Questions tagged [quantum-gate]

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

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How to simulate a $CNOT$ only using a single qubit?

I am looking to do a $CNOT$ on itself, i.e., if the qubit is in $|0\rangle$ it stays in $|0\rangle$ and if it is in $|1\rangle$ it becomes $|0\rangle$. We are allowed to use $H$, $X$, $Z$, and $CNOT$ ...
Sowrya Gali's user avatar
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What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?

Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
Song of Physics's user avatar
3 votes
2 answers
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Sufficient conditions for a single-qubit unitary to be the identity

Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$. First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
Hailey Han's user avatar
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Can you twist a qubit?

Is it possible to operate on a single qubit by a map which has a nonzero degree? Let $|c\rangle=c_0|0\rangle + c_1|1\rangle$ represent a qubit state where $c_0,c_1 \in \mathbb{C}$ and $|c_0|^2+|c_1|^2=...
Jackson Walters's user avatar
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How do qubits interact to form logic gates?

How do qubits interact to form, say, CNOT gates? There are very few comprehensive explanations of how quantum computing works. They all use obscure metaphors that don’t make sense (like Schrödinger’s ...
WhatsYourIQ192's user avatar
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Post-selection on pennylane

I want to do something like this: For a single-qubit Apply Hadamard -> Time_evolution -> Phase_damping -> Hadamard -> Post-selection -> Get CFI(classical fisher info) Density matrix ...
Donguk kim's user avatar
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Is it physically or algorithmically possible to implement continuous observation of parameter changes in a quantum gate?

Since direct observation of qubits collapses the quantum state and prevents the original state from being obtained, does continuously monitoring the parameters of a quantum gate collapse the quantum ...
Ren-Xin Zhao's user avatar
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How does error accumulate when entangling two distant qubits with limited connectivity?

My goal is to minimize accumulated error when entangling two qubits that cannot be entangled via a single native two qubit gate operation. I have a coupling map/graph for the qubits of an IBM quantum ...
ty.'s user avatar
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A Toffoli gate can be decomposed into a circuit of 1- and 2-qubit gates

While reseaching a way to implement a 3 qubit Toffoli gate, I came across this circuit: However, I cannot find a proper source for this circuit. Can anyone link a cited paper.
PhysicsQuestion's user avatar
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How to calculate number of qubits required for Grover Algorithm while constructing it's oracle and diffuser for any Specific Algorithm or Hash?

I am reading a paper titled, " (Towards Post-Quantum Secure Symmetric Cryptography: A Mathematical Perspective)". Here, I am able to understand the gate counts and T-depth calculations. ...
Syed Shahmir Kazmi's user avatar
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Is {U, CZ, S} universal for quantum computation, for appropriate single qubit unitary U?

In the paper arXiv:0205115, Shi proves that the gateset $\{CX, U\}$ is computationally universal for quantum computation, where $U$ is a single qubit unitary such that $U^2$ does not preserve the ...
Mary_Smith's user avatar
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Given a COMPLEX unitary matrix, how can I construct a unitary gate in Qiskit?

It seems that it is fairly easy to construct a unitary gate given a real unitary matrix. However, I have tried several methods with a complex unitary matrix, but they all seem to be not working. How ...
JiQing's user avatar
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What is the quantum circuit complexity of a multi-control Y-gate with n control bits and 1 output bit?

It is known that many multicontrol quantum gates consist of sets of elementary gates, and there seems to be no authoritative way to give the complexity of such multicontrol quantum gates. So using one ...
Ren-Xin Zhao's user avatar
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How can I implement this unitary operation using CNOT and single qubit gates?

How can I implement the following unitary operation using CNOT and single qubit gates? $$U =\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\\ 0 & ...
sriram Usc's user avatar
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Half Adder using CNOT Gates

As per this schematic of qubits, how this explanation is correct --"If you look again at the four possible sums, you’ll notice that there is only one case for which this is 1 instead of 0: 1+1=10....
Piyush Kumar Sinha's user avatar
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Can we write a sum of unitary gates as an equivalent product of unitary gates?

