Questions tagged [quantum-gate]

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

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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 ...
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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)\...
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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 ...
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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 ...
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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\...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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...
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For any two quantum states does there exist a gate that takes you from one to the other

For any two states $|\phi\rangle$ and $|\psi\rangle$ Does there exist a gate $U$ such that $U|\phi\rangle = |\psi\rangle$ ? I suppose that we know for a vector space $V$ then $\forall \quad a, b \quad ...
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2 votes
2 answers
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Qiskit CNOT-gate matrix mixup?

In the qiskit textbook chapter 1.3.1 "The CNOT-Gate" it says that the matrix representation on the right is the own corresponding to the circuit shown above, with q_0 being the control and ...
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Vector math of applying an X-gate on an $|i\rangle$ basis state

It is well known that the X-gate will apply a rotation about the x-axis on the bloch sphere. Knowing this, the $|i\rangle$ state should be converted to the $|-i\rangle$ state on the application of ...
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3 answers
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How does one interpret intuitively the CNOT gate?

How does one interpret the CNOT gate? The CNOT gate takes a separable state and turns into an entangled state. The oracle in the Deutsch algorithm does the same thing. But how does one understand this ...
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How to perform a plot histogram for a circuit?

I have created a circuit and I don't know how to plot a histogram. I tried to plot a histogram but it gives me output for 0000 case only, how to get to know the probability for all of the cases. The ...
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3 votes
1 answer
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Getting exponential sequence of coefficients with not so many $T$-gates

Let $\Psi \in (\mathbb{C}^2)^{\otimes n}$ be a $n$-qubit quantum state. In the computational basis, we can write $\Psi$ as $$\Psi = \sum_{(i_1, \dots, i_n) \in \mathbb{F}_2^n} \Psi_{i_1, \dots, i_n} |...
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Measuring the accuracy of a circuit output?

I have created a circuit and got the output which matches the truth table but, I'm not understanding the measuring the circuit output in terms of the probabilities, power or error. This is the circuit ...
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Circuit for fault tolerant syndrome measurements Steane Code

I was exploring this paper: https://arxiv.org/pdf/1505.07390.pdf The paper describes the syndrome measurement for the [7,1,3] code. I was looking a fault-tolerant syndrome measurement and found this ...
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Can such a transformation be implemented by using just polarizers?

Consider a transformation $U_a=\sigma_z^{a_1}\otimes...\sigma_z^{a_N}$, here $\sigma_z$ is the Pauli Z operator. $a_i$ is either 0 or 1. Hence, $\sigma_z^{0}=I$ where $I$ is identity matrix. If I use ...
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2 votes
2 answers
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How does a quantum circuit calculating the inverse of a non-injective function act?

Lets say I have a non-injective function $f()$, adding image for reference. Now lets say I build a quantum circuit to calculate $f^{-1}()$. If the input register has the value $i$, does the output ...
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1 vote
2 answers
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Can there be different gate implementations of same oracle implementation?

I have been reading about Bernstein-Vazirani Algorithm, and it uses what is known as a phase oracle. Basically, it is CNOT gate with several controls attached to the ancilla qubit $|-\rangle$ (it is ...
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4 votes
1 answer
117 views

How do you represent a Hadamard gate as a product of $R_x$ and $R_y$ gates?

I'm looking for a representation of Hadamard gate that uses only $R_x(x)$ and $R_y(y)$ gates. The values $x$ and $y$ may be the same, but they don't necessarily need to be.
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1 vote
1 answer
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What is a bipartite unitary?

What is a 'bipartite unitary'? I saw it appearing in a paper "Efficient verification of quantum gates with local operations" (https://arxiv.org/pdf/1910.14032.pdf) A reference to the ...
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Restrictions on Quantum Gates and Pure Partially Traced Output States

Suppose we have a quantum circuit that contains an arbitrary number of quantum gates and takes as an input more than a single qubit, say three. What are the restrictions on the quantum gates and the ...
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3 votes
3 answers
278 views

Is every single-qubit unitary just a rotation around some unit vector on the Bloch sphere?

