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.
1 vote
1 answer
45 views

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,...
3 votes
0 answers
131 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 ...
3 votes
2 answers
132 views

Is there a function in qiskit that allows me to insert quantum gates at certain indices of a circuit?

Here's my quantum circuit with mid-circuit measurements: ...
1 vote
2 answers
44 views

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 ...
2 votes
1 answer
37 views

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?
8 votes
2 answers
714 views

Is the Kraus representation of a quantum channel equivalent to a unitary evolution in an enlarged space?

I understand that there are two ways to think about 'general quantum operators'. Way 1 We can think of them as trace-preserving completely positive operators. These can be written in the form $$\...
2 votes
1 answer
50 views

What are the "higher moments" of the gate fidelity?

Reading the paper Gate fidelity fluctuations and quantum process invariants I came across the concept of higher moments of the gate fidelity, for example in the following excerpt from the introduction:...
5 votes
3 answers
3k views

What does quantum gate fidelity mean?

The formal definition states that it's the distance between two quantum states. What does that mean experimentally? Does distance here mean the distance between two states on the Bloch Sphere? I am a ...
0 votes
1 answer
79 views

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 ...
1 vote
1 answer
32 views

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 ...
1 vote
0 answers
33 views

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\...
1 vote
1 answer
76 views

How to implement *nested* Grover search (in Quirk)?

$\newcommand{\ket}[1]{|#1 \rangle}$ $\newcommand{\bra}[1]{\langle #1 |}$ PS: I suppose this question could also ask "How to implement $2 \ket{s}\bra{s} - I$ for any (identifiable) $\ket{s} \in \...
1 vote
0 answers
35 views

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 ...
0 votes
2 answers
51 views

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\...
3 votes
0 answers
78 views

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,...
4 votes
2 answers
77 views

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
3 votes
2 answers
86 views

What is the name of this "ancilla based" process to implement gates

I just want to know if there is a specific name for the implementation of a gate on the top qubit with the help of the bottom qubit, represented on this image: It looks like gate teleportation but it ...
1 vote
1 answer
53 views

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 ...
0 votes
1 answer
44 views

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 ...
1 vote
1 answer
53 views

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 ...
1 vote
1 answer
27 views

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 ...
5 votes
1 answer
723 views

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 ...
0 votes
2 answers
70 views

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 ...
3 votes
2 answers
171 views

In the Bernstein-Vazirani circuit, if the secret is all 0s, would the oracle just be nothing?

I'm self-studying quantum computing and have gone through the Wikipedia article on the Berstein-Vazirani algorithm and believe that I understand it. I'm looking to verify my understanding and hope ...
3 votes
2 answers
606 views

What gate combinations create entangled two-qubit states?

I know that in order to make a two quit entangled state, this quantum circuit is used: But I was wondering if there are any other gate combinations which also create entangled two quit states. If ...
2 votes
2 answers
86 views

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 ...
2 votes
0 answers
44 views

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 ...
2 votes
1 answer
36 views

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 $n$?
0 votes
1 answer
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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 ...
1 vote
1 answer
45 views

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 ...
1 vote
2 answers
130 views

Angle in qiskit

I have been working on Qiskit. Is it possible to display just the angle of each gate in a circuit as an output? For example, if the below code is my circuit is it possible to just print the angle of ...
0 votes
1 answer
60 views

Qiskit TwoQubitBasisDecomposer - how to properly decompose gates?

I'm new with Qiskit and I'm struggling with creating my own controlled gates. I'm trying to create a ZYZ decomposition of a controlled unitary gate I created. I'm trying to use the method ...
1 vote
1 answer
92 views

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 ...
4 votes
2 answers
830 views

Question About How Qiskit Reset Gate Affects Other Entangled Qubits

I am trying to understand how the reset gate in Qiskit affects qubits its entangled with. Consider the following circuit with qubits $q_0$ and $q_1$: Where circuit240 takes $|0\rangle$ to $a|0\rangle ...
7 votes
1 answer
184 views

Is the Clifford group a semidirect product?

This is from Is the Clifford group finite? "Define the Clifford group $ \mathrm{Cl}_n(p) $ of n qudits of prime dimension p as the unitary normaliser of the generalised Pauli group. Define the ...
1 vote
2 answers
313 views

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 ...
2 votes
1 answer
72 views

Duration of single qubit gate in IBM

how can we calculate the duration of single qubit gate using Qiskit in IBM? In other words if I have to insert a delay in the place of the single qubit gate, how would I know how much delay in ...
1 vote
1 answer
57 views

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} ...
0 votes
1 answer
28 views

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 ...
2 votes
1 answer
38 views

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 ...
4 votes
1 answer
50 views

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 ...
0 votes
1 answer
44 views

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 ...
1 vote
1 answer
41 views

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 ...
4 votes
2 answers
144 views

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 $$\left|\phi'\right>=\frac{1}{|{\rm norm}|}\sum_{i}\left|a_i,x_i\right>,$$...
2 votes
1 answer
39 views

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(...
11 votes
1 answer
3k views

General parametrisation of an arbitrary $2\times 2$ unitary matrix?

Following is an excerpt from QCQI: I can understand that this matrix satisfies a unitary matrix. Also, intuitively, I am able to understand it. However, what is the proof that any given Unitary ...
2 votes
1 answer
185 views

How fast is qiskit to_gate() method, which is used to convert circuit to gate?

I have prepared a quantum circuit, which is using 13 qubits. Now, I am converting this circuit to gate but it is taking around avg. 35s for conversion. It would have have been fine, if I require only ...
1 vote
1 answer
547 views

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 ...
2 votes
2 answers
60 views

IBM Quantum Experiment CNOT

I have a beginner question regarding CNOT-Gates on IBM Quantum. Assuming the following simple circuit: ...

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