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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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Qiskit cant run circuit with reset gate with error

In qiskit if i have a reset gate in a circuit. If i want to add noise to the circuit it wont transpile. For example: ...
Narcano's user avatar
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1 answer
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qiskit statevector ordering issue

I am currently studying Qiskit. I don't understand the two pictures below while studying. When I apply circuit.x(1), the X gate should be applied to the second qubit, resulting in the state |01>. ...
junghyunHa's user avatar
5 votes
2 answers
148 views

Equivalence of two unitary transformation with respect to local operations

Suppose that $U_1$ and $U_2$ are two (entangling) operators that act on a quantum system consisting of several subsystems. Is there any criterion to tell if these two are equivalent up to applying ...
george doultsinos's user avatar
1 vote
0 answers
90 views

How to determine the single-qubit phase?

In some works it is suggested to find the qubit phase by the following method: Apply $X/2$ (or $Y/2$) gate - preparing the qubit in superposition. Detune the qubit by flux pulse, for example here ...
Curious's user avatar
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Does the $\text{CNOT}$ gate activate if the control qubit is $-|1⟩?$

I understand how the $\text{CNOT}$ gate works intuitively: However, say we have a circuit where the $Z$ gate is applied to $|1⟩$, which turns $|1⟩ \to -|1⟩$. Then, there is a $\text{CNOT}$ gate with ...
Spike Spiegel's user avatar
1 vote
1 answer
62 views

References for mapping qudit gates to qubits equivalent

Let's assume that I'm modelling a d-levels qudit as a set of n qubits, where $d = 2^n$. I would need to map the application of quantum gates on the qudit to a set of operations of the relative qubits ...
Frank's user avatar
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2 answers
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general way to decompose a CZ gate on $n$-qubit system

Suppose I have a CZ(i,j) gate (or CNOT) acting on qubit $i$ and $j$, on a $n$-qubit system. Is there a general way to decompose this gate into a set of gates that only involve single-qubit gates and ...
user185671631's user avatar
4 votes
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74 views

A measure of entanglement created by a unitary operation

Let $U$ be a unitary matrix acting on a 3-qubit system. If there is no correlation among any pairs of the three qubits, the unitary operation can be represented as $U = U_1 \otimes U_2 \otimes U_3$, ...
user185671631's user avatar
1 vote
1 answer
97 views

Problem with the mathematical definition of the eigenvalue algorithm on a specific exercise

I think I understand well how the eigenvalue algorithm works but when I try to define it mathematically I have problems. Specifically I have the matrix U: $$ U = \begin{pmatrix} 0 & i \\ i & 0 ...
Francescov20's user avatar
6 votes
2 answers
189 views

Decomposition of a $4 \times 4$ unitary matrix

I am currently studying the paper "Decomposition of unitary matrices and quantum gates (2012)" and referring to the textbook Quantum Computation and Quantum Information. Among the topics, I ...
junghyunHa's user avatar
3 votes
1 answer
106 views

How much complexity is required to implement $\text{C$_\Pi$NOT}$ gate?

The projector-controlled not gate $\text{C$_\Pi$NOT}$ is defined as $$\text{C$_\Pi$NOT} \, \colon= \Pi \otimes X + (\mathbb{I}-\Pi)\otimes\mathbb{I}\,, \tag{1}$$ in András Gilyén et. al. (2018)[arXiv:...
Takimoto.R's user avatar
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1 answer
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Frequency of qubits in qiskit simulators

I am trying to study the effect of dynamical decoupling sequences (Hahn Echo and CPMG) using qiskit's qasm_simulator with an added noise model from ...
Neelesh Vij's user avatar
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1 answer
80 views

Netlist of the transpiled circuit in Qiskit

I am new to running quantum circuits in Qiskit. In the IBM quantum learning lab, I transpiled a simple 4-qubit quantum circuit using a 7-qubit IBM quantum computer. I received a tranpiled circuit ...
mridula's user avatar
1 vote
0 answers
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Adding measurement circuits to the singlet state circuit and want to create single circuit

I am trying to add the measurement of Alice and bob's circuit to the singlet circuit. Actually, I am trying to build the e91 protocol. But it is giving me an error like this. ...
Bloodknofsky's user avatar
1 vote
1 answer
86 views

Simulator able to run SwitchCase in qiskit?

