Questions tagged [quantum-gate]

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

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How can we represent a CNOT gate using a cascade of rotation gates?

I have been working using qiskit to implement the CNOT decomposition into a cascade of rotation gates from this source. After computing the unitary matrix, the resultant matrix is not the same as the ...
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1 answer
43 views

How to calculate c not, toffoli gate with additional line

How to calculate cnot gate(or toffoli) in red box Why is there additional line? And is it same as the two toffoli gate?
3 votes
2 answers
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Equivalent $[\![n,k,d]\!]$ codes and transversal gates

An operator on the Hilbert space of $ n $ qubits is called a local unitary if it is of the form $$ U=\bigotimes_{i=1}^n g_i $$ where each $ g_i $ is a $ 2 \times 2 $ unitary matrix. In other words if ...
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Quantum Algorithm to Solve a Maze

I am trying to understand the paper "Quantum Algorithm to Solve a Maze - Converting the Maze Problem into a Search Problem" by Debabrata Goswami and Niraj Kumar (here the reference https://...
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Decompose 8x8 Unitary Matrix into tensor product of three phased gate

We try to decompose 8x8 unitary matrices \begin{pmatrix} e^{ia} & & & & & & \\ & e^{ib} & & & & & \\ & & e^{ic} & & ...
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1 answer
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About swap gate [closed]

As I was reading Qiskit textbook and there is this problem ... How can I swap a $|+\rangle$ to a $|-\rangle$ Qiskit textbook --> Basic Circuit Identities
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3 votes
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What other discrete non-trivial non-Clifford groups of gates are there?

I do not know many groups (as in group theory) of quantum gates. Aside from trivial ones, I know there is Pauli group and the Clifford group. Recently I discovered another interesting group generated ...
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How can the result of 1 million transformations on a qubit be verified to be correct?

I tried to do almost a million transformations on a qubit. I made a three qubit circuit with equal superposition of |0> and |1> (using Hadamard gate) and on the first qubit (qubit 0), added one ...
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2 votes
2 answers
224 views

Matrix representation of SWAP on two qubit registers?

There is a matrix that can represent a swap gate-- a gate that essentially swaps two qubits. This matrix, $S$, is: $$ \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & ...
2 votes
2 answers
165 views

Quasiprobability decomposition of the CZ-gate

I was trying to obtain the quasiprobability decomposition of the CNOT gate by using the information in this paper. The authors give us the example for the CZ gate (Figure 2, i.e. the one below). The ...
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1 answer
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Are relative phase Toffoli gates universal for reversible circuits?

Let us define a new three qubit gate as: $$\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 ...
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1 answer
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Padding a quantum circuit to increase the amplitude by a constant

Let us be given the description of a quantum circuit $\mathsf{Q}$, acting on $n$ qubits, such that \begin{equation} \langle 0^n|\mathsf{Q}|0^n\rangle = \frac{\#0_f - \#1_f}{\sqrt{2^n}}, \end{equation}...
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How to read data from multiple qubits and feed it to a MLP

Being new in the field of quantum computing, I tried with the implementation of "https://qiskit.org/textbook/ch-machine-learning/machine-learning-qiskit-pytorch.html" using a single qubit. ...
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2 votes
1 answer
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How to generate CNOT-gates via Bell pairs

In this paper from Christophe Piveteau and David Sutter, the authors use Bell pairs to generate CNOT-gates. The procedure is shown in Fig.2 and Fig.3 of the paper. By doing the calculations about that ...
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9 votes
2 answers
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Non-entangling two-qubit gates

The non-entangling gates in $ SU_4 $ contains the entire group of gates of the form $$ SU_2 \otimes SU_2. $$ It also contains $$ \zeta_8 SWAP= \zeta_8 \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &...
1 vote
1 answer
533 views

AttributeError: 'list' object has no attribute 'values' [closed]

While implementing a code, getting the below error: ...
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Construct the unitaries U by decomposition in TSP Qiskit? [duplicate]

I'm stuck in here and really don't understand this stuff. In order to construct the unitary matrices for Quantum Phase Estimation, Qiskit decomposes the diagonal unitary matrices U(j) by tensor ...
1 vote
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50 views

How MCMT is implemented in Qiskit, what is the initiution behind it?

I have read about and used the MCMT qiskit gate (Multiple Control Multiple Target). But I wonder how they have implemented it, how is a gate (like CCCZ for example) is decopmosed into basic gates and ...
1 vote
1 answer
47 views

How to apply mid-circuit measurement and measurement based conditional operations in `amazon-braket`?

Is there any method to apply mid circuit measurements in amazon-braket? I'm implementing a circuit that has few operations conditioned to measurement. In ...
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1 vote
2 answers
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How do I draw a multi control cz gate or do I have to make my own gate?

I want to build a diffuser and an oracle so that's why I wanted a multi control cz gate but I looked everywhere I didn't get any
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4 votes
1 answer
153 views

How to represent a statevector in Dirac notation form using Qiskit?

I am learning from qiskit textbook, and I was wondering how may I get a statevector of the following form: $$ \frac{\sqrt{2}}{2}|00\rangle + \frac{\sqrt{2}}{2}|10\rangle $$ If I run code for this in ...
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Building Unitaries in TSP Quantum Phase Estimation Qiskit?

In the paper [https://arxiv.org/pdf/1805.10928.pdf] 2 published by IBM, they use Quantum Phase Estimation to solve the TSP problem. I don't understand the reason why they can decompose the diagonal ...
2 votes
2 answers
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How to find a circuit for a unitary operator $e^{-i s |v \rangle \langle v| t }$?

