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Questions tagged [quantum-gate]

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

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2 votes
0 answers
26 views

Do we really apply both single-qubit and two-qubit gates in the same layer in experiments?

I'm doing experiments using superconducting computers, and my question is as follows: Performing quantum gates requires isolating the coupling between a target qubit and other neighboring qubits. To ...
2 votes
1 answer
104 views

Do magic states only work for CSS codes?

Magic states are used to obtain universal fault tolerant quantum gates. The process involves distilling high quality magic states from many lower quality magic states using a state distillation ...
0 votes
2 answers
189 views

Modular addition in Qiskit

I want to implement the Jordan gradient estimation algorithm in Qiskit. I need a unitary operator $U_f$ that performs as follows: $$U_f: |x_1\rangle |x_2\rangle \cdots |x_d\rangle|y\rangle \...
2 votes
1 answer
69 views

Why do we use Z-gates in the following figure?

This is a picture of a 'T-gate gadget' and a proof for a circuit from “Quantum homomorphic encryption for circuits with low T-gate complexity” by Broadbent, Jeffrey (2015) (arXiv). My question is why ...
1 vote
1 answer
78 views

Modify Shor’s quantum order-finding algorithm in such a way that it uses as few qubits as possible

I am supposed to modify Shor’s quantum order-finding algorithm in such a way that it uses as few qubits as possible. Beforehand, I already did an exercise where I showed that the inverse Quantum ...
0 votes
0 answers
12 views

Custom pulse with fake backend not running for Cross Resonance Pulse

I am trying to create a cross resonance pulse by driving the control qubit at a non resonant frequency. My code runs but does not stop running. ...
4 votes
1 answer
114 views

How do the Type I and Type II fusions work?

I am going through the original paper on Type I and Type II fusions. But I cannot understand how this is actually implmented. They say they start with $$\frac{1}{2} |H,H\rangle+|V,V\rangle \otimes |H,...
2 votes
1 answer
86 views

What is the connection between an observable and a gate?

I am reading some introductory quantum mechanics and I don't understand the connection between an observable and a gate. I thought a gate just applies a rotation to a state while a measurement gives ...
6 votes
2 answers
226 views

Decomposition of a $4 \times 4$ unitary matrix

I am currently studying the paper "Decomposition of unitary matrices and quantum gates (2012)" and referring to the textbook Quantum Computation and Quantum Information. Among the topics, I ...
0 votes
1 answer
68 views

What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?

Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
2 votes
1 answer
56 views

Math Behind $X$ Gate With Arbitrary Phase is equivalent to $ZXZ$ Gate

An X gate where there is a phase shift $\phi$ to the applied sinusoidal wave $U = e^{-i\frac{\theta}{2}(cos(\phi)\sigma_x+sin(\phi)\sigma_y)}$ is equivalent to a series of gates $Z_{-\phi}X_{\theta}Z_{...
0 votes
1 answer
43 views

how do i get the sequence of resulting data on the ibm quantum computers platform?

I have been working on the ibm quantum computer platform, but i have faced a problem with the output. My circuit contains Hadamard gates and entanglement gate between two qubits. I want to get the ...
1 vote
3 answers
59 views

Intro book on classical and quantum computing by Thomas G Wong

Looking at his book, and am obviously new to studying this. Could someone help explain to me how the truth table is valid here? To my understanding, when $C=0$, the circuit behaves like a reversible ...
0 votes
1 answer
177 views

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 &...
2 votes
1 answer
571 views

Can IBM Quantum hardware handle any CSWAP at all?

I am designing quantum algorithms where the quantum circuit uses CSWAP gates a lot. The result is very noisy on the quantum hardwares. So I designed really simple circuits to test whether it is indeed ...
4 votes
2 answers
87 views

What does it mean for a gate to "commute with a measurement"?

I think I understand intuitively what this means. For example, I can apply an $X$ gate and then perform a measurement in the $X$ basis and I will get the same post-measurement states as if I measured ...
2 votes
1 answer
75 views

How to verify that a certain gate was applied to a quantum code

Suppose I have a quantum error correcting code $|\psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$, say the $[[7,1,3]]$ Steane code for concreteness. Suppose there is a black box that either ...
0 votes
0 answers
30 views

How to write Verilog code to describe a quantum system

I would like to ask everyone for some verilog code sources that implement quantum systems so I can refer to them
3 votes
0 answers
50 views

What do symmetric 2-qubits gates look like?