I am trying to run my circuit (shown below) on a simulator. However, the execution of the circuits fails with (almost) all the simulators, raising error ...
Navid Elyasi's user avatar
2 votes
2 answers
108 views

Conditioned gates with multiple classical bits

Consider a circuit where you have 6 qubits and apply some gates. Then, you measure qubits 1 , 2 , 3 with results $c_1 , c_2 , c_3$. Next you apply $X^{c_1}$ on the 4-th qubit, $X^{c_1 + c_2}$ on the 5-...
ar3q5dr9's user avatar
2 votes
1 answer
418 views

If_test() - Dynamic Circuits in qiskit

I am trying to run a dynamic circuit by having mid-measurement in my code as follows: ...
Navid Elyasi's user avatar
1 vote
0 answers
76 views

How to explain the output as $|-\rangle$

I am a complete newbie to quantum computing and qiskit. I am trying to implement $H$ gate in Measurement-Based QC architecture based on a paper "Qiskit As a Simulation Platform for Measurement-...
user27306's user avatar
2 votes
1 answer
101 views

Constructing a two 3-qubit state involving either X, Y or Z rotation gate

The goal is to construct the state $|\psi\rangle = \frac{1}{2}|010\rangle + \frac{\sqrt{3}}{2}|101\rangle$ Two issues I am facing: What is a good choice for initial state? What is a good choice for ...
Physkid's user avatar
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1 answer
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Phase accumulation for multiple Rabi driving pulses

When a single-qubit gate is operated by Rabi driving, the resulting operator is equivalent to $$ \hat{O} = R_z(\omega t) R_x(\Omega t)\tag{1}$$ where $\omega$ is the frequency of the driving field, $\...
jackphen's user avatar
2 votes
0 answers
133 views

How to do modular exponentiation in qiskit with gates?

I understand the following code on why the specific swaps take place, but when I try to replicate it with $N=35$, I get confused. ...
James Garcia's user avatar
1 vote
1 answer
140 views

How to fix two flip-bit errors in a 3 qubit input

Aware of how a 1-bit flip can be fixed for 3-qubit input by having 2 Ancilla bits, encoding, and using the Toffoli gate to fix the error and decode. How can this idea be extended for a 2-bit flip (...
codeit's user avatar
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3 votes
1 answer
122 views

Time evolution of Hamiltonian

I have given the following Hamiltonian $$\tilde H = - J_x (X_0 X_1 + X_2 X_3) - J_z (Z_0 Z_2 + Z_1 Z_3) - h\sum_j X_j + Z_j$$ Where, for example, $X_0 = \sigma^x \otimes I \otimes I \otimes I$ and I ...
Ruebli's user avatar
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3 votes
2 answers
146 views

What do the values in a unitary matrix represent/what do they mean? How do you figure out what gate a unitary matrix represents?

I am trying to learn Qiskit on my own. I am struggling with unitary matrices. I understand what a unitary matrix is, and why a matrix is unitary. But, I don't understand what the values inside of the ...
shard's user avatar
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1 vote
1 answer
194 views

Get parameters of a CU gate for implementing an erroneous CX gate with fidelity = 0.81

Let's say the definition of an erroneous CNOT gate is given as - CNOT is a 2-qubit quantum gate when the control qubit is at state 0, applies identity operation on the target qubit, when the control ...
codeit's user avatar
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0 votes
1 answer
265 views

The expectation values for the values of both qubits [closed]

Let’s consider the two-qubit state |Ψ⟩ =(1/2)|00⟩ + i(√3/4)|01⟩ +(3/4)|10⟩. a) Find the expectation values for the values of both qubits separately.
shiranrubatsirorwashe's user avatar
1 vote
0 answers
34 views

Why does unitary matrix acts only on input qubit state of a vector that is a result of add modulo 2?

Let $|\psi\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k \oplus b\rangle $ so that $|\psi'\rangle = \frac{1}{\sqrt{2}}[\sum_{k=2}^{1}(-1)^{ka}(U_{A}|k\rangle \otimes U_{B}|k \oplus b\rangle)]...
Physkid's user avatar
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2 votes
2 answers
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What are efficient methods for measuring gate noise?

In this question I'm concerned with getting detailed spectral information about analog noise in quantum gates. Assume we have imperfect control over transitions between $\vert 0\rangle$ and $\vert 1\...
Dr. T. Q. Bit's user avatar
1 vote
1 answer
63 views

What does Quantum Circuit Wires and Separated mean?

From Quantum Circuits, there are two statements that are not clear. Quantum Circuits Quantum circuits are collections of quantum gates interconnected by quantum wires. The actual structure of a ...
Moo's user avatar
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1 vote
0 answers
255 views

Is there a way to implement a noisy CNOT gate using CUGate in Qiskit

Wondering if there's a way to implement the noisy version of CNOT (or CX) gate via CUGate using qiskit library for a given fidelity p?
codeit's user avatar
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2 votes
1 answer
121 views

Hadamard gate for qudit (dimesion 8)

I am using the code for generating the gates for qu8it The resultant gate is not unitary (and so not hermitian too). I am a bit confused with the result. Is it possible for a quantum gate to be non-...
quest's user avatar
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1 vote
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57 views

In qubit phase tracking, does the phase $\delta$ have to be synchronized to the Larmor precession?

