parameters in $2\times 2$ unitary operators?

A complex $n \times n$ unitary operator has $n^2$ free real parameters. For example, a $2 \times 2$ unitary matrix can be parametrized as \begin{equation} \begin{pmatrix} e^{i(\alpha - \beta/2 - \...
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3 votes
1 answer
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How to use Cirq to transpile circuit to custom native gate set?

I am trying to use Cirq to compile arbitrary quantum circuits to custom native gate sets, e.g., to use the Cirq compiler to generate quantum circuits for different quantum computers (IBM, Rigetti, ...
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Quantum part on Regev's LWE paper

I know this is supposed to be in cryptography but I think this question is appropriate to be asked here. I am reading the Learning with Errors paper of Oded Regev and I am confused with the ...
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  • 185
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What is the matrix representation of a generic two-qubit controlled unitary operation?

I have been taught that an arbitrary two qubit controlled unitary (first qubit control, second qubit target) can be represented as \begin{matrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\...
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4 votes
2 answers
149 views

Qiskit CNOT matrix representation confusion

I wanted to look at the matrix representation of CNOT gate as defined in Qiskit. ...
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7 votes
1 answer
129 views

Circuit from finite group of gates and classical simulations

Let $ G $ be a finite group of quantum gates. Is it true that any circuit made using only gates from the finite group $ G $ can be efficiently simulated on a classical computer? Here by circuit made ...
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2 votes
2 answers
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Applying controlled unitary operations during quantum phase estimation

I am trying to understand Shor's algorithm for a personal research project. I am currently going through quantum phase estimation, and have came accross something I'm struggling to understand in the ...
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2 votes
1 answer
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How to interpret photon number 'gates' in quantum circuit?

Peng et. al. Describe a circuit for entanglement cloning (i.e. entanglement broadcasting) which on its own looks fairly straightforward: Confusingly however, the gates $U_1$ and $U_2$ are not logical ...
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Prove that adding any non Clifford gate to the Clifford group yields a universal gate set

I have seen it claimed in multiple places that adding any non Clifford gate to the Clifford group yields a universal gate set. It is, however, not easy to find an accessible proof of this fact. The ...
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How can the transformation between entangled states like two Bell states be derived?

As it is stated in this post: Transforming the first Bell state into the other Bell states, one can transform the $|\phi^{+}\rangle$ state to the $|\psi ^{-}\rangle$ by applying the tensor product of ...
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3 answers
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Why can a ZY decomposition not decompose an arbitrary single qubit gate?

To decompose an arbitrary single qubit gate, we need to do a "$e^{i \alpha}$ZYZ" decomposition. Intuitively however I do not understand why a "$e^{i \alpha}$ZY" decomposition is ...
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2 votes
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How to simulate these Floquet and Rotation operators for kicked top model?

In this and other papers relating to the kicked top model, it is mentioned that spin coherent states can be expressed as: $$\left|\theta,\phi\right>=R(\theta,\phi)\left|j,j\right>$$ for given ...
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1 answer
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Eastin Knill Theorem and groups of transversal gates

The Eastin-Knill Theorem shows that the transversal gates always form a group and that moreover this group is a finite subgroup of the group of all unitaries. For many codes, for example all self dual ...
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6 votes
1 answer
163 views

Is the controlled-Hadamard gate in the Clifford group?

Is the controlled-Hadamard gate a member of the Clifford group? I understand that Controlled Pauli gates are in the Clifford group. If controlled Hadamard is Clifford member, then is a controlled-...
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1 answer
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Matrix representation of multi-qubit operations when there's irrelevant qubit(s)

Suppose there are three qubits, q0, q1, and q2, if you perform a CX on q0 and q1, the entire matrix of the operation you performed on the whole quantum circuit will simply be the tensor product of CX ...
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In the solution of exercise 2.2(on this site) how can we see the new form of the operator A, in the beginning of the answer.?

this is the question I am referring to I am sorry to ask such a question, can someone explain how are we able to make the new form of the operator A. Thank you, any help would be great!
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1 answer
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EPR pairs (Bell states) preparation circuit in SymPy

I am trying to recretate this circuit from the book: https://www.elsevier.com/books/quantum-information-processing-quantum-computing-and-quantum-error-correction/djordjevic/978-0-12-821982-9 The ...
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1 vote
1 answer
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Understanding phase kickback caused by the CNOT gate

Applying the CNOT gate to the state |+-⟩ would result in the state |--⟩ as per: What has occurred is a "phase kickback". The relative negative phase from the target qubit has transferred to ...
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2 votes
1 answer
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Is there a way to prove that the number of gates in Exercise 4.22 of Nielsen and Chuang's book is the smallest possible number?

I've been going over Nielsen and Chuang's Quantum Computation and Quantum Information and I ran into Exercise 4.22, which says, Prove that a $C^{2}(U)$ gate (for any single qubit unitary $U$) can be ...
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Sequential Circuits in IBMQ and Qiskit and generating a clock pulse

I am trying to implement the Peres Gate with Feedback from Feynmann Gate feeding back into the third input to Peres Gate. This sequence needs to be repeated. There is also a clock pulse that needs to ...
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2 votes
2 answers
88 views

Commutation rules between Pauli $X$ and controlled-Hadamard

Are there any known commutation rules between the $X$ gate and the $CH$ gate?
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2 answers
111 views

How to decompose any arbitary unitary gate into just Rx and Ry rotation gates?

