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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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Is there a physical definition of barrier operation in qiskit?

As far as I know, we can use barrier method in qiskit to split circuits into two sets to prevent the optimization. However, is there any physical meaning of the barrier? Like a delay operation or ...
peachnuts's user avatar
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5 votes
3 answers
729 views

Quasiprobability decomposition of the CZ-gate

I was trying to obtain the quasi-probability decomposition of the CNOT gate by using the information in this paper. The authors give us the example for the CZ gate (Figure 2, i.e. the one below). The ...
stopper's user avatar
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2 answers
921 views

Rotations to encode $f(x)$ into ancilla qubit for quantum Monte Carlo

I'm trying to understand the quantum monte-carlo algorithm starting at the most basic version. A key step is rotating (Algorithm 1 p.g 8), an ancilla bit by rotation $R$ with respect to the value of a ...
Sam Palmer's user avatar
4 votes
2 answers
3k views

How to decompose this two-qubit unitary matrix to the standard gate set?

I have read some of the other decomposition questions here however still don't understand how to do it manually. The matrix I wish to decompose is the following for 2 qubits: $M=\frac{1}{\sqrt2}\...
desirooo's user avatar
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How does the CNOT gate work?

As defined, CNOT should for the two input states $|0\rangle = \pmatrix{1 \\ 0}$ and $\pmatrix{\alpha \\ \beta}$ should result in the second state unchanged: $\pmatrix{\alpha \\ \beta}$. However, to me ...
SlowerPhoton's user avatar
4 votes
1 answer
293 views

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 ...
epelaez's user avatar
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1 answer
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Reversibility and irreversibility of logic gates (quantum vs classical)

I have been told that one of the great keys that unlock quantum computing's potential is the reversibility of quantum logic gates as for classical gates there's some loss of information, but I cannot ...
Bidon's user avatar
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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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4 votes
1 answer
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Shorthand notation for the sign flip gate

I need to use the following matrix gate in a quantum circuit: $$\text{Sign Flip}=\left[\begin{matrix}0 & -1 \\ -1 & 0\end{matrix}\right]$$ $\text{Sign Flip}$ can be decomposed as (in terms ...
Sanchayan Dutta's user avatar
4 votes
1 answer
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How the real IBM quantum computers apply arbitrary Rz(θ) gate rotation? [closed]

I want to ask the following questions: (1) The basis gate set of IBM quantum computers is { Id, Rz(θ),√X, X, CNOT, reset}. Somebody said that IBM didn’t really apply Rz(θ) gate on the machine. The ...
劉承瀚's user avatar
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Basic gates sets

There are several basic gate sets allowing to construct any gate on a quantum gate-based computer, e.g.: $H$, $T$, $CNOT$ (sometimes enriched to $H$, $T$, $S$, $X$, $CNOT$), rotations $Rx$, $Ry$ and $...
Martin Vesely's user avatar
3 votes
3 answers
308 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
1 answer
152 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
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Where are the physical gates in the Google processor?

Google's article Quantum supremacy using a programmable superconducting processor states that the processor "53 qubits, 1,113 single-qubit gates, 430 two-qubit gates, and a measurement on each qubit, ...
vy32's user avatar
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How is the joint state of these qubits derived?

Can someone show to me the steps to derive the joint state at the bottom of this image, please? I tried to follow his explanation but I didn't get the same results… This is taken from the lecture ...
E.s's user avatar
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Trying to construct modular exponentiation gate in Qiskit

https://qiskit.org/textbook/ch-algorithms/shor.html in this tutorial I don't understand especially in how they define for the modular exponentiation gate with only swap gate (inside c_amod15 function)....
Taufiq Datau's user avatar
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1 answer
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What is the control qubit in this 1D ladder of controlled Z gates?

In the picture above, the last layer with dot-shape, is called 1D ladder of controlled Z gates. It is stated in this paper to show the barren plateau issue. I want to know which is the control qubit, ...
narip's user avatar
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1 answer
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What is the standard noise channel that is applied in simulations?

I know there are various quantum noise channels, which include the depolarizing channel, the dephasing channel and the bit-flip channel; We can apply them in simulators easily. However, is there any ...
Henry_Fordham's user avatar
3 votes
1 answer
170 views

What does a quantum NOT operation do to an entangled set of qubits?

Quantum computing is not my field, so answers understandable to a layman will be most useful. Please forgive any incorrect terminology in my question! Assume that a set of the states of N qubits ...
S. McGrew's user avatar
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How to translate the Hadamard gate matrix into Dirac notation?

