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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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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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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 ...
Aman's user avatar
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4 votes
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Where does this upper bound relating the $T$ count and $H$ count come from?

I am reading this paper on optimisation of the Hadamard gate count (Optimal Hadamard Gate count for Clifford + $T$ synthesis of Pauli rotations sequences). The idea of the paper is to optimise the ...
Callum's user avatar
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Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors

Let's say I have a circuit which contains x number of gates and a machine with quantum volume y, Can I relate x and y somehow to determine if the circuit can be succesfully run on the machine without ...
Vishnu Vardhan's user avatar
13 votes
1 answer
938 views

Does the Quantum Fourier Transform require universality?

Background: In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate. The Eastin-Knill theorem can be ...
Frederik Ravn Klausen's user avatar
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0 answers
38 views

Proof that if W is the image of a Unitary operator with an $n^O(1)$ size quantum circuit, then $R_W$ has an $n^O(1)$ circuit as well

I have been working on the following problem Suppose $H$ is the Hilbert space of n qubits. Let $W_0$ be the subspace of $H ⊗ H$ with basis $|x_0⟩$, x = 0,...,N −1 where $N = 2^n$. Suppose $U$ is a ...
user145282's user avatar
1 vote
1 answer
66 views

Proability of measuing a qubit in a two qubit system without having a perpendicular basis

I am trying to understand how to apply Born's rule on two qubit systems. From class, the teacher told us that we can write the state like so: only if $\theta_0$ and $\theta_1$ are ortogonal. But now ...
Filat Nicolae's user avatar
3 votes
1 answer
146 views

how to construct a ((7,2,3)) code and verify its properties

These two recent papers describe a process to construct (non-stabilizer) codes with "exotic" transversal gates : paper1 paper2 Most of the codes have distance $d=2$ which makes them less ...
unknown's user avatar
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Connection between a Pauli measurement and the corresponding Pauli gate?

Suppose I have a qubit and the ability to act a Pauli $Z$ gate on it. This is a black box that does the phase flip and I don't know how it works on the inside. Can I use this black box to implement a ...
Brendan's user avatar
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1 answer
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How to calculate quantum cost?

In the following two papers: Automatic Synthesis of Reversible Logic Circuit Based on Genetic Algorithm Particle Swarm Optimization based Circuit Synthesis of Reversible Logic a comparison ...
Dona's user avatar
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Is this quantum circuit design more prone to noise?

I am designing a quantum circuit which uses one qubit as the control of many $\text{CSWAP}$ operations. And then, this qubit will be measured. Will the result be more prone to noise since all the ...
Deren  Liu's user avatar
6 votes
1 answer
294 views

Clifford group without the phase gate

The Clifford group is generated by the Hadamard gate $H$, the phase gate $S=\sqrt{Z}$, and the $\text{CNOT}$ gate. I was wondering what happens if we dropped $S$, so that all matrices are real. I ...
Jun_Gitef17's user avatar
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1 answer
82 views

How to Use Stim for Noisy Simulation with Adaptive Circuit and Noise Tracking?

I am trying to learn stim to simulate noisy quantum circuits. My goal is to construct an adaptive circuit in which I can add quantum gates one by one and observe the changes in the circuit's check ...
iknownothing's user avatar
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What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
Mohsen's user avatar
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Two-level unitary gates are decomposed into single-qubit gates and CNOT gates

I am currently studying the following from the book 'QUANTUM COMPUTING: From Linear Algebra to - Mikio Nakahara' and trying to apply it to Qiskit. But there is one point that I don't quite understand....
junghyunHa's user avatar
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1 answer
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How to convert one state of a quantum system to a desired state?

I have a state of 3 qubits: The first number inside the brackets gives the probability of each state, and the second number gives the phase. $$\begin{align} |000\rangle &= (12.5,0^{°}),\\ |001\...
Root Groves's user avatar
1 vote
2 answers
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How to generate the Bell state $\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$ from the state $|00\rangle$ using Qiskit?

I want to generate the Bell state $(|01\rangle+|10\rangle)/\sqrt{2}$ from the state $|00\rangle$ in qiskit, applying the Hadamard gate followed by the $\text{CNOT}$ gate. But it generates $(|11\rangle-...
Xilot Xilot's user avatar
2 votes
1 answer
77 views

The time complexity of quantum circuit

I want to figure out how to evaluate the time complexity of a quantum circuit. An simple understanding is that if there are more quantum gates in a quantum circuit. The time complexity is higher. (...
tangyao's user avatar
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1 answer
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Help with a lemma on the argument of a qubit after transformation

From: King, R. (2023). An improved approximation algorithm for quantum max-cut on triangle-free graphs. Quantum, 7, 1180. I have trouble understanding item 3 of the above lemma. Here $n_k \cdot \...
Matteo's user avatar
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4 answers
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How do I transform a $ZZ$ interaction unitary into a $\text{CZ}$ gate?