I have the following exercise: I tried to ask my university TA for some advice on how I could solve such questions and he literally just told me that I should try a bunch of combinations of rx and ry ...
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3 votes
1 answer
119 views

Deutsch's algorithm makes no sense

Here are the 4 classical functions over $1$ bit we're examining, $f(x) = \{0,1\}, x \in\{0,1\}$: identity (balanced) -> $f(x) = x$: \begin{bmatrix}1&0\\0&1\end{bmatrix} negation (balanced) ...
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1 answer
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Qiskit TwoQubitBasisDecomposer - how to properly decompose gates?

I'm new with Qiskit and I'm struggling with creating my own controlled gates. I'm trying to create a ZYZ decomposition of a controlled unitary gate I created. I'm trying to use the method ...
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2 votes
1 answer
77 views

How to generate matrix for swap(a, b) gate for n qubits

I am trying to simulate a swap gate that swaps two qubits of indices a and b where there are n qubits total. I understand how to make a truth table and generate a matrix based off of that for each ...
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0 answers
47 views

Gray codes to Lower the Gate count in Arbitrary State Synthesis

I am presently trying to understand the state synthesis circuit as done in qiskit. Qiskit recommends a paper "Synthesis of Quantum Logic Circuits" on its website: https://arxiv.org/abs/quant-...
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4 votes
1 answer
160 views

What is the reasoning behind the Toffoli gate implementation?

I am studying quantum computing and came to the implementation of the Toffoli gate. I can't find anywhere what is the reasoning behing this derivation. What confuses me the most is the need of the ...
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3 votes
1 answer
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How does mapping a two qubit gate to a pyramid scheme like this work?

In this video from the QHACK2019 event, Gavin Crooks is visualizing two qubit gates by using a 3D pyramid. How does this mapping process work and what is the reason to do it? I could not find any ...
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0 answers
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Strangeworks (Silq compatibility)

Hi I was wondering what the compatibility is for the future for integrating Silq into the Strangeworks platform.
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1 vote
1 answer
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XY and YZ rotations in QISKIT

I noticed that QISKIT only has RZX rotation as a standard gate. Is there a simple way for me to define RYX and RYZ rotations? Why didn't they implement those rotations yet? I need those rotations to ...
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Implementing Quantum Walks at IBM

a question about quantum walks, would this circuit be correct to start a quantum walk in a hypercube? I saw something about increment and decrement, but I didn't quite understand how they would work ...
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1 vote
1 answer
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Can we design a circuit that outputs desired estimates?

If we have state $\lvert\psi\rangle \in (\mathbb{C}^{2})^{\otimes n}$ in an $\textit{n}$-qubit system with Pauli operators $P$ such that $P \in \{I, X, Y, Z\}^{n}$, how can we design a circuit/...
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How to use the csv dataset file imported as a dataframe in QSVM Qiskit code

I am trying to run QSVM qiskit code with my custom dataset which I am loading as a pandas dataframe. When I execute the part below with my own dataset in the place of breast_cancer, it gives error &...
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0 votes
1 answer
63 views

Phase estimation using $U_3$ gate

I'm trying to understand how to implement quantum phase estimation (QPE) for a generic single-qubit Hamiltonian. The general time-evolution could be simulated using $U_3$ gate, in Qiskit documentation,...
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0 answers
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Quantum Haar Wavelet Transform

I am working on understanding the quantum haar wavelet transform and trying to understand how it actually do the dimension reduction mathematically. A lot of people suggested me to read this paper : ...
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1 answer
38 views

Error Model on id gate, is not giving any error

I am trying to play with NoiseModel of qiskit, and I noticed that error on id gate is not giving any error results, while error ...
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1 answer
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Parameterized swap test and perfect swap test

Suppose one has parameterized a swap test by using an ansatz $U(\theta) = \exp(-i\theta \text{ CSWAP})$, and one tries to find an angle $\theta$ such that one can distinguish given two quantum states ...
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2 votes
3 answers
105 views

Find a circuit implementing a 3-qubit unitary matrix preparing $|b\rangle\simeq(0,c,c,c,c,c,c,0)$ with $c=1/\sqrt6$

I am trying to find a circuit to represent a 3 Qubit unitary matrix such that $U|0\rangle = |b\rangle$ for $b = \left[0~c~c~c~c~c~c~0\right]$, where $c = 1/\sqrt{6}$. Although I am working in Qiskit, ...
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2 votes
0 answers
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What is the explicit best known quantum algorithm for LWE?

Consider the learning with errors(LWE) problem which is known to be hard for quantum computers. Let $q \geq 2$ be a prime integer. Consider us being given (polynomially many samples of) either: $$A, ...
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2 votes
1 answer
47 views

Multiplication using nearest neighbour quantum gates

Let $A$ be an $n \times m$ matrix, and $x$ be an $m \times 1$ vector and $q$ be a number such that $q$ is polynomial in $n$. Let us be given both $A$, $q$, and $x$ as input and let us also have a 2D ...
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5 votes
1 answer
80 views

Does the Eastin-Knill theorem hold for repetition codes?

The Eastin-Knill theorem states that For any nontrivial local-error-detecting quantum code, the set of transversal, logical unitary operators is not universal. see original paper. Does this theorem ...
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1 vote
1 answer
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Quantum Image Processing Application

I have been reading about Quantum Wavelet transform and finding some problems. One of its application is that image is given as input and same image is retrieved as output with reduced size(Please ...
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