Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
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How does an $\sqrt{X}$ error propagates through an $T$ gate?
I wonder whether there is a compact way of describing a noise $\sqrt{X}$ propagating through a $T$ gate. Possibly in terms of Pauli and/or Clifford operators.
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Multi qubit states and the CNOT gate
I'm stuck on this passage from a book:
Suppose we try to copy a qubit in the unknown state $|ψ\rangle =
a|0\rangle + b|1\rangle$ in the same manner by using a $\text{CNOT}$
gate. The input state of ...
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Can you construct a 3-qubit XOR state?
I'm wondering if it is possible to build a 3-qubit quantum circuit that creates the following pure state: $$\frac{1}{2}\left(|000\rangle+|011\rangle+|101\rangle+|110\rangle\right)=\frac{1}{2}\left[1,0,...
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How does the Pauli Y gate act in the $|+\rangle, |-\rangle$ basis?
The X gate in the $|+\rangle$, $|-\rangle$ basis becomes the Z gate and vice versa.
What is the Pauli Y gate as a matrix transformation in the $|+\rangle$, $|-\rangle$ basis?
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Is there the number of CNOT restriction?
I know that there is connectivity restriction when implementing physical CNOT gate.
But, I wonder if there is a limit to the number of physical CNOT gates that can be performed at the same time.
For ...
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I have question about cost of 'modular multiplication unitary' in Shor's algorithm
Here modular multiplication unitary means $U_a : |s\rangle \to|as\mod N\rangle$.
My main question is, can the modular multiplication unitary $U_a$ can be constructed in time polynomial in the number ...
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Slight issue with QFTing two qubits
Let's consider two qubits and the corresponding computational basis $\{|0\rangle\, |1\rangle, |2\rangle, |3\rangle\}$. In binary form, any of these vectors can also be written as a product $|x_1\...
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How to simulate $H(\theta) = B(\sin\theta S_1^x +\cos\theta S_1^z +\sin\theta S_2^x +\cos\theta S_2^z)+aS_2^zI_z$ on IBM Qiskit
I am trying to simulate this Hamiltonian on IBM Qiskit, for varying values of $\theta$:
$H(\theta) = B(\sin\theta S_1^x +\cos\theta S_1^z +\sin\theta S_2^x +\cos\theta S_2^z)+aS_2^zI_z$
Where S is ...
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What is the correct name of this quantum gate? Possibly state control gate
Let $\vec v \in \mathbb{C}^2 $ be the following quantum state:
$$
\vec v = \frac{1}{\sqrt{2}}\begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix},\space \lvert v_1 \rvert = 1,...
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math behind rotation gate
$R_Z(\theta) = e^{-i\frac{\theta}{2}Z}$ and $R_{ZX}(\theta) = e^{-i\frac{\theta}{2}XZ}$
My question is, why is the rotation gate defined in an exponential format? Where does the $\frac{1}{2}$ come ...
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Gate times for photonic quantum computers
I am trying to understand the landscape of one- and two-qubit gate times for various quantum computing architectures. It is not so hard to find gate times for various gates such as Hadamard, CNOT and ...
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Is 60% accuracy high when calculating 1+1 on a quantum computer?
A financial firm has criticized the quantum computer of a company called IonQ.
Part of the content is that IonQ's quantum computer is only 60% accurate for 1+1 calculations, and only 50% for 2+3 ...
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Counting the number of CCX and CX gates in controlled modular addition
If we do a controlled modular addition of an adder with 2n ccx and 4n cx gates for example the CDKMRippleCarryAdder, what will be the resultant count of ccx and cx ...
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How do I generate gates for qudits with $d=4$?
So I was working on a project with qudits (specifically d = 4) and came across a problem. How do I generate gates for these? I can construct Hadamard and X gates for these, but how does one approach ...
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What is the average amount of gates needed to implement a random Clifford gate?
Given a Clifford gate acting on $n$ qubits is implemented using its generators, what is the average number of gates needed to implement a random Clifford gate as a function of $n$?
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Create a 2-qubit quantum circuit with given state probabilities
Let's say we are given two probability values $p_1 > 0$ and $p_2 > 0$, with $p_1+p_2 \leq 1$ but not necessarily equals to $1$. We are asked to create a 2-qubit quantum circuit with state $|01\...