Hadamard gate matrix is: $$\frac{1}{\sqrt 2}\begin{bmatrix}1 && 1 \\ 1 && -1\end{bmatrix}$$ The Dirac notation for it is: $$\frac{|0\rangle+|1\rangle}{\sqrt 2}\langle0|+\frac{|0\...
Kumar's user avatar
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2 answers
369 views

Generators for single qudit Clifford, d=4

The generators for single qubit Clifford are phase $ P $ and Hadamard $ H $. The generators for single qutrit Clifford can be found for example here What is the set of generators for the qutrit ...
Ian Gershon Teixeira's user avatar
3 votes
1 answer
455 views

Implementing a controlled-controlled-U using controlled-U

Suppose I know how to implement a 2 qubit gate $C-U$ (i.e controlled U), and I want to implement $CC-U$ using $C-U$ and other 1 or 2 qubit gates, is that possible?
Lost In Euclids 5th Postulate's user avatar
2 votes
2 answers
3k views

How to make a circuit for the CNOT using $H$ and $CZ$ gates?

How can we draw a circuit that is based on the gates $H, CZ$ that implements $CNOT$. I know that the $H$ gate is like that: And also the $CZ$ gate is: But I'm not sure how to draw this with the ...
Xavi's user avatar
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2 votes
4 answers
316 views

Quantum circuit with one unknown gate

You are given a quantum circuit with around 4-5 gates connected. The catch is that you know all the gates and the connection except one gate. For as many times as you want you can check what the ...
wizzywizzy's user avatar
2 votes
1 answer
107 views

Can a circuit map $|x,y\rangle$ to the reflection of $|y\rangle$ with respect to $|x\rangle$?

Statement of the problem. I want to consider/design a quantum circuit that takes as input two vectors $\vert x \rangle$  and $\vert y \rangle$. The output of this quantum circuit must contain the ...
Cristian Dumitrescu's user avatar
2 votes
1 answer
937 views

Decomposition of an arbitrary gate using given matrix in Qiskit

If I have an arbitrary non-unitary matrix of say $$ U = \begin{pmatrix} 1.5 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1.6 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ \end{...
Monica's user avatar
  • 311
1 vote
1 answer
600 views

A problem with application of multi controlled rotation gates [closed]

This message pops up when I run an mcrx gate The mcrx gate needs a single qubit as target. Here is a part of code I run: ...
Luqman khan's user avatar
0 votes
3 answers
742 views

How does one interpret intuitively the CNOT gate?

How does one interpret the CNOT gate? The CNOT gate takes a separable state and turns into an entangled state. The oracle in the Deutsch algorithm does the same thing. But how does one understand this ...
snickers_stickers's user avatar
28 votes
2 answers
2k views

Why is it important to eliminate the garbage qubits?

Most reversible quantum algorithms use standard gates like Toffoli gate (CCNOT) or Fredkin gate (CSWAP). Since some operations require a constant $\left|0\right>$ as input and the number ...
Be Brave Be Like Ukraine's user avatar
19 votes
2 answers
2k views

Do multi-qubit measurements make a difference in quantum circuits?

Consider the unitary circuit model of quantum computation. If we need to generate entanglement between the input qubits with the circuit, it must have multi-qubit gates such as CNOT, as entanglement ...
Kiro's user avatar
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18 votes
2 answers
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How to implement the 4 Bell states on the IBM Q (composer)?

I would like to simulate the 4 "Bell States" on the IBM composer? How can I best implement those 4 Bell states using the existing set of gates ? Here below you see the definition of the 4 Bell ...
JanVdA's user avatar
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17 votes
4 answers
2k views

How do the probabilities of each state change after a transformation of a quantum gate?

Quantum gates are represented by matrices, which represent the transformations applied to qubits (states). Suppose we have some quantum gate which operates on $2$ qubits. How does the quantum gate ...
ItamarG3's user avatar
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13 votes
2 answers
616 views

What are the possible non-entangling two-qubit gates?

The non-entangling gates in $ SU_4 $ contains the entire group of gates of the form $$ SU_2 \otimes SU_2. $$ It also contains $$ \zeta_8 SWAP= \zeta_8 \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &...
Ian Gershon Teixeira's user avatar
12 votes
1 answer
2k views

Are circuits with more than 1000 gates common?