In many textbooks (e.g. LaPierre 2021 or Byrd 2022), when dealing with the physical implementation of quantum gates in spin qubits, Larmor precession is usually introduced first as a way to rotate the ...
jackphen's user avatar
2 votes
1 answer
49 views

How does application of a gate on one qubit/amplitude affects the rest of the multi-qubit system

Hadamard and Toffoli Gates form a universal set of gates, thus all quantum circuits can be created out of them. My question is assume any circuit with some $N$ inputs and $K$ gates. For any such ...
TheoryQuest1's user avatar
0 votes
1 answer
73 views

What does any 2 Qbit Universal Gate in any Quantum Circuit with an N Qbit Input "operate on" mean mathematically

I am very new to Quantum Computing thus please excuse the layman question. I am aware that just like classical gates Quantum Computation also has a set of universal gates. Moreover, a universal set of ...
TheoryQuest1's user avatar
2 votes
0 answers
60 views

Which the sequence of gates providing the following unitary?

I am struggling with a problem which has been anticipated in a different question here for 3 qubits. I need a sequence of gates (Pauli, controlled also), such that the unitary matrix associated with ...
francler's user avatar
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2 answers
100 views

What are the correct gates for the following unitary matrix?

I need a set of gates, even controlled, which are providing the following unitary matrix with three qubits: $$ U = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 &...
francler's user avatar
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1 vote
0 answers
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constructing $6$ GHZ-like states from the GHZ state

In a $3$ - qubit system, the $GHZ_{3}$ - state can be constructed in the following manner: $|\psi \rangle _{1} = (H \otimes I \otimes I)(|0\rangle \otimes |0\rangle \otimes |0\rangle) = |+\rangle \...
Physkid's user avatar
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2 votes
1 answer
130 views

How to figure out whether a truth table can correspond to a valid quantum gate

I am new to quantum computing and trying to wrap my head around this exercise from Wong's introduction to classical and quantum computer. I can interpret it mentally that first is a valid quantum ...
Ri dev's user avatar
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3 votes
1 answer
230 views

How to apply rotation about X and Z in stim?

I have a quantum circuit illustrated in the provided image, where I perform a series of quantum operations followed by a projective measurement.. Using Qiskit, I've already written the code for this ...
Manna's user avatar
  • 31
1 vote
1 answer
67 views

What is the unitary matrix for this two qubit circuit with $H$ and $I$?

Above is a circuit I am provided. I am asked to write down the matrix representation of a $4 \times 4$ matrix representation of a unitary matrix for this circuit. Using small endian notation (left to ...
Physkid's user avatar
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1 vote
1 answer
83 views

Compute the output of a quantum circuit with classically controlled operations

Consider the following circuit : where $|\psi\rangle$ is a qubit in $\mathbb{C}^2$, $|0\rangle= \begin{pmatrix}1 \\ 0 \end{pmatrix}$, $T= \begin{pmatrix}1 & 0\\ 0 & e^{i\pi/4} \end{pmatrix}$ ...
NotaChoice's user avatar
1 vote
1 answer
43 views

An operator that checks the second qubit

Applying Hadamard gate to classical bit $|0, \psi, \phi\rangle$ $$H|0\rangle =\frac{1}{\sqrt{2}}\begin{pmatrix}1 & 1\\ 1 & -1\end{pmatrix}|0\rangle = \frac{1}{\sqrt{2}}|0, \psi, \phi\rangle + \...
Koray's user avatar
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1 vote
0 answers
44 views

How are these circuit diagrams in Grover's algorithm understood and why are they designed this way?

As shown in the figure, there are two labelled quantum states 000, 101. why are 3 $Z$-gates placed first in the phase oracle and then 2 controllable $Z$-gates in sequence? What is the logic that makes ...
Ren-Xin Zhao's user avatar
2 votes
2 answers
100 views

How to prove that these equations are correct for $CZ$ and $CX$?

How do I prove that the equation on the right is $CX$ and $CZ$ gate? I don't think that reaching the matrix of the CX or CZ is possible with the given equation. For (b) I keep getting $I \otimes I$ ...
seopr's user avatar
  • 21
1 vote
3 answers
139 views

Exercise 4.16 in the Nielsen & Chuang book

In the 4.16 exercice in the Quantum Computation and Quantum Information (Michael A. Nielsen & Isaac L. Chuang), I don't understand why the correct answer is not this matrix : $$ \left[ {\begin{...
Matodo's user avatar
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0 votes
1 answer
99 views

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
0 votes
1 answer
64 views

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
301 views

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
4 votes
1 answer
160 views

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
0 votes
1 answer
164 views

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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