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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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Do all physical architectures for quantum computers use the same universal gate sets?

Now I have understood that physical implementation of quantum computer need a universal quantum gate set like Clifford+T to realize any unitary quantum gate. However, I don't know if it is all the ...
Henry_Fordham's user avatar
4 votes
1 answer
3k views

How is data encoded in a quantum neural network?

I am a newbie to quantum machine learning. I am trying to build a quantum neural network (QNN). What I studied so far about QNN is that input would be qubits and hidden layer parameter can be set ...
Muhammad Kashif's user avatar
4 votes
2 answers
3k views

Measuring T1 and T2 constants on IBM Q

We have been asked to measure relaxation and dephasing times T1 and T2 on the IBM Q using the composer only, Qiskit not allowed. I am a bit confused about the way to do so. Can someone explain the ...
Aviv Azran's user avatar
4 votes
1 answer
149 views

types of states that can be created with a given number of entangling gates

I want to know if it is possible to say something in general about the "richness" or "complexity" of quantum states that can be created using a given number of entangling 2-qubit ...
Lior's user avatar
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Is the cost Hamiltonian unitary in QAOA?

I am trying to implement QAOA and there are things I don't understand at all. The expansion of $H$ into Pauli $Z$ operators can be obtained from the canonical expansion of the cost-function $C$ by ...
Himera Ephemera's user avatar
4 votes
2 answers
148 views

Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?

I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits. Is there an example of a quantum algorithm that is better than it's classical ...
Pranav Jain's user avatar
4 votes
1 answer
337 views

How to interpret the matrix representation of a quantum gate?

I am trying to understand how the quantum gates work, so I started with the simplest one, the Pauli X gate. I get that it turns $|0\rangle$ into $|1\rangle$ and $|1\rangle$ to $|0\rangle$. So my ...
Aleksandar Kostovic's user avatar
4 votes
1 answer
2k views

How to prove universality for a set of gates?

Which of the following sets of gates are universal for quantum computation? {H, T, CPHASE} {H, T, SWAP} And how do we prove it?
hey0god's user avatar
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3 answers
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Creating a parameterized Operator in Qiskit

I'm trying to run a VQE for a specific custom Anzats. The Anzats is built up of an unitary matrix $U_H$, which I'm trying to created in this way: ...
Paco Bontenbal's user avatar
4 votes
2 answers
1k views

Why isn't the circuit performing a measurement in the Bell basis?

Nielsen and Chuang (on page 188 exercise 4.33) says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how. The matrix representing the ...
bilanush's user avatar
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Is there a higher dimensional Fredkin gate?

The Fredkin gate is CSWAP gate. Given a control register in $0$ or $1$, the gate does nothing or swaps two target registers respectively. Is there a higher dimensional version of this gate? I have ...
user1936752's user avatar
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How are two different registers being used as "control"?

On page 2 of the paper Quantum Circuit Design for Solving Linear Systems of Equations (Cao et al.,2012) there's this circuit: It further says: After the inverse Fourier transform is executed on ...
Sanchayan Dutta's user avatar
4 votes
1 answer
107 views

Does every code have a strongly transversal Pauli group?

A transversal logical gate for an $ n $ qubit code is a gate from the group of local unitaries $$ \bigotimes_{i=1}^n U(2) $$ which also preserves the codespace. For an $ ((n,K,d)) $ code we say a ...
Ian Gershon Teixeira's user avatar
4 votes
2 answers
754 views

Why can't a fanout be made with a CNOT gate?

I know this question has been answered here, but the answers leave some things confusing to me. When broken down (and used to calculate), the idea that the states are entangled doesn't seem to be ...
SpaceChicken's user avatar
4 votes
2 answers
740 views

Generate a 3-qubit SWAP unitary in terms of elementary gates

I wish to generate the following unitary ...
LOC's user avatar
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1 answer
341 views

How to create an $n$-qubit normally controlled gate?

Suppose I have a quantum gate $U$ and it's a controlled gate. In particular, I have a $2\times 2$ matrix formulation of the gate's action on 2 adjacent qubits. How can I make this work on an $n$-bit ...
Isky Mathews's user avatar
4 votes
1 answer
914 views

Implementing a complex circuit for a Szegedy quantum walk in qiskit

Problem definition I'm implementing a quantum circuit in qiskit for a Szegedy quantum walk, (reference, Fig 21.). It uses two registers of dimension $N$ ($N=3$) each one. The challenges I'm facing are:...
German Alamilla's user avatar
4 votes
1 answer
408 views

Square root of NOT as a time-dependent unitary matrix

I want to express the square root of NOT as a time-dependent unitary matrix such that each $n$ units of time, the square root of NOT is produced. More precisely, I want to find a $U(t_0,t_1)$ such ...
Alejandro Díaz-Caro's user avatar
4 votes
1 answer
345 views

What applications does the quantum gate [(i,1),(1,i)] have?