I have a unitary gate given as \begin{equation} e^{-i\theta Z \otimes Z} = \cos(\theta)I - i \sin(\theta)Z \otimes Z\,. \end{equation} When I insert $\theta = \pi/4$ I get the maximally entangling, \...
NikNack's user avatar
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2 answers
252 views

What goes above this code fragment?

I have given this circuit: The question goes as follows: What is a code of the above circuit if the barrier is removed? Now I have a code fragment, which is this: ...
Ark Rana's user avatar
2 votes
1 answer
63 views

Under what conditions are two sets of Pauli operators Clifford-equivalent?

Suppose I have two set of $N$-qubit Pauli operators $\mathcal{S} = \{P_1,\ldots,P_K\}$ and $\mathcal{T} = \{Q_1,\ldots,Q_K\}$. In this context, a Pauli operator is a Hermitian element of the Pauli ...
Solarflare0's user avatar
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26 views

How to deal with logical gates which map Logical Paulis to non-Pauli products?

I am trying to figure out the action of logical gates on quantum codes. I am trying to check the logical operations that the logical gate performs on the code. I can do it in simple cases, for example ...
am567's user avatar
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1 vote
3 answers
186 views

Equivalence of quantum circuits

I have these 2 quantum circuits: Are they equivalent?I think they are but I cannot understand how this could be possible.Lets assume that the initial condition of the first circuit is:] Lets assume ...
Root Groves's user avatar
2 votes
2 answers
88 views

Fault Tolerance of 2-transversal gates

Suppose I have a single block $n$-qubit stabilizer code that can correct a weight 1 error (so the distance is $d=3$). If I apply a $1$-transversal gate of the form $U = U_1 \otimes U_2 \otimes \cdots \...
Eric Kubischta's user avatar
5 votes
4 answers
114 views

$U_1\oplus U_2$ decomposable into $I\oplus U$ and 1-qubit gates?

TL;DR Let $U_1, U_2, U$ be arbitrary 1-qubit quantum gates. Can 2-qubit gates of the form $U_1\oplus U_2$ always be decomposed into a combination of controlled gates ($I\oplus U$) and single qubit ...
upe's user avatar
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0 votes
2 answers
72 views

Help finding mistake when modifying $T$ injection protocols

I am a little confused about where I am going wrong when computing the action of the following circuit: My understanding is that the CNOT gate acts on the second qubit as a control and the first ...
am567's user avatar
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3 votes
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71 views

How to perform logical operations between logical qubits in a $[\![8,3,2]\!]$ quantum code?

I have a small question on codes like $[\![8,3,2]\!]$, which encodes physical qubits to multiple logical qubits. How do we perform logical operations in between these logical qubits? Of course, if I ...
AndyLiuin's user avatar
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1 vote
1 answer
196 views

Quantum Circuit evaluation Qiskit vs. AWS Braket SDK

I am examining a simple circuit using both Qiskit and the AWS Braket SDK (Python). The circuit is very simple. ...
badgerduke's user avatar
4 votes
1 answer
153 views

Can you decompose a 4-qubit Toffoli gate (CCCX) into basic gates without an ancillary state?

I have a problem relevant to the circuit depth of a $\text{CCCX}$ gate, but I can't find any literature on decomposing this gate into basic gates without an ancillary qubit. Is this possible, and are ...
Braedin Tabler's user avatar
1 vote
1 answer
71 views

How many gates are necessary to implement an arbitrary n-qubit permutation unitary?

How many gates are necessary to implement an arbitrary n-qubit permutation unitary, using only 1- and 2-qubit gates? An n-qubit permutation unitary is a $2^n$ x $2^n$ unitary matrix where each entry ...
QNA's user avatar
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0 answers
48 views

How to decompose a permutation matrix into two-level unitary matrices?

Assume a have a SBox and want to make quantum circuit for it. The unitary transform matrix for a SBox is special - a permutation matrix. I found an algorithm to decompose any unitary matrix into two-...
Huy By's user avatar
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4 votes
1 answer
175 views

Is it possible to implement the controlled-S gate, such that the inner gate between the CNOTs belongs to the Clifford?

It's well known how to implement a controlled-U gate when $U$ is a single qubit gate via the decomposition of $U$ into the product $U=e^{i\phi}AXBXC$ where $ABC=I$. My question is: is it possible to ...
Dudu Ponar's user avatar
3 votes
1 answer
110 views

Is it possible to decompose a controlled gate with control qubit in the $|+\rangle$ state?

$\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}$ Given a quantum circuit with 2 qubits that executes a controlled gate $CU$ where the control qubit is in the $\ket{+}$ state, ...
upe's user avatar
  • 311
1 vote
1 answer
134 views

What is the formula for the matrix representation of a general controlled gate?

