Questions tagged [quantum-gate]

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

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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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189 views

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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Physical implementation of gates on IBM Q

There is a lot of quantum gates in IBM Q Composer, however, only few are implemented physically while others can be composed of them. When one looks at description of a quantum processor in IBM Q ...
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130 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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Equivalence checking of quantum circuits up to error

Suppose you are given two circuit descriptions $A$ and $B$ where by a circuit description I mean a sequence of gates (in the order they are applied) and the qubits they are applied on. (For the sake ...
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73 views

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 ...
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139 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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57 views

Preparation of states that correspond to efficiently integrable probability distributions

I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph. It is stated that there exists an ...
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68 views

Question Regarding Quantum Period-Finding Fourier Transform Approximation

I am following the 5.4.1 Period-Finding Algorithm in Nielsen and Chuang as shown below: My confusion lies with the second expression of point 3 in the procedure. Why is the second expression an ...
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43 views

Why are two qubits gates more noisy?

I would like to understand why two qubit gates are generally more noisy. If I am interested in single qubit gates, I can have an effective modelling as a master equation: $$\dot{\rho}=\frac{1}{i \...
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36 views

What limits speed of quantum gates?

I would like to check something. Consider I am working on cQED (superconducting qubits), or ion trapped, or silicon qubits (I would like to exclude "exotic for me" quantum computing like photon based,...
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46 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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42 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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70 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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76 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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43 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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152 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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1answer
376 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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2answers
54 views

Making custom gate in Qiskit?

I have been trying to make a gate in qiskit in terms of the basic gates, but I keep on getting an error when I apply it to a circuit. This is my gate: ...
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19 views

What are the practical limitations of complementing quantum computations with memristors?

Considering the current state of research into quantum memristors, and the advantages/disadvantages of quantum and memristor driven computing architectures: Quantum Memristors Quantum Memristor ...
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45 views

Hadamard Overlap Test

I am trying to understand a test called Hadamard Overlap Test, which consists of a destructive swap test (section IV of swap test and Hong-Ou-Mandel effect are equivalent) right after a Hadamard test. ...
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34 views

What is the explicit action of the non-linear gate in CV quantum computing on the quadratures?

In this excellently answered question 'How are gates implemented in a continuous-variable quantum computer?' the typical gates for CV quantum computing were listed and described. In particular for ...
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35 views

Shifting amplitude from one basis to another with a control qubit

I was reading a forum where people were talking about a proposed quantum algorithm that solves an NP-complete problem in polynomial time. The algorithm appears to have flaws (after all, none of you ...
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42 views

Easiest hash function to implement on Qiskit

Trying to build an Oracle circuit for Grover's algorithm that will try to find a desired input in order to get a certain output of a hash function. Was wondering if there were any 4 or 8 bit hash ...
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3answers
125 views

Pauli I in eoh procedure doesn't become a global phase gate in qiskit evolution_instruction method. Possible consequences

If one has two qubits in arbitrary stats and wishes to apply a controlled version of some global phase gate $P(\varphi) = \begin{pmatrix} e^{i\varphi} & 0 \\ 0 & e^{i\varphi} \end{pmatrix}$ ...
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36 views

Gate times for different qubit technologies

Different qubit technologies exist and for each, operations are implemented differently. My question is what the typical times are for the standard gates (single qubit rotations, Hadamard, CNOT, T, ...
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37 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 ...
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51 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

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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31 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 ...
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51 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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60 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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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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20 views

Is there a name for Z1(|GHZ>)?

The GHZ state is defined as $|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}$. Is there a name for the phase flipped GHZ state, i.e. $Z_1(|\mathrm{GHZ}\rangle)=\frac{|000\rangle - |...
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28 views

Generalized construction of W basis

Although this question deals with the construction of a W-state, I was looking for a general way to find all the orthogonal W-states, given a number of qubits. For example, for three qubits, the first ...
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52 views

A question about quantum noise model

Now, I try to understand some concept of Quantum Noise Model and Quantum Channel. The Quantum Noise can be represented as a quantum operator with their own probability. As far as I concerned,(I dont ...
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26 views

How to calculate destabilizer group of toric and other codes

Some papers use the "destabilizer group" for more efficient simulations; see for example (page 3): https://www.scottaaronson.com/showcase2/report/ted-yoder.pdf "In addition to ...
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28 views

What do coupling coefficients mean in terms of Pauli gates, and why are they time dependent?

Hi I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian. I have only seen coupling ...
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49 views

Screening procedure in an iterative qubit coupled cluster (iQCC) ansatz

The paper Iterative Qubit Coupled Cluster approach with efficient screening of generators describes a new screening procedure for generators of the QCC ansatz. How does one get from defining the ...
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Long range two qubit gates in superconducting qubits

In superconducting qubits, all the method that I have seen until now are based on short range interaction. For example you have two qubits to process information around a middle qubit that is ...
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26 views

Error in qiskit.aqua.operator

I want to implement this thing: Operator([[3, Pauli([1,0,0], [0,0,0])], [2, Pauli([0,0,0],[0,0,3])]]) But while doing this there is an error in ...
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1answer
37 views

IBM quantum circuit - order of tensor product for equivalent matrix

I'm trying to understand how to apply tensor products on a 3 qbit systems (or well at least 2 qbits). Let's take a basic example: where $$\lvert \psi \rangle = \lvert q2q1q0\rangle $$ with q2 being ...
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30 views

Decompose Toffoli gate with minimum cost for IBM quantum computer

The known decomposition of toffoli gate that can be used on IBM quantum computer is : I want to know any other Toffoli gate decompositions that can be used on IBM quantum computer and have a cost ...
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1answer
125 views

What is the general matrix for the Swap gate?

In section 3.3.2 of this PDF, The general SWAP gate is defined as $ S (\alpha, \hat{y}) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\alpha/2) & -\sin(\alpha/2) & ...
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220 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{...
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Can we apply Grover to meet-in-the-middle attack?

$\newcommand{\Ket}[1]{\left|#1\right>}$ If we have the superposition $$\displaystyle \sum \dfrac{1}{2^n} \Ket x \Ket{ f(x)} \Ket 0 \Ket y \Ket{g(y)} \Ket 0 \Ket {\delta_{x,y}} ,$$ here $\delta_{x,...
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553 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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56 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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79 views

Kronecker notation of an operator

Suppose I have the state $|A\rangle=|x\rangle^l\otimes |y\rangle^l \otimes |z\rangle^l \otimes |0\rangle_x^l\otimes |0\rangle_y^l\otimes |0\rangle_z^l$. I perform the transformation between the $|x\...