I've been working through the great introduction to quantum computing on Quantum Country. One exercise there is to find a possible quantum gate matrix that is not the $X,I$ or $H$ matrix. I thought ...
dv02's user avatar
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3 answers
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Is every single-qubit unitary just a rotation around some unit vector on the Bloch sphere?

I remember reading this somewhere... Is there an elegant proof for this?
Quantum Guy 123's user avatar
3 votes
1 answer
241 views

Is the square-root-of-SWAP for a pair of 4-dimensional qudits isomorphic to two square-root-of-SWAPS for two pairs of qubits?

This may be a very naïve question indicative of a lot of confusion, but I am trying to understand more about Hamiltonian simulation. I'm starting to intuit that the $n^{th}$-root-of-SWAP acting on a ...
Mark Spinelli's user avatar
3 votes
1 answer
469 views

How to use Cirq to transpile circuit to custom native gate set?

I am trying to use Cirq to compile arbitrary quantum circuits to custom native gate sets, e.g., to use the Cirq compiler to generate quantum circuits for different quantum computers (IBM, Rigetti, ...
nils's user avatar
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2 answers
404 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 ...
glS's user avatar
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Where can I find a comprehensive list of gate decompositions used by transpilers?

Does anyone know of a web site, paper etc. that has a list of "gate decompositions" e.g. the kind of decompositions that occur when the transpiler decomposes non-native gates to native gates....
John's user avatar
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1 answer
141 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
  • 2,187
3 votes
2 answers
203 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 ...
Marco Fellous-Asiani's user avatar
3 votes
3 answers
282 views

Matrix representation of the qutrit gate analogous to Pauli-$X$ gate

What is the qutrit gate analogous to the $X$ gate for qubits, i.e. NOT gate? and what is the matrix representation of that gate? I have searched on the Internet but couldn't find anything related. ...
Root Groves's user avatar
3 votes
2 answers
313 views

Which gate set should be used when I measure the depth of a circuit?

I want to measure the depth of a circuit, but I do not know which quantum gates should be used when the circuit is decomposed. For example, $ZZ$ rotation (i.e. $e^{i\theta \sigma_z^i\sigma_z^{i+1}}$) ...
sotowa's user avatar
  • 131
3 votes
2 answers
726 views

Computing expectation value of $|\langle z|C|0^n\rangle|^2$ over Haar random circuit

I am trying to understand the integration on page 4 of this paper. Consider a Haar random circuit $C$ and a fixed basis $z$. Each output probability of a Haar random circuit (given by $|\langle z | C |...
BlackHat18's user avatar
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3 votes
1 answer
494 views

Can we understand multi-qubit gates in terms of rotation groups?

I'm trying to reconcile (i) the statement that swapping two subsystems constitutes a rotation by $2\pi$ and (ii) the angle that is implied by the Hermitian generator of a SWAP gate. I haven't tracked ...
forky40's user avatar
  • 7,073
3 votes
2 answers
205 views

Expressing CNOT in the eigenbasis of $X$ (Preskill lecture notes eq. 7.6)

In chapter 7, equation 7.6 says CNOT works as follows: CNOT: $\frac{1}{\sqrt{2}} (|0\rangle + |1\rangle )\otimes |x\rangle \rightarrow \frac{1}{\sqrt{2}} (|0\rangle + (-1)^x |1\rangle ) \otimes |x\...
Blackwidow's user avatar
3 votes
2 answers
188 views

Minimal quantum OR circuit

The quantum OR circuit between $|a\rangle$ and $|b\rangle$ can be made out of 1 Toffoli and 2 CNOT gates, 1 ancillary qubit. Is there any other implementation? Or is this the minimal in the sense of ...
Upstart's user avatar
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3 votes
1 answer
581 views

How does the cnx gate work in Qiskit (Python)?

Could somebody explain the cnx operator, and how it operates on its qubit parameters to flip the target qubit in Qiskit (Python)?
user1319236's user avatar
3 votes
4 answers
222 views

Can you use Rz to flip from $|+\rangle$ to $|-\rangle$?

Here's the Rz matrix: $$ Rz(\theta) = \begin{bmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{bmatrix} $$ As I understand it, Rz rotates around the Z axis on the Bloch sphere. Since $|+\...
ahelwer's user avatar
  • 4,138
3 votes
1 answer
1k views

What is the connection between $RX$ gates and $X$ gates (similar for $Y$ and $Z$)?

I am new to quantum gates but do not understand the connection between the $RX$ and $X$ gates. I know that $$R X(\theta)=\exp \left(-i \frac{\theta}{2} X\right)=\left(\begin{array}{cc} \cos \frac{\...
Jason Fring's user avatar
3 votes
1 answer
2k views

Transforming the first Bell state into the other Bell states

As I understand it, you can transform the different Bell states into one another by applying various gates. Wikipedia has the Bell states written out as follows: And says that you can generate bell ...
Yuerno's user avatar
  • 309
3 votes
3 answers
1k views

How can we construct a square root of NOT gate in Qiskit and IBMQ circuit composer using universal gates?

