Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
1,005
questions
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1answer
31 views
Prove $E(R_n(\alpha),R_n(\theta)^n)<\epsilon/3$ from $E\big(R_n(\alpha),R_n(\alpha+\beta)\big)=|1-\exp(i\beta/2)|$
where $E(U,V)=\max_{|\psi\rangle}||(U-V)|\psi\rangle ||=||U-V||$ is the error when $V$ is implemented instead of $U$. See page 196, Quantum Computation and Quantum Information by Nielsen and Chuang.
I ...
2
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2answers
45 views
Do we need ancillary qubits to implement orthogonal measurements?
Consider an $n$ qubit state $|\psi\rangle$. Let's say I want to implement an $m$ outcome orthogonal measurement on $|\psi\rangle$, where $m \neq n$. Denote the set of $m$ orthogonal measurement ...
0
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1answer
44 views
How is transformation for measurement in an arbitrary basis derived?
I started with Qiskit today and find it very exciting.
As a first question I want to understand how to measure an arbitrary state $|\Psi\rangle$ not in the basis of ...
-2
votes
1answer
48 views
Decomposition of U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate [closed]
Can we express U1 gate $U_1(\lambda)$ , Phase Shift gate $\phi(\delta) $, and Swap gate
$$ U_1(\lambda) = \begin{pmatrix}1 & 0 \\ 0 & e^{i\lambda}\end{pmatrix}$$
$$ \phi(\delta) = \begin{...
1
vote
1answer
23 views
how to know the appropriate time to know the SWAP gate operation in dipole interaction
Consider dipole-dipole interaction between two qubits,$H_{int} = g \boldsymbol\sigma_{1}\cdot\boldsymbol\sigma_{2}=g(X_1X_2+Y_1Y_2+Z_1Z_2)$. How can I show that by turning on this interaction for an ...
3
votes
1answer
76 views
Conditional lower bound on approximate stabilizer rank of magic states
I am currently reading about the approximate stabilizer rank and properties of the same.
I will quote the definitions from this paper.
The stabilizer rank of a quantum state $|\psi\rangle$ is the ...
0
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1answer
60 views
Measurement of single qubit operator $U$ which is both Hermitian and unitary with eigenvalues $±1$
Suppose we have a single qubit operator $U$ with eigenvalues $±1$, so that $U$ is both Hermitian and unitary, so it can be regarded both as an observable and a quantum gate. Suppose we wish to measure ...
2
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2answers
47 views
What is the name of this "ancilla based" process to implement gates
I just want to know if there is a specific name for the implementation of a gate on the top qubit with the help of the bottom qubit, represented on this image:
It looks like gate teleportation but it ...
3
votes
1answer
39 views
Where does the "correction" in quantum error correction occur, specifically when using repetition codes?
I'm reading the part of the qiskit textbook that deals with this (https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html) and so far it seems as though they're just ...
1
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1answer
124 views
Getting non-Clifford after performing several Clifford gates in qiskit
I'm trying to test Clifford gates in qiskit according to the table in Fault-tolerant SQ, page 101. I tried 4 Cliffords in the test $$-X/2 - X -X/2,Y/2,X/2 - -X/2,Y/2,-X/2$$
using the following code
<...
2
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1answer
39 views
Why can the Hamiltonian $H=P_x(t)X+P_y(t)Y$ make an arbitrary unitary $U=R_x(b)R_y(c)R_x(d)$?
p.281 of Nielsen and Chuang's book says that
A single spin might evolve under the Hamiltonian $H = P_x(t)X + P_y(t)Y$, where $P_{\{xy\}}$ are classically controllable parameters. From Exercise 4.10, ...
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1answer
37 views
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2answers
294 views
When can pairs of states be transformed into other pairs of states via unitary mapping?
The states $|+\rangle, |-\rangle$ can be mapped to $|0\rangle, |1\rangle$ by a simple rotation.
But if I now have other states ($|\psi_0\rangle, |\psi_1\rangle$) which are not orthogonal, does a ...
1
vote
1answer
62 views
Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations?
Is it possible to perform $z$ rotation in Qiskit with just $x$ and $y$ rotations?
I tried the following:
...
2
votes
1answer
121 views
Is the CNOT in the standard three-qubit circuit for the GHZ state necessary?
This is a very basic question about the GHZ state. I know the standard construction:
A Hadamard on one qubit, and then CNOT gates with targets on all the other ones.
However, why can't I just have $n$...
3
votes
1answer
41 views
How to apply Euler's formula to $Z$ rotations such as $e^{i\pi/8 Z}$?