If I did it correctly, in an answer to a question about Bell's states preparation, I found true that: $$CNOT \space \space (H \otimes I) \space CNOT = ( X \otimes X + Z \otimes I ) \frac{1}{\sqrt{...
Matteo Vitturi's user avatar
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1 answer
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Computing the evolution of expectation values of the Pauli observable

I have a quantum state described by $N$ qubits, and I don't know anything about this quantum state except the expectation value of the single-qubit Pauli observables of the $i$-th qubit ($\langle X_i \...
stopper's user avatar
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CNOT and quantum entanglement

I have the following problem: "Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩ Show that Alice can teleport ...
Samuel Jaramillo's user avatar
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2 answers
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Conditional quantum circuits

Let's suppose that we have the following $\text{GHZ}$-state $$|\psi\rangle = \frac{1}{\sqrt{2}}|a_1a_2a_3a_4\rangle + \frac{1}{\sqrt{2}}|b_1b_2b_3b_4\rangle$$ By using quantum gates, can we evaluate $...
Supergravity's user avatar
2 votes
2 answers
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CNOT gate effect on 2 qubits

If the CNOT gate applies a NOT on the target qubit if the control qubit is a 1 and the control qubit was in superposition (for example in the $|+\rangle$ state), wouldn't this break the superposition ...
Omeglac's user avatar
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How to alter the result of (somewhat) randomly generated circuits?

I create randomly generated circuits by iterating through a list of the gate set (in my case [$CX,SX,RZ,X$]) and adding the gate to the circuit. (In the case of the $CX$ gate we look at the topology ...
Qubii's user avatar
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Application of transformation $U_d$ that maps any qudit state to $|d-1\rangle$

When giving examples of universal gate sets in the paper Qudits and High-Dimensional Quantum Computing, the authors first define the transformation that maps any given qudit state to $|d-1\rangle$: $$ ...
banercat's user avatar
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Quantum Crosstalk in gate scheduling with different gates

I am working on quantum crosstalk, specifically on CNOT and SWAP gate operations that lead to crosstalk. I have encountered works that decompose CNOT and SWAP with iSWAP and CZ gates. I would like to ...
Indu's user avatar
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Why can we simulate any measurement involving $U=R+iQ$ using $U'=R\otimes I+Q\otimes R_x(2\pi)$ instead?

In a book named "INTRODUCTION TO QUANTUM ALGORITHMS VIA LINEAR ALGEBRA", the authors say: For any complex $N×N$ matrix $U$, we can uniquely write $$U = R + iQ$$ Assume we have $$ U' = R \...
Huy By's user avatar
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Functional form of the drive of IBMQ machines

I am trying to apply some ML techniques to try and find out pulse sequences to implement different kinds of gates using Qiskit Pulse. For the ML part, it is necessary for me to know the Hamiltonian of ...
MAAN2498's user avatar
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What is the mathematical intuition behind deferred measurement? [duplicate]

Please give a complete proof of the principle of Deferred Measurement Principle, including careful notation (preferably explaining the meaning of each symbol) and rigorous mathematical reasoning (...
Ren-Xin Zhao's user avatar
1 vote
1 answer
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Obtaining the unitary matrix of a gate in analytic form in qiskit

Is there any way to obtain the unitary matrix of single way in analytic form? In numerical form, I could use a workaround like this (i.e. for an X Gate): ...
Julen Larrucea's user avatar
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Amplitude amplification in Grover algorithm

In "Quantum Computation and Quantum Information", they talk about Grover search. One part of the Grover search is Amplitude amplification: But i think the red line is not true. Because i do ...
Huy By's user avatar
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Can any Qiskit circuit be converted to a gate?

I am trying to convert the following qiskit QuantumCircuit to a gate using to_gate() method. ...
squareroottwo's user avatar
2 votes
1 answer
227 views

New mode of Quantum and - or gate

I’m Aurelio, a computer engeneering student and I would propose a new quantum gate that maybe could be interesting to implement and use. I don’t know if such idea is already known but I have not found ...
Aurelio Marotta's user avatar
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1 answer
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RY rotation on a qubit

The classical representation of a state on the Bloch sphere is given by $|\psi\rangle = \cos \frac{\theta}{2} + e^{i \varphi} \sin \frac{\theta}{2}$. If I want to apply a rotation around the $Y$-axis, ...
JMark's user avatar
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1 answer
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Are equiprobable state same as superposition state

How qc.h(0) qc.h(1) helps quantum circuit qc=QuantumCircuit(2) to put the given qubits in a equiprobable states? Are ...
Khilesh Chauhan's user avatar
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2 answers
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Visualizing Y-gate operation to achieve quantum state

In the below snippet how qc.y(1) helps to achieve the quantum state $i|10\rangle$ ? ...
Khilesh Chauhan's user avatar
1 vote
1 answer
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Inverse channel of the Pauli 4 POVM

I'm currently grappling with a challenge in comprehending the inverse channel of the Pauli 4 POVM. The POVM elements are defined as follows: $ M_0 = \frac{1}{3} |0\rangle\langle0|, \quad M_1 = \frac{1}...
Yuval Idan's user avatar
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Superposition of circuits (d-level case)

In this post: Superposition of quantum circuits, the two states are qubits. Is it possible to generalize this question to two qudit case? ie, given quantum circuits $C_1$ and $C_2$ that generates $\...
Irene's user avatar
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2 votes
1 answer
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Exact synthesis of Toffoli gate from CNOT and rational single-qubit gates?

