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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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Measuring vs gate - what is the relation?

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 ...
Katie's user avatar
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31 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,...
GaussStrife's user avatar
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1 vote
3 answers
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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 ...
anthony's user avatar
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2 votes
1 answer
550 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 ...
Deren  Liu's user avatar
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0 answers
27 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
Bakeu's user avatar
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4 votes
2 answers
85 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 ...
user29393's user avatar
1 vote
0 answers
33 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....
Ian Gershon Teixeira's user avatar
3 votes
0 answers
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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 & ...
NotaChoice's user avatar
3 votes
3 answers
265 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 ...
Htar's user avatar
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1 vote
1 answer
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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 $(c, d)^T$, ...
NotaChoice's user avatar
4 votes
2 answers
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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 + \...
karavan's user avatar
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0 answers
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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 ...
Ian Gershon Teixeira's user avatar
2 votes
2 answers
83 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) \...
Andrej's user avatar
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1 answer
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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 ...
Ian Gershon Teixeira's user avatar
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0 answers
17 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&...
Samuel Hagh Shenas's user avatar
2 votes
0 answers
31 views

Creating a cross resonance pulse in qiskit and running

I have a simple circuit in qiskit which is designed to exploit a $ZZ$ interaction between qubits: ...
idislikecoding's user avatar
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0 answers
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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, ...
Son100's user avatar
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6 votes
3 answers
482 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 ...
Frederik Ravn Klausen's user avatar
1 vote
1 answer
179 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 ...
Ian Gershon Teixeira's user avatar
6 votes
0 answers
139 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 ...
Ian Gershon Teixeira's user avatar
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....
Anonymous's user avatar
-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 ...
Anonymous's user avatar
-2 votes
1 answer
81 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 .
Anonymous's user avatar
1 vote
1 answer
52 views

Definition of fault tolerant gate gadgets

I am trying to understand fault tolerance for gate gadgets a bit better. Here Gottesman provides the following definition: I generally understand this definition but I have two questions. (1) Why is ...
Eric Kubischta's user avatar
2 votes
1 answer
73 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 ...
Eric Kubischta's user avatar
0 votes
0 answers
17 views

How do I perform measurements in the X basis for qutrits in cirq?

After applying the hadamard gate to a 0 state qutrit, I should be able to get it into the + state, but how do I then measure the circuit in the X basis as opposed to the computational basis?
Son100's user avatar
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0 votes
1 answer
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Hypothesis on faster-than-light communication

I'm having a hard time understanding why it is not possible to communicate faster than light with entangled qubits. Now, this is my hypothesis. A and B have a pair of qubits, and 2 synced clocks at 12:...
carrotsaybye's user avatar
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1 answer
128 views

Is there a tool to decompose 4-Qubit unitaries (aka 16x16 matrices)?

I was wondering if there is a tool that can decompose such a matrix in gates on 4 qubits? I found one for 3-qubit gates (9x9 matrices) in Cirq but nothing for bigger matrices. (The matrix is not ...
Schrödinger314's user avatar
3 votes
1 answer
83 views

Implementing the reflection in Grover's algorithm with $\{\mathtt{CNOT}, H, X\}$

Suppose we have a boolean function $f : \{0, \cdots, N - 1\} \to \{0, 1\}$ and want to determine $x$ such that $f(x) = 1$ given a reduced quantum oracle $V_f$ defined by $$ V_f | x\rangle := (-1)^{f(x)...
Olly Britton's user avatar
0 votes
0 answers
23 views

Constructing amplitude oracle for complex-valued matrix

Let $a, b \in \mathbb R$ such that $\vert a + ib \vert < 1$. Does there exists a generic $2$-qubit unitary such that $$(a |0\rangle + \sqrt{1 - a^2}| 1 \rangle) \otimes (b|0\rangle + \sqrt{1 - b^2}|...
SescoMath's user avatar
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1 vote
1 answer
46 views

Implementation of a unitary operator scaled by a factor

Is it possible to implement a unitary operator scaled by a factor on a quantum computer? Let's say the unitary operator is $U$: $$U=\begin{bmatrix} u_0 & u_1 \\ u_2 & u_3 \end{bmatrix}\...
upe's user avatar
  • 311
0 votes
1 answer
60 views

Unable to extract the quantum registers information from qiskit quantum circuit data

Consider the following code: ...
Vikram Dorbala's user avatar
0 votes
1 answer
55 views

Realization of the gate $(I\pm U)/2$

The state after applying the Hadamard test (before measurement) is $$\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}\ket{0}\frac{I+U}{2}\ket{\psi} + \ket{1}\frac{I-U}{2}\ket{\psi}.$$ ...
upe's user avatar
  • 311
2 votes
2 answers
57 views

The result of qiskit calculating T-depth and its calculation method

I have encountered doubts when using qiskit to calculate T-depth. I am not sure whether it is a problem with the way the code is written, or I am still a little vague about T-depth, so I would like to ...
Dona's user avatar
  • 21
3 votes
2 answers
84 views

Is $\{CNOT, CZ, T\}$ a universal gate set?