I have tried it with decomposing controlled S then conjugating with H gate. But I want to construct it using a minimum number of gates.
jayanti singh's user avatar
3 votes
2 answers
477 views

How can I find a quantum channel connecting two arbitrary quantum states?

Given two arbitrary density matrices $\rho, \sigma\in \mathcal{H}$ (they have unit trace and are positive), how do I go about finding a possible quantum channel $\mathcal{E}$ such that $\mathcal{E}(\...
Confinement's user avatar
3 votes
1 answer
186 views

How can I factor Hadamard gates according to $U=e^{i\delta}R_x(\alpha)R_y(\beta)R_z(\gamma)$

According to the formula $U=e^{i\delta}R_x(\alpha)R_y(\beta)R_z(\gamma)$, We know that a single quantum gate can be decomposed arbitrarily, But according to the book Quantum Computation. by Nielsen, I ...
Chuang Lee's user avatar
3 votes
1 answer
348 views

Grover's Algorithm on a Database with more than 50% matching entries

The Setup for Grover's Algorithm is the following: Given an oracle $f_O^{\pm}$ representing a Query on a Database with total $N$ entries $N$ of which $k$ are matching. Grover's Algorithm is used to ...
vasjain's user avatar
  • 802
3 votes
0 answers
320 views

Clock matrix vs matrix clock

In the process of research leading up to my previous question, I found out about matrix, vector & logical clocks. The citation in the aforementioned question mentions clock and shift matrices. ...
user820789's user avatar
  • 3,302
3 votes
1 answer
422 views

Is it possible to express $U_1(\lambda)$ through the gates $R_x, R_y, R_z$ while maintaining the phase? In Qiskit for example

Is it possible to express gate $U_1(\lambda)$ through the gates $R_x, R_y, R_z$ while maintaining the phase? Both in principle and in practice (in Qiskit for example)? The single gate $R_z(\lambda)$ ...
Aleksey Zhuravlev's user avatar
3 votes
2 answers
602 views

How to implement the exponential of an outer product?

In exercise 6.7 page 258 in Nielsen and Chuang book, they have a Hamiltonian $H = \left| x \right\rangle \!\!\left\langle x \right| + \left| \psi \right\rangle \!\!\left\langle \psi \right|$ and the ...
walid's user avatar
  • 335
3 votes
1 answer
186 views

What's the point of quantum gates being 'continuous'?

Besides the 'continuous' which I don't fully understand the term. It's all the time said that arbitrary gates can only be estimated but not necessarily be accurate. I don't understand the claim. So ...
bilanush's user avatar
  • 881
3 votes
1 answer
556 views

Question Regarding Simulating Hamiltonian With Quantum Circuit

There have been a few other questions about this section of Nielsen and Chuang, but when working through the output of the circuit, there are some inconsistencies that are probably due to some mistep/...
Rehaan Ahmad's user avatar
3 votes
2 answers
1k views

How do I embed classical data into qubits?

How do I embed classical data into qubits? I have a classical data [0 1] and I want to encode it as quantum amplitude to a superposition? What are the gates used to achieve that? I am a beginner to ...
Ebtehal Ali's user avatar
3 votes
1 answer
1k views

Quantum addition and modulo operation using gates

I have a matrix equation $X_{\text{new}}=AX_{\text{old}}$, where $A=\begin{bmatrix}1 & 1 & 1\\ 2 & 3 &2\\ 3&4&4 \end{bmatrix}\bmod 64$, and $X_{\text{old, new}}\in \{1,2,...64\}...
Upstart's user avatar
  • 1,430
3 votes
1 answer
150 views

In quantum teleportation, does Bob's qubit depend on Alice's $\alpha$ and $\beta$ coefficients?

Does applying an operation to one half of an entangled pair affect the other? As in the case of quantum teleportation when Alice applies CNOT to her half of the pair and the qubit she wants to send ($\...
Aarsh Chaube RA1911027010105's user avatar
2 votes
1 answer
853 views

How do I compute the square root of the $Y$ gate?

I am trying to compute the square root of the Y gate. $$Y_\theta =\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$$ There are many ways for doing this. I ...
Nicholas Sathripa's user avatar
2 votes
2 answers
377 views

How to construct a CU3 gate using only CX and U3 gates?

Knowing that CX and U3 (taking 3 parameters $\theta, \phi$ and $\lambda$) form a set of universal gates how can I construct an arbitrary CU3 gate using a decomposition of only CX and arbitrary U3 ...
AdonaiH's user avatar
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