Suppose I have $n$-qubit circuit. I have a single-qubit gate (e.g. a Pauli gate) at qubit $a$ and it is controlled by the qubit $b$. What is the matrix representation for this controlled gate? The ...
user1747134's user avatar
1 vote
1 answer
56 views

Circuit equivalence for cotrolled-controlled-$R_y$ gate

Could someone explain the following equivalence to me? I can build an example for the case when the first two lines of qubits are equal to 1. However, what happens if they are both equal to 00, 01 or ...
aghin's user avatar
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1 vote
0 answers
23 views

Implementing scalar multiple of a polynomial using quantum signal processing

Let $p(x)$ be a degree $d$ polynomial such that $|p(x)|\leq 1$ for $x \in [-1,1]$. Assume I have constructed a quantum circuit, $V(x)$, that implements $p(x)$ in the upper left entry of a $2$ by $2$ ...
user82261's user avatar
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-3 votes
1 answer
73 views

How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$

Suppose you have a qudit with $n$ decoherent states. How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$
Root Groves's user avatar
3 votes
2 answers
51 views

Why is the linear combination of Pauli matrices $G =I-XX-YY-ZZ$ PSD?

Define $$G = I \otimes I - X \otimes X - Y \otimes Y - Z \otimes Z,$$ where $X,Y$ and $Z$ denote the Pauli matrices, and $I$ the identity. I can plug this matrix in my computer and note that $$G = \...
Matteo's user avatar
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2 votes
2 answers
100 views

How is involution defined for qudit gates?

A gate is involutory if $G^{2}=I$. This is true for all Pauli gates. Does the definition change if it is a gate for qutrits and beyond? Is there a good article for this?
Root Groves's user avatar
1 vote
0 answers
56 views

Transversal CNOT implementation on stim

Re: a recent paper on the arXiv, Correlated decoding of logical algorithms with transversal gates (https://arxiv.org/abs/2403.03272). As MWPM (pymatching and stim) cannot handle errors that flip more ...
user avatar
4 votes
1 answer
207 views

Why do we have an infinite number of possible quantum gates?

This question came to me during an online lecture by Prof. Nike Dattani, he mentioned that we have "an unlimited number of quantum gates". Simply my question is: why do we have an unlimited ...
JaafarMehrez's user avatar
6 votes
0 answers
47 views

Resources on the energy consumption of IBM quantum computers?

I am seeking information regarding the energy consumption of IBM Quantum Computers, specifically inquiring about the energy requirements associated with individual gate operations. Could you also ...
goga suknidze's user avatar
0 votes
1 answer
123 views

What are the quantum gates necessary for universal quantum computation?

I recently have gained an interest in quantum computers and quantum computation, and I was wondering, what is the minimum number set of quantum gates that allow for arbitrary quantum computation?
Steve Mucci's user avatar
4 votes
1 answer
70 views

Show that conjugating $\text{CNOT}$ by $H\otimes H$ exchanges control and target qubits

I have gotten so far to show that $$(H⊗H)\text{CNOT}(H⊗H) = (H⊗I)CZ(H⊗I)\,.$$ How do I proceed from here in first proving the identity and then using the identity to show that on the dual basis, when $...
Aparna Gupta's user avatar
1 vote
1 answer
63 views

Converting $H$ gate to $R_x$ and $R_z$

EDIT: My solution is supposed to work for $|1\rangle$ state too. See https://imgur.com/a/7F1cHu4 Right of the bat the answer is $$H=R_z(\pi/2)R_x(\pi/2)R_z(\pi/2)\,.$$ My question is, I cannot reach ...
Minh Triet's user avatar
2 votes
1 answer
231 views

Qiskit Runtime forbids reset gate?

Some parts of my quantum circuit uses initialize to prepare specific amplitudes to the qubits. However, the Qiskit Runtime outputs error: ...
Deren  Liu's user avatar
1 vote
0 answers
55 views

Clarification on Matrix Representation of a Quantum Gate

I came across a matrix representation in my quantum computing studies and I'm seeking clarification on its interpretation. The matrix I encountered is: $$\left[\begin{matrix} 1 - i & 0 & 0 &...
user29259's user avatar
2 votes
2 answers
106 views

How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

Let $G=([n],E)$ be an undirected graph, which is represented by a $n \choose 2$ bit string, by indicating for each $i < j$ if $(i,j) \in E$. We also denote the state $| G \rangle$ as the $n \choose ...
Gabi G's user avatar
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2 votes
1 answer
126 views

Is it possible to modify the QFT circuit to use only 1-qubit gates?

[Measured Quantum Fourier Transform] I've recently learned the Quantum Fourier Transform, and was shown its circuit. The circuit I've seen is composed of Hadamard gates and controlled Rotation gates. ...
Gabi G's user avatar
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