Is it possible to implement a Toffoli gate exactly using just CNOT gates and single qubit complex rational gates (i.e. with entries in $\mathbb{Q}(i)$), possibly with ancillas? I know this works with ...
D0r1an's user avatar
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1 vote
1 answer
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The Qiskit code's output doesn't seem to be what I expected

...
Anees Ur Rehman's user avatar
2 votes
1 answer
54 views

How to go from matrix to bra-ket representation of the CNOT?

I have the following definition for CNOT gate form my notes: I am trying to derive the bracket notation form the matrix version, can someone help me to see where I am going wrong: $$U ̂_{CNOT} ...
PhysicsQuestion's user avatar
1 vote
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How to add a value of -1/2 on the amplitude of a quantum state?

I have a quantum state which is in $ \cos(c*f(x) + \pi/4) |0\rangle + \sin(c*f(x) + \pi/4) |1\rangle$ by using bunch of RY gates. Now I want to measure the probability of getting the state at $|1\...
Another Random Guy's user avatar
1 vote
0 answers
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Quantum Computer Basics [closed]

I am a newbie to Quantum Computing world. My collage professor asked me to do presentation on quantum computing. I have read many articles online but still I think I am not satisfied with what I found....
Poojan Solanki's user avatar
5 votes
1 answer
57 views

Existence of Hamiltonians such that the time evolution unitary becomes identity

Can we always find a set of coefficients ${k_i}$ (where not every $k_i = 0$) for a given Hamiltonian $H = \sum k_i H_i$, such that the unitary operator becomes the identity operation: $e^{-iH} = e^{i\...
Hailey Han's user avatar
1 vote
1 answer
108 views

A question on the structure of the Clifford group

Let $P_n$ be the Pauli group on $n$ qubits defined by $P_n=\{i^k \sigma_1...\sigma_n: k=0, 1, 2 \; \mathrm{or}\;3, \sigma_j\in \{I, X, Y, Z\}\}$, where $I, X, Y, Z$ are Pauli matrices. The Clifford ...
Star21's user avatar
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2 votes
3 answers
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Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations

The Solovay-Kitaev theorem shows that "this approximation can be made surprisingly efficient, thereby justifying that quantum computers need only implement a finite number of gates to gain the ...
138 Aspen's user avatar
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2 votes
1 answer
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What are the theoretical minimum times for quantum and classical logic gates?

I'm interested in better understanding the ultimate limits on how fast quantum and classical logic gates can be performed. Based on principles like the time-energy uncertainty relationship, there ...
Saul_better's user avatar
2 votes
1 answer
106 views

Can every unitary be approximated by gates from the Clifford Hierarchy?

For $k > 1$, we recursively define $\mathcal C^{(k)}$ as $$ \mathcal C^{(k)} = \Bigl\{ U \in \mathbf U(2^n) \mathrel{\Big\vert} \forall P \in \mathcal C^{(1)} : U P U^\dagger \in \mathcal C^{...
Ian Gershon Teixeira's user avatar
4 votes
1 answer
145 views

How to get resultant statevector after applying parameterized gates in qiskit?

I want to check the expressibility of my ansatz and calculate the resultant statevector on paper seems difficult. Is there a way I can do this in qiskit? I have the circuit for the ansatz which has ...
Cheshta Joshi's user avatar
3 votes
1 answer
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On unitary matrix form suggested in the Elementary gates paper

In the Elementary gates for quantum computation paper by Barenco et al authors start their proofs by defining a generic form of 2x2 unitary matrix of $\mathbb{C}$ as follows: Can you help me with the ...
Grwlf's user avatar
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Implementation of two qubit gate decomposition in local operations

My questions is regards to this paper: https://arxiv.org/abs/1909.07534 The above is the decomposition of a two qubit gate into local operations. Please note they are using a Super Operator formalism....
AP110's user avatar
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-1 votes
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What is Gate time of single and multi qubit?

How much quantum gate need time do computation in superconducting quantum computer. For all types of single and multi qubit gate.
Jagadeesh Pitchai pazham's user avatar
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1 answer
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How to translate a problem for a gate-based quantum computer into an equivalent problem for a quantum annealer?

There is an offhand claim (somewhere) in https://www.youtube.com/watch?v=eFIk7wpU5vA that a quantum annealer is in principle a completely equivalent machine to a gate-based quantum computer, in the ...
James's user avatar
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