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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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What is the difference between quantum control and quantum optimal control?

In the context of quantum control theory, it is common to see references to both quantum control and quantum optimal control (e.g. 0910.2350 or the guide on qutip quantrum control functions). ...
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49 views

Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
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121 views

How many qubits and how many gates, are required for finding the eigenvalues of a matrix?

Say I have an $N \times N$ matrix and I want to know the eigenvalues to a precision of $\pm \epsilon$. How many qubits and how many gates do I need?
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How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
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Exact functions of a single-iteration Grover Search Algorithm's operators

I'm doing a practice assignment where I'm asked to identify specific features of the Grover Search Algorithm's second operator (picture in post, further on "$Us$"), which mirrors the system relative ...
4
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1answer
115 views

Quantum Fourier Transform without SWAPs

The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here: In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits". ...
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99 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. ...
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31 views

Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
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49 views

Is there a way to develop a multiple controlled X or Z gate on Qiskit without using ancillary qubits?

I know for instance I can derive a cccX gate using 2 Toffoli gates on 5 qubit wire or ccccX with 3 Toffoli gates and 7 qubits and so on. you will notice the depth is increasing as the number of ...
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33 views

How to derive a circuit from given equations?

I was reading a paper on Quantum Neural Networks where the authors discussed a new back propagation algorithm. They shared a schematic of the circuit. However, I am unable to understand how the ...
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58 views

How can I express controlled unitary operation in QPE of this implementation of HHL?

I have found this implementation of HHL, and I don't understand why the controlled unitary operation is expressed in the form of $\exp(i t_0 A/2)$ and $\exp(i t_0 A/4)$. The rotation of $\pi$ and $\...
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51 views

N&C quantum circuit for Grover's algorithm

In the chapter about the Grover algorithm, it is suggested that the gate which executes the phase shift is given in the following form: Now I have looked at this gate in detail and come to the ...
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107 views

Decomposition of any 2-level matrix into single qubit and CNOT gates

I saw an example which takes a 2 level matrix. Which is a $8\times8$ matrix that acts non trivially only on 2 levels of only states $|000\rangle$ and $|111\rangle$. The way they do it is by using a ...
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39 views

Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?

In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that: This role of measurement gates in state preparation follows from the Born rule if ...
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34 views

How would one implement a 4-qubit CCCNOT gate (equivalent to controlled-Toffoli)?

I've been meaning to implement Grover's Algorithm for the 3-bit case, wherein I need to implement a CCCNOT gate. How can this be done efficiently (i.e. as few Toffoli and/or CNOT as possible)?
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1answer
63 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.
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33 views

Identity Gate Timing Discrepancy

I have been examining problems where gate timing is important. When implementing an identity gate, the issue of timing has resulted in a few verification experiments to compare the gate time to that ...
2
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48 views

I thought we had already passed this error and qubit threshold?

As outlined in Quantum Computing Progress and Prospects published this year, on page 169-171 there is the diagram showing that we are at the 10's of qubits mark. Looking into the diagram further there ...
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32 views

There seems to be a problem with the implementation of identity gates on Qiskit as compared to the circuit composer

I have been experimenting with slowing down the decay of qubits, and as a control, I implemented a circuit with just identity gates for comparison. However, when I implement such circuits in Qiskit, ...
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23 views

How to perform quantum logic gates on plasmons?

In the link provided researches utilize strong two-plasmon absorption in graphene nanoribbons to create a “square-root-of-swap”, could such a device be utilized to perform other quantum logic gates? ...
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27 views

Understanding CNOT gate for indirect measurement

I am trying to write a simple circuit to understand the process of finding the set of parameters such that the cost function of that circuit in question is minimized. For that I understand one has to ...
2
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0answers
48 views

Restoring an initial state after computation

Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\...
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57 views

Tensorial notation for this quantum XOR circuit

Suppose I have this quantum XOR circuit; this is a quantum circuit for the classical XOR operation $$\begin{eqnarray*} x_1'= x_1\oplus x_2\oplus x_3\oplus x_4,\\ x_2'=x_2\oplus x_3\oplus x_4\oplus x_5,...
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60 views

Writing the transformation matrix for the following in terms of Kronecker products of elementary 2-qubit gates

I have a set of transformations that transforms $|11001\rangle\to |10101\rangle$ which is basically keeping the leftmost qubit as it is and then it is just the CNOT between the successive qubits, I ...
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1answer
67 views

How to reduce circuit elements of a decomposed $C^2(U)$ operation?

This question refers to Nielsen and Chuang's Exercise 4.22: Prove that a $C^2(U)$ gate (for any single-qubit unitary U) can be constructed using at most eight one-qubit gates, and six controlled-not ...
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1answer
76 views

How is it possible to perform a c-not on 4 qubits using the same control qubits on IBM Q computers?

I was wondering after seeing ibmq_16_melbourne layout how it is possible to perform this circuit : It seems when looking at ibm q computers that a qubits can at max target 3 qubits because the arrow ...
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226 views

How to implement controlled u3 gate from Qiskit using simpler gates?

I am trying to implement the u3 controlled gate (able to rotate the qubit in any specified direction in 3 dimensions if the control is 1, for two qubits) using simpler gates. The simpler gates ...
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47 views

About a Qiskit Function

I want to understand this Qiskit function (a function for creating the gate CNX with Python): more specifically i don't understand what's the rotations (Y and Z) over the qubits for ? I added inline ...
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68 views

Transferring classical OR gate in a quantum gate

I would be interested to know how to transform the classic OR gate into a quantum gate. I thought a little about myself. The OR gate can also be rewritten as a NAND gate: So, I have now tried to ...
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25 views

Implementing B92 protocol on IBM Qx

I wanted to implement the B92 protocol on IBM Qx. Implementing the protocol would require that a particular qubit should not be measured when using a particular base i.e. there should be no output at ...
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19 views

Help with understanding Unitary Operator of Quantum Optical Fredkin Gate

I'm referring to the textbook "Quantum Computation and Quantum Information" 10th Anniversary Edition by Nielsen and Chuang. Chapter 7.4 has a Box 7.4 which introduces the Quantum Optical Fredkin Gate....
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83 views

Why does Qiskit swap gate accept registers, but cswap doesn't?

In Qiskit, I am trying to perform controlled-Swap (cswap) of two registers, but an error occurs: ...
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How to decompose U3 gate into smaller basis?

From my understanding, the U3 gate has an infinite basis of angles. However, is there any way to decompose the set of U3 gate into a smaller set?