I was following the Qiskit textbook and wanted to show that $R_z (\pi/4) = e^{i \pi/8 Z}$.
Plugging $\pi/4$ in for $\theta$ in the matrix from this page $ \begin{bmatrix}
e^{-i \pi/8} & 0 \\
0 &...
1
vote
1answer
42 views
Decomposition of the multi-controlled gate in tensorflow quantum
In TensorFlow Quantum 0.5.0, the support for Cirq gates that have arbitrary control via the gate.controlled_by function is added.
I would like to know which kind of ...
2
votes
1answer
53 views
What is "gate length" in quantum computing?
I am working on adding a new provider to Qiskit, and I have to specify the properties of the backend.
What is "gate length" (in ns) referring to?
0
votes
1answer
81 views
Definition of Deutsch gate and meaning of $\theta$
I'm trying to understand the definition of a Deutsch gate.
In particular what does $\theta$ mean in its presentation? Is it derived from the coefficients of the input state or a free parameter or ...
3
votes
0answers
40 views
Writing circuits in Qiskit using only Clifford and T gates
Is there a way in Qiskit to write my circuit using only Clifford and T gates (CX, S, H, T and I think also $S^\dagger$ and $T^\dagger$)? With the function compile (with aer simulator) it gives me some ...
3
votes
1answer
85 views
Is the square-root-of-SWAP for a pair of 4-dimensional qudits isomorphic to two square-root-of-SWAPS for two pairs of qubits?
This may be a very naïve question indicative of a lot of confusion, but I am trying to understand more about Hamiltonian simulation. I'm starting to intuit that the $n^{th}$-root-of-SWAP acting on a ...
3
votes
1answer
42 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 ...
2
votes
2answers
81 views
Are composite gates within superconducting hardware implemented as a single pulse or as a series of pulses?
If we have for example a gate $U^{\otimes2}$, then within superconducting hardware, is the $U$ applied onto the first qubit and then the second or is a pulse corresponding to a composite gate (tensor ...
2
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1answer
40 views
What are the "higher moments" of the gate fidelity?
Reading the paper Gate fidelity fluctuations and quantum process invariants I came across the concept of higher moments of the gate fidelity, for example in the following excerpt from the introduction:...
6
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1answer
129 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?
1
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1answer
24 views
Why does the output from FANOUT appear on the second and third bits?
Figure 1.16: FANOUT with the Toffoli gate, with the second bit being the input to the FANOUT (and the other two bits standard ancilla states), and the output from the FANOUT appearing on the second ...
4
votes
1answer
110 views
Qutrit analogues of controlled Z and cc-Z gates
I am trying to look for the qutrit analogues of a controlled-Z, and a cc-Z (Z gate with two controls) for qubits.
There is a previous answer that gives a qutrit analogue of a CNOT gate, but does not ...
4
votes
1answer
79 views
Cliffordness of the qutrit Hadamard gate
Consider a simple generalization of the Hadamard gate to qutrits, defined as follows.
\begin{equation}
\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0\\
\frac{1}{\sqrt{2}} &...
2
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3answers
438 views
Are these two circuits equivalent in performing controlled time-evolution?
I want to perform the controlled time-evolution of some 2 or 3-qubit Hamiltonian. Say we have this example:
$$
H= Z_0\otimes Z_1 + Z_1\otimes Z_2
$$
The circuit performing the time-evolution ...
1
vote
1answer
75 views
Can we do error correction for entangled particles?
There are several quantum error correction techniques, such as 3-qubit bit-flip code, and Shor’s 9-qubit code. 3-qubit bit-flip code is a straightforward technique for correcting a single error (...
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1answer
70 views
Implementation of FANOUT using Toffoli gates
Consider the following implementation of FANOUT using Toffoli gates:
I'm confused about the following statement: "the second bit being the input to the FANOUT and the other two bits standard ...
0
votes
1answer
51 views
Why isn't FANIN required to be able to simulate all other elements in a classical circuit
In Nielsen and Chuang, there's the following paragraph:
The Toffoli gate can be used to simulate NAND gates and can also be used to do FANOUT. With these two operations, it becomes possible to ...
2
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1answer
30 views
Different statevectors with different quantity of complex numbers for same single-qubit states in Qiskit
I have several questions, but before ask, I want to write some theoretical.
As we know, we can represent any single-qubit quantum state by the next representation:
$$
|\psi\rangle=c_0|0\rangle+c_1|1\...