A gate $U= (u_{ij})_{i,j= 1}^4$ is symmetric if the action of the gate is the same as the action of $Swap\ U\ Swap$ where the swap gate is $$Swap= \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & ...
0 votes
1 answer
143 views

How does the V gate perform modular exponentiation?

The V gate is defined such that $V^2=X$: $$ V|0\rangle = \frac{1}{2}\begin{bmatrix} 1+i&1-i\\1-i&1+i\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix} = \frac{1+i}{2}|0\rangle + \frac{1-i}{2}|1\...
3 votes
2 answers
142 views

general way to decompose a CZ gate on $n$-qubit system

Suppose I have a CZ(i,j) gate (or CNOT) acting on qubit $i$ and $j$, on a $n$-qubit system. Is there a general way to decompose this gate into a set of gates that only involve single-qubit gates and ...
7 votes
1 answer
219 views

Which Clifford groups are 2-designs?

Let $ X $ be the $ q \times q $ shift matrix sending $ |y \rangle \mapsto |y+1 \rangle $ where the ket index $ y=0,\dots, q-1 $ is taken mod $ q $. Let $ Z $ be the diagonal $ q \times q $ clock ...
4 votes
2 answers
269 views

Equivalent $[\![n,k,d]\!]$ codes and transversal gates

An operator on the Hilbert space of $ n $ qubits is called a local unitary if it is of the form $$ U=\bigotimes_{i=1}^n g_i $$ where each $ g_i $ is a $ 2 \times 2 $ unitary matrix. In other words if ...
1 vote
0 answers
36 views

Are transversal entangling gates possible for stabilizer codes other than CSS?

It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304....
5 votes
1 answer
555 views

Building a state with parallel execution

I'm trying to implement the main algorithm described in the Quantum Recommendation Systems paper. In order to do this, I have to create a quantum state $|x\rangle$ corresponding to a real vector ...
6 votes
1 answer
164 views

Qutrit Steane Code

There is a well known 5 qubit code $ [[5,1,3]] $ with stabilizer generators $$ XZZXI \\ IXZZX \\ XIXZZ \\ ZXIXZ $$ There is a corresponding $ [[5,1,3]]_3 $ code for qutrits given by \begin{align*} &...
3 votes
3 answers
276 views

Mathematical expression of controlled Ry gate

"How can I describe the controlled Ry gate transformation on the ground state qubit using a mathematical formula similar to the one below, which is for the CNOT transformation?" The example ...
1 vote
1 answer
42 views

Why is the controlled-Z gate a symmetric gate?

I want to understand why this gate is symmetric. Consider a two qubits circuit (q1, q2) with a gate CZ controlled by the first q1, then if q1 is in the state $(a, b)^T$ and q2 is the state $(c, d)^T$, ...
4 votes
2 answers
82 views

unitary that transform $\sigma^x \pm \alpha \sigma^z$ into $\sigma^x$ and $\sigma^z$

Consider $\sigma^x \pm \sigma^z$, where $\sigma^x$ and $\sigma^z$ are Pauli $X$ and $Z$ matrices. Let unitary $U$ be a $\pi/4$ rotation matrix around $Y$-axis. Then, \begin{equation} U(\sigma^x + \...
2 votes
0 answers
55 views

Is every code with a universal set of transversal gates trivial?

The quantum repetition code is an $ [[n,1,1]] $ stabilizer code with stabilizer generators $ Z_iZ_{i+1} $ for $ i=1, \dots, n-1 $. The Eastin-Knill theorem states that a $ d >1 $ code cannot have a ...
2 votes
2 answers
84 views

Show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \right\rangle$ is unitary [duplicate]

I am reading Quantum Computation and Quantum Information by Chuang and Nielsen and they claim that it is easy to show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \...
1 vote
0 answers
23 views

Doing Quantum State Tomography on a custom-made gate with Qiskit Pulse

In this simple example I took the Qiskit CX gate, obtained the pulses' schedule and then tried to do Tomography on that. In theory, everything should run smoothly (I think) but I get this "error&...
0 votes
1 answer
259 views

Building Unitaries in TSP Quantum Phase Estimation Qiskit?

