Questions tagged [quantum-gate]

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

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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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110 views

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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1answer
31 views

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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3answers
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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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1answer
59 views

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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33 views

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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36 views

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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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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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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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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1answer
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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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1answer
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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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78 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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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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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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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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How to get the $a^{(\gamma)}_L(x)$ in Fixed-Point Quantum Search with an Optimal Number of Queries

How is $a^{(\gamma)}_L(x)=\frac{T_L(x/\gamma)}{T_L(1/\gamma)}$ with $T_L(1/\gamma)=1/\delta$ obtained from equation (15), of this PDF?
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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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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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115 views

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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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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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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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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1answer
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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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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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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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1answer
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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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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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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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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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2answers
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ibmq_16_melbourne system of Qiskit giving wrong result for Bernstein-Vazirani Algorithm

I have just started learning Qiskit and to begin I tried running the Bernstein Vazirani Algorithm(secret number detector) on qasm_simulator and the ...
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Who was the first to call the phase gates $P(\pi/2)$ and $P(\pi/4)$ the $S$ and $T$ gates, and were they motivated by generators of the modular group?

Within the theory of quantum gates, a common pair of single-qubit phase gates are the $P(\pi/2)=S$ and $P(\pi/4)=T$ gates, with $$S= \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix},\:T = \begin{...
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1answer
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Can an arbitrary circuit be represented using two commands (qsel package)?

I was watching this entertaining video by David Bacon (as in "Bacon-Shor code", Cirq, ...) : video of talk where he mentions the package he wrote: (qsel), that describes simulating quantum ...
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Is a black-box gate whose output is conditional on the value of an input amplitude possible?

Suppose we have a qubit in the state $|q\rangle = a |0\rangle + b |1\rangle$, and another ancilla qubit $= |0\rangle$. I wish to have the following black-box gate: ...
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Circuit to transform $|0\rangle$ into $\alpha|0\rangle + \beta|1\rangle$ for any $\alpha, \beta$

Hi I'm new to QC and doing some katas in Q#. I got stuck on this excercise and would appreciate help: Quantum circuit to get following state qubit: $\alpha|0\rangle + \beta|1\rangle$ when the input is ...
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How do I construct a Breidbart gate in Qiskit?

Based on this : https://qiskit.org/textbook/ch-states/single-qubit-gates.html How do I construct a Breidbart gate (which is like the Hadamard gate but with $\pi/8$ instead of rotating by $\pi/4$)? I ...
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Good resources for seeing qubit control pulse shapes (Transmon qubits)

I'm looking for resources which can show the pulse shapes for various single-qubit and two-qubit gates. More specifically, is there any resource which can show me calibrated pulse shapes so that I can ...
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How to implement the power of a product of quantum gates as a circuit?

Suppose I have quantum gates (i.e. unitary matrices) $A$ and $B$, and I want to implement $(AB)^x$ in a circuit. If $x$ is integer, I can simply apply $A B$ repeatedly $x$-times. But what if $x$ is a ...
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1answer
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How to construct an $n\times n$ unitary matrix taking an arbitrary $|\psi\rangle$ to a target state $|\phi\rangle$?

I came across Lecture 12 here https://viterbi-web.usc.edu/~tbrun/Course/ that does this but I was not able to understand. An example would be very helpful
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1answer
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Is the cost Hamiltonian unitary in QAOA?

I am trying to implement QAOA and there are things I don't understand at all. The expansion of $H$ into Pauli $Z$ operators can be obtained from the canonical expansion of the cost-function $C$ by ...
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Can Dirac notation be used with 2 or more gates?

Can Dirac notation be used with 2 or more gates? I've been trying to do the math with the $X$ and $Z$ ($X\otimes Z$) gates but I'm not getting the answer I should. In fact, the answer makes no sense. ...
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1answer
58 views

Can I freely rearrange the controlled-shift gates in this 3-qubit circuit?

Consider a fixed set of gates of the kind $\land_n(P_{\varphi})$. With $P_{\varphi}$ being a relative phase shift gate by $\varphi$. Can I assert that any permutation of that set is equivalent? ...
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1answer
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Entanglement properties of $SU(8)$ quantum circuits vs nearest-neighbor $SU(4)$ quantum circuits

For this question, fix three qubits $q_1, q_2, q_3$. I'll use the notation $U_{123} \in SU(8)$ to denote an arbitrary quantum circuit/unitary on the three qubits, and $U_{12}, U_{23} \in SU(4)$ to ...
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Are SU($n$) operations enough for quantum computation?

Usually we want a quantum computer that can perform all foreseeable unitary operations U($n$). A quantum processor that can naturally perform at least 2 rotation operators $R_k(\theta)=\exp(-i\theta\...
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Are circuits with more than 1000 gates common?

I have seen circuits with 30 qubits and around 500 gates. Also circuits with 32 qubits and 6000 gates. Are circuits with more than 1000 gates common in quantum computing? Are there many quantum ...
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How does the pulse.Shiftphase instruction in Qiskit Pulse work? [closed]

I have some questions regarding the mechanism of Qiskit pulse.ShiftPhase instruction: Does it work like a Phase Shift $P(\theta)=\begin{bmatrix} 1 & 0 \\0 &...

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