2
votes
1answer
104 views
How to formulate Dynamical Decoupling passes in Qiskit to improve result upon circuit execution
First, let me say that I am not familiar with the idea of Dynamical Decoupling. The goal of this question is to understand how to set up a circuit with dynamical decoupling to improve my hardware ...
1
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1answer
93 views
How to use the output state $\frac1{\sqrt2}(|0,f(0)\rangle+|1,f(1)\rangle)$ given by this quantum circuit?
In Nielsen and Chuang, for the following circuit that demonstrates quantum parallelism, I have the following question:
since the output state of the circuit is
$$\frac1{\sqrt2}(|0,f(0)\rangle+|1,f(1)\...
1
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0answers
25 views
How to measure the error rate (or fidelity) of a particular gate (such a H, T) by Qiskit
We know the calibration data of IBM's quantum devices can be retrieved through the randomized benchmarking method, which is included in Qiskit. However, the calibaration data about gates just gives ...
1
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1answer
110 views
How to design Multi qubit Controlled Z rotations
I need some help in multi-qubit controlled -Z rotation.
Below is the qiskit code of triple controlled z rotation
...
6
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1answer
618 views
Are anti-unitary gates possible?
According to Wigner’s theorem, every symmetry operation must be represented in quantum mechanics by an unitary or an anti-unitary operator. To see this, we can see that given any two states $|\psi\...
2
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0answers
62 views
Accuracy of rotational gates on IBM Quantum
As a computer memory is finite, it seems reasonable to assume that a rotational angle of gates $Rx$, $Ry$ and $Rz$ (and $U1$, $U2$ and $U3$ gates as well) has some smallest step which can be ...
1
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1answer
101 views
Does anyone have some references on EigenGate used in Google's cirq framework?
I am trying to understand the code below but can not find any references other than the code itself.
https://github.com/quantumlib/Cirq/blob/v0.11.1/cirq-core/cirq/ops/eigen_gate.py
I am not clear ...
3
votes
2answers
81 views
Can we use reversible computation to construct oracle circuits?
One of the question while I discussed with my colleague in the math department was the construction of oracle circuit.
In computer science, specifically in algorithm, we take oracle as granted and ...
2
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1answer
72 views
About projective measurement and eigenspace
I have read an article Unified derivations of measurement-based schemes for quantum computation.
In page 3, Section A it says that The classical outcome j corresponds to the measurement of $(U^\dagger ...
1
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1answer
112 views
Can someone explain using H and T gates repeatedly?
The Qiskit textbook says it is used because $R_x$, $R_y$, and $R_z$ are not accurate single qubit rotations.
Can someone elaborate what the repeated $H$ and $T$ gates actually do?
In what scenario ...
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votes
1answer
49 views
The use of modulo 2 in state representation after CNOT
The following circuit with a CNOT gate has the following effect on a computational basis state $|a, b\rangle$, where all additions are done modulo 2.
Why is the state of the second qubit changed to $...
1
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0answers
44 views
Defining native gate dictionary in pyGSTi
In pyGSTi in order to construct Randomized Benchmarking circuits, we first need to define a pspec object that contains information about the number of qubits, basis ...
2
votes
1answer
98 views
How to derive the rotations caused by the H gate?
In Nielsen and Chuang, there's the following paragraph:
The Hadamard operation is just a rotation of the sphere about the ˆy axis by 90◦, followed by a rotation about the ˆx axis by 180◦.
I am ...
2
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1answer
223 views
Why is H gate called a ‘square-root of NOT’ gate?
In Nielsen and Chuang, there's the following paragraph:
I understand that
\begin{align*} \sqrt{NOT} =
\frac{1}{2}\left( {\begin{array}{*{20}{c}}
\sqrt 2 e^{i\pi / 4}&\sqrt 2 e^{-i\pi / 4}\\
\sqrt ...
2
votes
3answers
742 views
Why do quantum gates have to be unitary?
In my textbook, it's said
the unitarity constraint is the only constraint on quantum gates. Any unitary matrix specifies a valid quantum gate!
Why do quantum gates have to have to be unitary? How do ...
2
votes
1answer
94 views
Measuring tensor products of Pauli operators
Is there a neat way to derive and efficiently implement a measurement circuit for tensor products of arbitrary Pauli operators like $XZZXZ$ in Qiskit ?
I tried using the ...
0
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1answer
36 views
Apply a custom gate to qubits in separate quantum registers
Let there be a custom gate (simply called gate that takes $N$ qubits as input. Also, let $A$ of those qubits be in first_register...