I have seen circuits with 30 qubits and around 500 gates. Also circuits with 32 qubits and 6000 gates. Are circuits with more than 1000 gates common in quantum computing? Are there many quantum ...
Alejandro Arcila's user avatar
12 votes
2 answers
5k views

How can a controlled-Ry be made from CNOTs and rotations?

I want to be able to applied controlled versions of the $R_y$ gate (rotation around the Y axis) for real devices on the IBM Q Experience. Can this be done? If so, how?
James Wootton's user avatar
11 votes
3 answers
1k views

What's an example of building a circuit $U_f$ that implements a simple function $f$?

I'd like to be able to program simple functions into simulators such as QCL. I read that any function $f$ can be implemented, but I don't know how to get say a unitary matrix that implements $f$. $\...
R. Chopin's user avatar
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11 votes
2 answers
703 views

Is the controlled-Hadamard gate in the Clifford group?

Is the controlled-Hadamard gate a member of the Clifford group? I understand that Controlled Pauli gates are in the Clifford group. If controlled Hadamard is Clifford member, then is a controlled-...
Isolated Information's user avatar
11 votes
1 answer
4k views

Implementing a CCCNOT gate using only Toffoli gates

A CCCNOT gate is a four-bit reversible gate that flips its fourth bit if and only if the first three bits are all in the state $1$. How would I implement a CCCNOT gate using Toffoli gates? Assume ...
chuster's user avatar
  • 255
10 votes
2 answers
1k views

Show that these two expressions for the oracle transformation are equivalent

Suppose $x \in \{0,1\}^n$. The standard way to make a query is with an oracle $O_x$ that given an input $|i,b \rangle $ returns $|i,b \oplus x_i \rangle$. Via the phase kick-back trick, this can be ...
Karl's user avatar
  • 359
10 votes
2 answers
1k views

Where is the parallelism in Deutsch-Jozsa algorithm?

I am newbie on Quantum Computing. Actually I am a software engineer but I want to understand how quantum computers work. So my question may be absurd. Sorry about that. I tried to understand Deutsch-...
overlord's user avatar
  • 203
10 votes
1 answer
755 views

How do you apply a CNOT on polarization qubits?

I read that a qubit can be encoded in a polarization state (horizontal or vertical polarization of a photon). How do you perform two-qubit operations on a polarization qubit?
Daniel Tordera's user avatar
10 votes
1 answer
897 views

What is the set of generators for the qutrit Clifford group?

According to this article, any Clifford gate, acting on $n$ qubits, can be generated by Hadamard, CNOT, and S gates. What are the set of generators for qutrit Cliffords?
BlackHat18's user avatar
  • 1,363
9 votes
2 answers
2k views

Possibility of a "reset" quantum gate

I wish to have a "reset" gate. This gate would have an effect to bring a qubit to the $\mid0\rangle$ state. Clearly, such a gate is not unitary (and so I'm unable to find any reliable implementation ...
Ntwali B.'s user avatar
  • 453
9 votes
1 answer
3k views

Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates?

Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates? Why is it simple for Clifford gates to implement ...
Wang's user avatar
  • 129
9 votes
2 answers
2k views

How to prove that the query oracle is unitary?

The query oracle: $O_{x}|i\rangle|b\rangle = |i\rangle|b \oplus x_{i}\rangle$ used in algorithms like Deutsch Jozsa is unitary. How do I prove it is unitary?
Divyat's user avatar
  • 93
9 votes
3 answers
896 views

Does conditional gate collapse controller's superposition?

I've created a simple circuit in Q-Kit to understand conditional gates and outputted states on each step: In the beginning there is clear 00 state, which is the input The first qubit is passed ...
CodeSandwich's user avatar
9 votes
3 answers
947 views

Universal Gate Set, Magic States, and costliness of the T gate

The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In ...
Eric Kubischta's user avatar
9 votes
2 answers
567 views

Could the Hadamard gate have been constructed differently with similar characteristics?

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&...
Nate Lowry's user avatar
9 votes
1 answer
1k views

Prove that adding any non Clifford gate to the Clifford group yields a universal gate set

I have seen it claimed in multiple places that adding any non Clifford gate to the Clifford group yields a universal gate set. It is, however, not easy to find an accessible proof of this fact. The ...
Ian Gershon Teixeira's user avatar
8 votes
3 answers
6k views

Composing the CNOT gate as a tensor product of two level matrices

I don't understand, why is the control not gate used so often. As far as I understand it, if you apply two 2 level operations on two qubits then you get a 4 x 4 matrix by the tensor product. So how ...
bilanush's user avatar
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