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Rxx gate as a set of rotations
I'm trying to represent Rxx gate as a set of physical rotations of two qubits in 3D space (or as rotations of Bloch Spheres that is the same). In some simple cases it works well:
If q0 is in the ...
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Sending messages via CNOT gates
Consider a situation in which each of Alice, Bob and Charlie holds a qubit,
where the three qubits are acted on by a 3-qubit gate $U$. Assume that the gate $U$ can
be implemented by first performing a ...
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Qiskit library.gaussian() does not accept parametric expression
I'm trying to build a gaussian pulse in qiskit where I keep the amplitude as a parameter but for the followig code
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Quantum gates defined in SpinQ desktop computers
There is manufacturer of desktop quantum computers:
https://www.spinquanta.com/products.
There are few models on the market:
Gemini
Gemini-Mini
Triangulum
Lyra
Does anyone know where to find quantum ...
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Can anybody explain the following circuit?
I think I understand what it does. But i can't agree with output for sertain inputs. For example: if a=1 and b=1 then how the output on 4 line could be xor(a, b). Because as far as I know xor(1,1)=0 ...
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Generating a random 32-byte hex integer using Qiskit
Hello I posted here yesterday about generating random 16 digits using Qiskit, and a gentle guy helped me but how about a string? How can I generate random 256 bit key in hex format in a superposition ...
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Question about mock backends!
I recently learned about the mock backends or the fake backends provided by Qiskit and I was wondering, do they behave the same way IBMQ systems backends like (ibmq_brooklyn)? also, can I depend on ...
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Generating a random 16-digits in a superposition state using Qiskit
Im trying to create a script using Qiskit for a days but somehow i couldn't seem to get it done!! Im new to QuantumComputing, so pardon me if i don't explain something properly. I need to create a ...
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Quantum gates for more than two basis states
Lets say I have a time dependent hamiltonian of the form $$H(t) = H_0 + f(t) H_{drive}$$ (where $H_0$ may represent the hamiltonian for a superconducting qubit) and I want to find the optimal pulse $f(...
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How does a quantum computer find the correct password faster than classical computers using brute-force?
I didn't get this part right! For example, we have an online box with a 16-digit password, and we don't know what the password is! How can a quantum computer find the correct password faster than ...
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Grover's Search Number of iterations for M > 1
In Grover's Search algorithm, how to determine the number of iterations for any $M$ such that $1 < M < N/2$?
The calculations given in the Nielsen and Chuang book say that $R \leq \frac{\pi}{4} ...
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There exists an efficient gate that swaps values of different superposition kets?
Is there an efficient gate that swaps values of different superposition kets?
Let $ \alpha_i, \beta_i $ be string in $ \{0,1\}^n$, I'm wondering if there are a known results about the existence of ...
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IBM Quantum Experiment CNOT
I have a beginner question regarding CNOT-Gates on IBM Quantum.
Assuming the following simple circuit:
...
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What is the time overhead for fault-tolerant gate teleportation?
The gate teleportation protocol (https://arxiv.org/abs/quant-ph/9908010) has a step where it utilizes cat state measurement of transversal operators. Since cat states can not detect phase errors it is ...
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Is there a way to convert a superposition $\sum_i a_i |x_i\rangle$ into $\sum_i |a_i,x_i\rangle$?
I am wondering if there is a way to convert a superposition $$\left|\phi\right>=\sum_{i}a_i\left|x_i\right>$$ into $$\left|\phi'\right>=\frac{1}{|{\rm norm}|}\sum_{i}\left|a_i,x_i\right>,$$...
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What is a realistic model for simulating physical tampering of a channel? (ex: nearby vibrations)
Somewhat related to this question.
Imagine a fully functioning quantum network, where qubits are transported via fiber optic cable. If vibrations were to physically tamper with a channel in such a ...
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Why does gate teleportation allow to implement nonlocal operations via local ones?
In (Gottesman and Chuang 1999), when discussing quantum gate teleportation, they mention how it can be used to implement nonlocal gates such as a CNOT, by only using (classically controlled) local ...
glS♦
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How does quantum gate teleportation differ from state teleportation?