If one would like to drop the Hadamard from the usual $\{CNOT, H, T\}$ gate set, what is a suitable replacement? It seems like $CZ$ might work here but I don't really know how to prove or disprove it. ...
John Doe's user avatar
2 votes
2 answers
70 views

Better constant for linear depth incrementers

Currently working on some quantum arithmetic and was wondering if we have a better constant factor for a linear depth incrementer. As an example (and the best I could currently find), Craig Gidney ...
LukasM's user avatar
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1 vote
0 answers
58 views

Are there any instances of the "Lights Out" puzzle only solvable with square-root-of-NOT gates?

TL/DR: Can we solve a classically unsolvable instance of "Lights Out" when the lightbulbs neighboring the switch that we flip see a $\sqrt X$ gate, instead of being fully negated? If so, ...
Mark Spinelli's user avatar
1 vote
2 answers
146 views

Definition of a quantum gate

A quantum gate is usually defined as a unitary transformation, like the definition found in "Mathematics of Quantum Mechanics" by Scherer. According to this definition, can we consider a ...
Josh's user avatar
  • 417
3 votes
0 answers
32 views

methodology for design quantum circuits according to a given unitary

This is a general question. Given an arbitratry unitary matrix. How to desigin a quantum circuit to implement it? I am not asking for a specific unitary matrix, but for a general methodology to tackle ...
tangyao's user avatar
  • 171
0 votes
1 answer
106 views

How to convert states |0011⟩, |1100⟩, |0101⟩ to |1111⟩?

How can I use X gate (quantum not) to convert each of the pure states |0011⟩, |1100⟩, |0101⟩ to |1111⟩ with Qiskit? My programming assignment is Using the idea of a multi-controlled phase gate, now ...
Jettapol's user avatar
0 votes
1 answer
45 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 ...
Dona's user avatar
  • 21
2 votes
1 answer
34 views

How to apply gates on a subspace of a superposition of qubits?

Let us say that I have the state $a|00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$. I wish to apply a one-qubit unitary (a $2\times2$ matrix) U on the subspace spanned by $|01\rangle$ and $|10\...
Soumyadeep sarma's user avatar
0 votes
0 answers
13 views

"Session has been closed" Error in solving Maxcut problem by QAOA

I am trying to run this code- https://learning.quantum.ibm.com/tutorial/quantum-approximate-optimization-algorithm same way as they mentioned. After running this code, my qiskit Dashboard show 10-12 ...
Maths_hawk's user avatar
1 vote
1 answer
28 views

Moving pauli product rotations past measurements

I'm trying to understand how the clifford + T compiler works in "A Game of Surface codes". How do I move a pauli product rotation block past a pauli product measurement block? More ...
Palash Goiporia's user avatar
1 vote
0 answers
20 views

Are reset gates allowed on IBM quantum computers?

My circuit involves many "reset" gates. After running on the IBM real backend, the experiment status says "Failed" with error message that says: Failed - Unknown operation type ...
Deren  Liu's user avatar
  • 121
2 votes
1 answer
93 views

Alternative gate sets for universal Clifford computation?

The standard universal set of gates for Clifford computation is CNOT, H and S. Are there other options, in particular, gate sets that don't use the S gate? If yes, what are some examples?
Cairo's user avatar
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0 answers
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How to physically implement a CNOT gate with a photon and a cold atom?

If I have qubits in the same platform (superconducting, photon or cold atoms), the implementation of CNOT gates is relatively well-known. However, if I have a photon and a cold atom, how am I supposed ...
AndyLiuin's user avatar
  • 386
3 votes
3 answers
254 views

How to mathematically describe the action of CNOT on the control qubit alone?

Basically the title. From what I know, starting from the $|{+0}\rangle$ state where the reduced density matrix of the first qubit $|+\rangle$ is $\frac{1}{2}\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{...
Jack Nathan's user avatar
1 vote
1 answer
106 views

Constructing a block unitary from non-unitary matrices

Background: I have a function $f(s_i, s_f, x)$ where $s_i \in \{0,1,2,3\}; \quad x,s_f \in \{0,1\}$ which is defined as: $$ f(s_i, s_f, x) = \begin{cases} 1, & \text{if } (s_i, s_f, x) \in\{(0,0,0)...
Enigma's user avatar
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0 votes
0 answers
42 views

How to interpret result for an OR problem solved in Qiskit

I solved "01 KnapSack problem" in Qiskit optimization module. Though the iterations doesn't gets converged but I got an answer (may be infeasible). But my question is that how to interpret ...
Maths_hawk's user avatar

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