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

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
52 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
40 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
52 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
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0 answers
14 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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-4 votes
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three qubit quantum Fourier transform [closed]

Perform the three qubit quantum Fourier transform on the IMB Quantum computers for (|0⟩+|7⟩)/√2. Perform the quantum state tomography to reconstruct the density matrix of the output state.Pleasr use ...
Zoe's user avatar
  • 1
0 votes
1 answer
51 views

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
115 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
71 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
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0 answers
22 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 answer
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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
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1 answer
37 views

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

Consider the following code: ...
Vikram Dorbala's user avatar
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1 answer
53 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
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2 votes
2 answers
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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
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3 votes
2 answers
75 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
66 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
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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
136 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
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3 votes
0 answers
30 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
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1 answer
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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
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1 answer
32 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
29 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
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0 answers
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"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
27 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
18 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
2 votes
1 answer
87 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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45 views

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
  • 351
3 votes
3 answers
249 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
82 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
  • 11
0 votes
0 answers
36 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
1 vote
0 answers
11 views

What is the method for representing a quantum circuit from a bit equation?

I am currently studying this paper(https://arxiv.org/abs/quant-ph/9503016). I'm having trouble effectively utilizing the content depicted in the image below from the paper. It seems that one could ...
junghyunHa's user avatar
2 votes
1 answer
30 views

Relation between Rz gate and Phase gate

As I know, the $Rz(\frac{\pi}{2})$ gate is equivalent to the Phase gate $S$ up to the global phase. However, I found using qiskit, the $Rz(\frac{-\pi}{2})$ is also equivalent to the Phase gate $S$. I ...
Amanli's user avatar
  • 57
0 votes
0 answers
12 views

Particle number expectation value in QuTip

I am learning now to use QuTiP by going through their documentation site. I am trying to understand what does the argument - particle number expectation value in thermal density matrix do? How does it ...
CuriousMind's user avatar
1 vote
0 answers
13 views

On the construction of quantum circuits for S-boxes with different criteria based on the SAT solver

I'm reading this paper: On the construction of quantum circuits for S-boxes with different criteria based on the SAT solver. Here's the link: https://eprint.iacr.org/2024/565.pdf#page=29&zoom=100,...
Huy By's user avatar
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1 vote
0 answers
16 views

Why we do SWAP operations for applying a mode N function in Shor algorithms and How we do this swapping? [duplicate]

I am working on implementing shor algorithm for finding prime factors of N = 15. I am trying to understand a code of qiskit, but i am confused how and why the code editor is using swap codes to define ...
Tayyab Yahya's user avatar
0 votes
2 answers
82 views

What's the result of applying a CNOT gate followed by a Hadamard?

Say I have the following circuit And the input is $|\psi\rangle=\frac12(|00\rangle+|11\rangle+|01\rangle+|10\rangle)$. To find the output sate, I would first apply the CNOT to the second bit, ...
afebs's user avatar
  • 63
1 vote
1 answer
53 views

Finding the effect of conjugate transpose on a state $|b\rangle$

Say that I have a unitary gate $U$ such that $U|b\rangle=|b+1$ mod $N\rangle$. How would I go about finding $U^\dagger|b\rangle$?
afebs's user avatar
  • 63
0 votes
0 answers
38 views

Is there any well defined notion of "the state of a qubit X" if $X$ is a member of a larger qubit system

I'm trying to understand the effect of "measurement" as a gate. But my question is more elementary than that. Consider the following simple quantum circuit: $(X,Y)$ begins in the state $1 ...
Sidharth Ghoshal's user avatar
2 votes
2 answers
141 views

Universality of adding gate to Cliffords without inverses

In this answer it is explained how adding any non-Clifford gate $G$ to the Clifford gate set gives a universal gate set. However, that defines the gate set as the group generated by $G$ and the ...
John's user avatar
  • 504
1 vote
1 answer
24 views

How is the controlled-n NOT gate represented in Qiskit?

I want to decompose an 8-control qubit gate like the one in the picture on the right using Qiskit, similar to the decomposition shown. To do this, I need a C7XGate for 7 control bits, but it seems ...
junghyunHa's user avatar
1 vote
1 answer
45 views

IBM quantum computer backend cycle time and real gate duration

I am new to dynamical decoupling and is trying to study this from qiskit: https://docs.quantum.ibm.com/api/qiskit/qiskit.transpiler.passes.PadDynamicalDecoupling . There, they are specifying the ...
Tianqi Chen's user avatar
3 votes
2 answers
415 views

Is there a strategy for a single-shot identification of a Pauli gate?

I am given a single qubit gate $\in$ {I,X,Y,Z}. I can prepare any state, send it, and measure the result - but once. Is there a strategy to identify the gate?
trurl's user avatar
  • 131
1 vote
0 answers
17 views

Implementation of identity block initialisation strategy for mitigating barren plateaus

I have been trying to implement this paper on identity block initialisation strategy for barren plateau mitigation but I don't really understand how one would apply it to a parameterised circuit with ...
Moto's user avatar
  • 11
2 votes
1 answer
136 views

How to analyse a quantum circuit with an uncertain gate F?

The following quantum circuit consists of two CNOT gates in the middle of the circuit. The two-qubit input quantum register $|x\rangle$ is an arbitrary quantum state and can be set by the user. The ...
Xiling's user avatar
  • 21
2 votes
0 answers
84 views

When does $G^{\otimes n}$ vs $G^{\dagger \otimes n}$ implement $G$ transversally

Given an $[[n,1]]$ or $((n,2))$ code and a $2 \times 2$ matrix $G$ in its transversal group. There are cases when $G^{\otimes n}$ acts on $|\bar 0 \rangle,|\bar 1\rangle$ the same way as $G$ on $|0\...
unknown's user avatar
  • 2,217
2 votes
1 answer
105 views

What are classical analogies for the notions of superposition, entanglement, and interference?

I'm working on a conceptual explanation of quantum computing properties and have used analogies to make the ideas more accessible. I'd appreciate feedback on the validity of these analogies from those ...
qwerty's user avatar
  • 21
0 votes
0 answers
47 views

Axis and Angle of rotation of $\frac{1}{\sqrt{2}}\begin{bmatrix}-i&-1\\1&i\end{bmatrix}$

I have made use of the following formulas, \begin{align} \theta&=2\cos^{-1}\bigg(\frac{e^{-i\alpha}Tr(X)}{2}\bigg)\\ n_i&=\frac{e^{-i\alpha}Tr(X\sigma_x)}{2\sin\theta/2}\\ e^{i\alpha}&=\...
Sooraj S's user avatar
  • 831
1 vote
2 answers
71 views

Construct operator for controlled gate with qubits in-between

How can I construct the operator of a circuit with a controlled quantum gate where between the control and target qubits are other untouched qubits. Given a controlled quantum gate $C(U) = I\oplus U$ ...
upe's user avatar
  • 311
3 votes
1 answer
944 views

Expressing a quantum state as a polynomial

Let us consider the state $\left|\psi\right>$ obtained by applying $m$ 1- and 2-qubit gates to $n$ qubits, starting from the state $\left|0,0,\dots\right>$. Let us express it as: $$ \left|\psi\...
Doriano Brogioli's user avatar
1 vote
1 answer
54 views

What is the input when simulating a quantum state?

Currently I am simulating a quantum gate using verilog. I learned that: $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$ I want to ask: when simulating, should I let alpha and beta be complex ...
Bakeu's user avatar
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