In the paper [https://arxiv.org/pdf/1805.10928.pdf] 2 published by IBM, they use Quantum Phase Estimation to solve the TSP problem. I don't understand the reason why they can decompose the diagonal ...
0 votes
1 answer
67 views

Can we initialize two arrays in two different qubits in a 2-qubit quantum circuit in IBMq?

Can we initialize two different arrays in two different qubits in a 2 qubit quantum circuit? I tried in IBMq but it showing error. So don't understand. from qiskit import QuantumRegister, ...
4 votes
1 answer
348 views

Preparation of states that correspond to efficiently integrable probability distributions

I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph. It is stated that there exists an ...
5 votes
2 answers
479 views

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 ...
0 votes
0 answers
24 views

How can I measure qutrits in the X basis using cirq?

I attempted to create a custom measurement class which, in my case, allows us to go from the z basis to x basis using a hadamard gate transformation, and then we measure wrt that new basis. However, ...
0 votes
1 answer
47 views

How to understand the matrix representation of the Toffoli produced by qiskit?

I would like to ask about the results of running the Toffoli gate matrix and circuit diagram on colab Possible reasons for inconsistent results with the following correct matrix results. I would also ...
6 votes
0 answers
140 views

Universal gate set for the $ [[15,1,3]] $ code

The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is ...
3 votes
2 answers
391 views

What are the transversal gates of the $[[5,1,3]]$ code?

What are the transversal gates of the perfect 5-qubit code ( [[5,1,3]] code) ? Since this is a stabilizer code we have transversal Pauli gates. Are there any others? I am primarily interested in ...
2 votes
1 answer
147 views

Generating Equal Amplitude Superposition States from Another Equal Amplitude Superposition State

Can we prepare a state regarding a transformation in quantum computing that seems to generate another equal amplitude superposition state when applying a Hadamard gate? Specifically, I observed that ...
6 votes
3 answers
487 views

Why focus on T gates and not some other single qubit rotation R making Clifford + R universal?

Background: In many error correction codes in particular the surface code, the Clifford operations generated by the S,H and CNOT are transversal for quantum computation (meaning that these logical ...
1 vote
1 answer
293 views

Decomposition of unitary operator into rotations around Bloch sphere

I apologize in advance for any mistakes as I am new to this field and come from a programming, rather than mathematical/physical background. I am looking for a way to decompose a given operator $U$ ...
1 vote
1 answer
103 views

Julia codes for unitary gate decomposition

I am looking for a way to decompose any given operator U into ZYZ rotations. And then plug the values back into ei∗α∗Rz(θ0)∗Ry(θ1)∗Rz(θ2), to 'recompose' the gate and check if the gate decomposed ...
1 vote
1 answer
183 views

Single bit teleportation for Hadamard gate

The circuit in Figure 13.7 of Gottesman's book https://www.cs.umd.edu/class/spring2024/cmsc858G/QECCbook-2024-ch1-15.pdf shows how to take the magic state $ T | + \rangle $ and use single bit gate ...
1 vote
1 answer
41 views

Transpile not working properly for decomposing single qubit gates into Rx Ry and Rz

I used the above code to decompose hadamard gate into RxRyRz but i am getting wrong angles which on multiplying don't match hadamard gate . Interestingly when i am using inbuilt hadamard hate using q....
0 votes
1 answer
184 views

How do qubits interact to form logic gates?

How do qubits interact to form, say, CNOT gates? There are very few comprehensive explanations of how quantum computing works. They all use obscure metaphors that don’t make sense (like Schrödinger’s ...
2 votes
3 answers
288 views

Pauli I in eoh procedure doesn't become a global phase gate in qiskit evolution_instruction method. Possible consequences

If one has two qubits in arbitrary stats and wishes to apply a controlled version of some global phase gate $P(\varphi) = \begin{pmatrix} e^{i\varphi} & 0 \\ 0 & e^{i\varphi} \end{pmatrix}$ ...
-2 votes
1 answer
40 views

How to determine the single-qubit gate if we know an initial and corresponding final state [closed]

HOW TO FIND A QUANTUM GATE IF WE KNOW THE INITIAL AND FINAL SINGLE QUBIT STATES? I tried thinking by using projection vectors like ket 0 goes to ket I, then we can take the ket 0 bra I, but the ...
-2 votes
1 answer
82 views

Decomposition of a quantum gate into Rx Ry Rz

Can we break any quantum 2 qubit gate as a product of Rx Ry and Rz gates if yes then please provide a python code to do so .

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