Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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Can W gate be written only using H,T?

I want to write the decompose the gate $W=(X+Y)/\sqrt{2}$ using only $H$ and $T$ (and all the derived Clifford gates basically). I know $H=(X+Z)/\sqrt{2}$ is it possible to obtain exactly $W$ from ...
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Some of the qubits are not evaluated at Qiskit

When I implement a 3-qubit circuit in Qiskit, circuit is executed smoothly at the simulator but counts I read back as results does not contain all of the qubits that are defined and included in the ...
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PhD topics in quantum computing [closed]

I am looking for PhD topics in quantum computing related to computer Engineering background (I don't have a background in physics). I tried searching for Machine learning, neural networks and Quantum ...
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Qiskit: How to implement a classical function?

I'm quite lost, I have to implement the following function with qiskit $$ f(x,y,z) = (\lnot x \land y \land z) \lor (x \land \lnot y \land z) $$ but how can we do that ? I don't understand how to do ...
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Are there hardware platforms that natively implement parametric two qubit gates?

For example, is it possible to implement RXX gate with an arbitrary angle on an ion computer in a single native operation? The RXX gate with an arbitrary angle can be decomposed into two RXX gates ...
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Reshaping the 4x4 CNOT gate into 2x2x2x2 in a tensor network

I'm learning how to perform tensor network contraction for simulating a quantum circuit by looking at the documentation for the JET simulator: link. Specifically, I'm trying to do all the calculations ...
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How to calculate eigenvalues by phase estimation?

I have been learning Quantum PCA recently but I came across a problem. How can I get the eigenvalues of a matrix by phase estimation? And what on what kind of matrix can we implement this algorithm?(...
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What role does Landauer's principle play in quantum reverisbility?

In section 3.2.5 of Nielsen and Chuang (starting page 153) they talk about Landauer’s principle, where they discuss the lower bound on the thermodynamic cost of erasing information. In irreversible ...
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Converting data into a SHA256 hash using Qiskit quantum computer

I was wondering how can we convert data into a hash using Qiskit quantum computer? e.g, this code below will generate a SHA256 hash based on random data. ...
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3 votes
2 answers
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Is a "Bell measurement" equivalent to a projective measurement in a different basis?

Let \begin{align} H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1\end{bmatrix}\in M_2(\mathbb C), \quad \mathrm{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 &...
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How to calculate parameters of U3 gate from a certain quantum state?

I'm trying to do Quantum PCA but I came across a problem. I now have a quantum state, say $\frac{|00\rangle+|01\rangle+|11\rangle}{\sqrt{3}}$ and I want to know how to prepare it from two $|0\rangle$ ...
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Why can the CNOT representation $e^{i\frac{\pi}{4}\left(I-Z\right)\otimes\left(I-X\right)}$ hardly be found in books?

The CNOT gate is usually written as $|0\rangle\langle0|\otimes I + 1\rangle\langle1|\otimes X$ (with $X,Y,Z$ being the Pauli Basis and $I$ the Identity). I have yet to stumble across the ...
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Computing characteristic polynomial of unitary operation

I am trying to replicate a calculation from the linked paper but I am unsure if I understand their math. A locally invariant function defined as the characteristic polynomial is as follows: $$F_U(t) = ...
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1 answer
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How to retrieve a quantum state after passing through a series of quantum gates?

Consider a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ Now if i pass this through a series of quantum gates or any typical ...
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Can I Convert a Qubit in complex form to polar form?

Let's say I have a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ Can I able convert this to polar form $$|\psi \rangle = \cos\...
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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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1 vote
1 answer
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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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1 vote
1 answer
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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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1 vote
1 answer
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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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0 votes
2 answers
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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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1 vote
1 answer
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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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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 ...
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1 answer
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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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2 votes
1 answer
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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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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(...
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2 votes
1 answer
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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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1 vote
1 answer
58 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} ...
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4 votes
1 answer
62 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 ...
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2 votes
2 answers
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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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1 vote
1 answer
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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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4 votes
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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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2 votes
0 answers
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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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2 votes
2 answers
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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 ...
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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 ...
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1 vote
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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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