As described e.g. in this post, quantum gate teleportation can be framed as a variation of quantum state teleportation where a gate is applied beforehand on the receiver, and this results in the final ...
glS♦
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Manually calculating quantum circuit with custom gate
I am trying to calculate the state of this Quirk circuit by hand:
where U is a custom gate with 2x2 matrix:
From what I've read, I should be able to calculate the resultant amplitudes as:
(U⊗I⊗I).(...
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Given a non-Clifford quantum circuit $U$, is it possible to construct a commuting Clifford circuit $C$?
Given a non-Clifford circuit $U$, say $U = \prod_{i=1}^k e^{i \theta_i P_i} $ for $P_i \in \{ I,X,Y,Z\}^{\otimes n} $ and $\theta_i \in \mathbb{R}$.
Is it possible to construct a non-trivial Clifford ...
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Is the Eastin-Knill Theorem incorrect?
I am reading through this paper (the Eastin-Knill Theorem) and there is a step in the proof of the main theorem that I do not understand.
Let $Q$ be a composite quantum system supporting a quantum ...
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What’s the proper gate use for the following code? (Python)
I am trying to find a proper way to write a code that will give me the resulting quantum state $i|10\rangle$ using qiskit in Python (using Jupiter notebook). I think I have figured out that the ...
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State Initialization of quantum circuit
I am trying to understand how to initialize a quantum circuit with classical input. By browsing on the internet, I came to the conclusion that there are some fixed circuits which can be used to ...
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Is there a way to rotate an unknown state towards another known state?
I would like to rotate my $|\Psi\rangle$ state towards $|1\rangle$:
$$ |\Psi\rangle= a|0\rangle + b|1\rangle \ \rightarrow \ |\Psi'\rangle= a'|0\rangle + b'|1\rangle$$
with $|a'| < |a|$, $|b'| > ...
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Standard name for CZ gate conjugated by Hadamards?
Is there a standard name for a $CZ$ gate conjugated by $H \otimes H$ gates? See below for circuit
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Direction of rotation operators
The rotation operators for a single qubit are defined as $R_{v}(\theta) = e^{-i \theta X/2}$, with $v \in \{ X,Y,Z\}$. If we look at the direction of rotation of $R_v$ w.r.t. the positive eigenvalue, ...
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What justifies using tensor product of matrices for parallel gates when applying them to an entangled state?
In my university we defined tensor product of two matrices $A$, $B$ as a matrix $A \otimes B$ such that for any vectors $\left| \phi \right>$, $\left| \psi \right>$ the following is satisfied:
$$...
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Does the CX gate always leave the first qubit unchanged and swap the amplitudes of the second one?
I'm a self-learner of quantum computing and is at the very beginning. I do have some math and coding background though. I'm trying to understand how working with entangled qubits helps performing ...
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Is there relation between IonQ native gates and the rotation gates $R_x$, $R_y$, $R_z$? [closed]
I know $GZ = R_z$ and $XX = MS$ but what about $GPI$ and $GPI2$?
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How to extract solution from HHL statevector on qskit?
I want to extract the HHL solution from the StateVector.
I am doing this on a $4\times4$ matrix. For a $2$ by $2$ the solution is available in the StateVector $8$, $9$. However for a $4$ by $4$ matrix ...
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Local Hermitian operators can be written as sums over local error operators?
In this paper, near the bottom of the left half of page 3, the authors claim that any local Hermitian operator (one which acts only on a single subsystem of a larger composite system) can be expressed ...
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Quantum Gate - Negating qubit whose state is known to lie in the equatorial x-y plane
Given a qubit whose state is known to lie in the equatorial x–y plane in the
Bloch sphere is it possible to find a quantum gate that will always negate this qubit?
If so, exhibit such a gate. If not, ...
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How can I solve problems with quantum computers ? (Methodology)
I am reading these days a book about programming quantum computing using the language Silq. I reached half the Silq book. The good thing about the Silq book is that it teaches the mathematics of ...
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Is there a way to map the Cu3 gate to represent a unitary matrix whose elements are complex in nature
I have this 2*2 unitary matrix one looks like
U =[ -0.2840 - 0.5319i, -0.0000 - 0.7978i; -0.0000 - 0.7978i ,-0.2840 + 0.5319i]
I want to represent this unitary matrix by a CU3 gate which looks like
...