I remember reading this somewhere... Is there an elegant proof for this?
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1 answer
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Quantum fourier transform with classical vibrations

Is there any difference in effect between a quantum circuit and a carefully constructed analogue one relying on interference? For example, why couldn't I take a series of $N$ carefully shaped pipes, ...
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5 votes
1 answer
198 views

What is the correlation between Toffoli and a more generic rotation shown in qiskit textbook

Can someone help me understand the correlation between the 2 diagrams in the qiskit textbook.
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7 votes
2 answers
150 views

Explicit states with high $T$ count

It is well known, that the Clifford $+T$ gate set consisting of the gates $\lbrace H, S, CNOT, T \rbrace$ is universal for quantum computation, that is, for any n-qubit unitary $U:\left( \mathbb{C}^2\...
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1 answer
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How can I simulate the Avg CNOT Error on IBMQ Backends?

I want to know exactly how to estimate the Avg CNOT Error rate for IBMQ Backends? For instance, I tried to estimate the Avg CNOT Error rate for Belem Backend; I randomly prepared the 00,01,10,11 ...
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4 votes
0 answers
72 views

Universality for reversible classical computation

Is there any way to check whether a set of gates (for example, take the set comprising of the CNOT gate and the Hadamard gate) is universal for reversible classical computation? I can think of trial ...
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6 votes
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Postselection and hardness of estimating amplitudes

Let $A$ be a class of quantum circuits such that \begin{equation} \text{Post}A = \text{Post}BQP, \end{equation} where $\text{Post}$ indicates post-selection. Is only this amount of information ...
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6 votes
1 answer
328 views

How efficient is Qiskit's unitary decomposition?

In Qiskit's extension package we have the UnitaryGate module that you can initialize using a unitary matrix and then add it to your circuit. How efficiently is this ...
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Understand the circuit of Normal Distribution

This is the circuit for NormalDistribution(3, mu=1, sigma=1, bounds=(0, 2)). How do I understand what this circuit is doing?
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3 votes
2 answers
333 views

How to construct a controlled $V$ gate in qiskit?

I have come across most of the quantum circuit which contains gate such as controlled $V$ and $V^{\dagger}$ but I dont know how to code it in Qiskit.
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4 votes
0 answers
67 views

Extract the Crosstalk noise of a circuit in Qiskit

I'm new to Quantum Computing. How to extract the cross-talk noise of a quantum circuit using qiskit? Can someone provide an example code for this?
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4 votes
0 answers
81 views

An algorithm to perform Gram-Schmidt orthogonalization of linearly independent state vectors

In the first paragraph of the 2nd section of this article, it is stated that given a set of linearly independent $n$-qubit state vectors, Alice can perform the Gram-Schmidt procedure to obtain ...
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4 votes
1 answer
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Exercise 4.41 in N&C book QCQI: how can i implement $R_z(\theta)$ using the circuit shown and $Z$?

I'm studying Nielsen and Chuang's book. I cannot solve one of the questions in the exercise 4.41. The question is the last one that is Explain how repeated use of this circuit and Z gates may be used ...
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2 votes
0 answers
42 views

Marginal output probability of first bit for constant-depth circuits

Consider a constant depth $1\text{D}$ quantum circuit, which is applied to the input state $|0^{n}\rangle$, and whose output is measured in the standard basis. You can assume that the gates of the ...
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7 votes
2 answers
282 views

Complexity of $n$-Toffoli with phase difference

I'm interested in the $n$-Toffoli gates with phase differences. I found a quadratic technique in section 7.2 of this paper. Here's the front page of the paper. Here's an image of the section that I'm ...
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2 votes
1 answer
206 views

How the single qubit unitary (U) calculates when apply a gate to only one qubit at a time?

Qiskit Textbook, Chapter 2, Section 2.2. Single Qubit Gates on Multi-Qubit Statevectors (here). In here, they have described that: If we want to apply a gate to only one qubit at a time (such as in ...
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6 votes
2 answers
933 views

How to visualize Hadamard gate as $X$-$Z$-$X$ decomposition?

In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of $R_x$, $R_z$ rotations and ...
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3 votes
0 answers
41 views

Is there a way to directly construct controlled gates in continuous variable (CV) quantum computation?

We know that a universal gate set for CV quantum computation is that of squeezing, beam splitters, and some nonlinear gate (e.g. this answer). We also know from Knill, Laflamme, and Milburn that ...
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1 vote
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Matrix for $U^{2^j}$ from Shor's algorithm for any $a$ and $N$

I'm implementing Shor's algorithm from scratch and therefore want to implement a unitary gate $U$ such that $U^{2^j}|y\rangle = |a^{2^j}y \: \text{mod} \: N\rangle$. I know that an efficient way of ...
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