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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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### How to check if a two-qubit gate is entangling?

I would like to know if there's an analog for Schmidt rank that can tell me if a two-qubit unitary is entangling? Suppose I have a parametrized two-qubit unitary $U^{(2)}(\theta)$. I would like to ...
171 views

### What are the relations between the permutation group and the Clifford group?

I'm trying to understand the relation between the permutation group on all the $2^n$ bitstrings and the Clifford group. My question arises from the fact that the Toffoli gate (which can be thought of ...
134 views

255 views

### Processing density capabilities in a quantum processor

Given the theoretical infinite quantum states that a qbit can be expressed as is there any practical limit to the processing density in any given quantum processor as compared to the absolute limits ...
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 ...
514 views

### What are the transversal gates of Shor's $[\![9,1,3]\!]$ code?

What are the transversal gates of Shor's $[\![9,1,3]\!]$ code? Since this is a stabilizer code we have transversal Pauli gates. Indeed, transversal $X^{\otimes 9}$ implements logical $\overline Z$ ...
349 views

### How to factor the output of a CNOT acting on the input $|-,+\rangle$

I am trying to implement the Deutsch oracle in classical computer, using direction from this talk. There is this slide where they show how the CNOT gate modify 2 Hadamard transformed Qubits: While ...
3k views

### Why do quantum gates have to be unitary?

In my textbook, it's said the unitarity constraint is the only constraint on quantum gates. Any unitary matrix specifies a valid quantum gate! Why do quantum gates have to have to be unitary? How do ...
292 views

### Exotic transversal gate group

What are examples of interesting $[[n,1,d]]$ or $[[n,2,d]]$ stabilizer codes, $d \geq 2$, whose group of transversal gates is not isomorphic to a subgroup of the Clifford group (on 1 and 2 ...
625 views

### Applying CNOT with local operations and two EPR pairs

Suppose Alice and Bob hold one qubit each of an arbitrary two-qubit state $|\psi \rangle$ that is possibly entangled. They can apply local operations and are allowed classical communication. Their ...
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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 ...
308 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 ...
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### 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 ...
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### Applying $R^{'\dagger}_{xz}$ in gate teleportation

In figure 4 of the paper Quantum Teleportation is a Universal Computational Primitive, the authors show a circuit for applying a unitary $U$ fault-tolerantly via teleportation. I'll paste the figure ...
120 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 ...
386 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 ...
790 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:...
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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 ...
282 views

### 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 ...
1k 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?
281 views

### 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 ...
1k views