Let $|v \rangle$ be an eigenstate of an $n$-qubit and $2$-local Hamiltonian $$H = \sum_{i=1}^n \left (X_i + a_i Z_i \right) + \sum_{(i,j)} b_{i,j} Z_i Z_j,$$ where $\sigma_i = I \otimes \cdots \...
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2 votes
0 answers
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How to implement an unitary operator expressed as a linear combination of unitaries without qubits ancilla

Let's say that I know the decomposition of a unitary operator $\hat{A}$ in terms of other unitary operators $U_{k=0, \dots, M}$, i.e: $$ \hat{A} = \sum_k \alpha_k U_k$$ I know how to implement in ...
2 votes
2 answers
86 views

Preparing a superposition state modulo $k$

Consider being given the description of a function $f: \{0, 1\}^n \rightarrow \{0, 1\}^m$ and the binary representation of an integer $k$. Is the state \begin{equation} |\psi_{f, k}\rangle = \frac{1}{\...
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Sample random unitary at a given distance from a given unitary

Is it possible? I.e., what is the most natural procedure of such sampling? The sampling has to be 'uniform' in a vicinity (of radius $\epsilon$) of given $U$ (can I say "according to Haar measure ...
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6 votes
2 answers
251 views

How to intuitively understand why $T$ gate can't be implemented transversally?

Suppose we have all to all connectivity and can implement fault-tolerant logical gates in the Clifford group. Why can't we just apply a physical $T$ gate to every physical qubit in the code block? (...
4 votes
1 answer
257 views

Are there Clifford gates that preserve some computational basis states while otherwise generating superpositions?

Consider a two-qubit Clifford gate that maps $|00\rangle$ to $|00\rangle$, up to a phase. Can it map at least one of the other computational basis states $|10\rangle, |01\rangle, |11\rangle$ into a ...
2 votes
1 answer
71 views

Encoding arbitrary quantum gates using qubits

Given an arbitrary 3-qubit state $\sum_{xyz} c_{xyz}|xyz\rangle$, is there a circuit (possibly with measurement) that creates the state $\sum_{xy} c_{xyy}|x\rangle$, up to a normalization constant? As ...
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3 votes
1 answer
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Does a fidelity of $\mathcal{F}(U_1|0\rangle, U_2|0\rangle)=1$ imply that $U_1=U_2$?

I'm now studying quantum ML and now studying about fidelity ($\mathcal{F}$). To my knowledge, fidelity means the distance between two quantum states, $\textit{i.e.,}$ if $\mathcal{F} ==1$, then the ...
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1 vote
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CNOT gate path interference

I have a question on paper https://doi.org/10.1038/nature02054. In this paper, the CNOT gate is realized using a beam displacer for higher stability. The figure below shows a 1:1 mapping from (a) to (...
4 votes
1 answer
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If you had a 1000 qubit NISQ machine with arbitrary connectivity, what would you do?

Many current devices are constrained to nearest neighbor connectivity or small system sizes, but suppose that a NISQ machine with 99-99.5% level two-qubit gate fidelities and arbitrary connectivity ...
1 vote
0 answers
24 views

Can a Quantum computer simulate classical hack and exploit in a network ? Also how would it be any different from the classical computer [closed]

I'm trying to write a realistic story around Quantum computing and was wondering how different a network exploit/hack would look if a Quantum computer was to hack into a private network, instead of ...
2 votes
2 answers
153 views

Does the ZX calculus allow for Y-axis rotations?

I'm trying to understand how Y-axis rotations are represented in ZX Calculus. In the paper, wikipedia, everywhere I look, it's as if there is no such thing as Y-axis rotations, only X and Z. I ...
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Mapping a classical cipher into quantum implementation of Grover Oracle

I am translating simple ciphers into quantum implementation in order to create oracle for Grover algorithm. I have started the task with a light weight SPECK cipher (got both classical and quantum ...
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4 votes
1 answer
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Regarding the inductive proof that any Clifford gate can be made of Hadamard, phase and c-not

In Exercise 10.40 of Nielsen and Chunang's textbook, the reader is supposed to construct an inductive proof of Theorem 10.6 that any Clifford gate can be made of Hadamard, phase and c-not. There it is ...
1 vote
1 answer
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How to create a quantum circuit with 800+ features using PennyLane

I am new to Quantum ML, and I am currently using PennyLane to do the QML activity. As per this article, total number of features is equal to the total number of qubits. (In the example, they have ...
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2 votes
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Approximating the concatenation of two approximate circuits

Suppose I have two quantum circuits $A_n,B_n$ that I have already found to approximate the operations $U,V$ within some error $\epsilon_n$ and each with an overall circuit depth $\ell_n$ using $n$ ...
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1 answer
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CIRQ How to iteratively apply a multi qubit gate to first n qubits

I've got an arbitrary n qubit circuit, with a "for Q in range(n):", which creates a custom gate class that affects (Q+1) qubits, which I want to apply to first (Q+1) qubits of the circuit ...
2 votes
3 answers
220 views

CNOT entangling a third qubit and how measurement impacts entanglement

I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better. About entanglement: I know that the circuit below will entangle the two qubits: ...
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2 votes
1 answer
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Ungroup a custom quantum gate in QASM 2.0

Is there any API provided by Qiskit to ungroup a custom quantum gate into its component quantum gate. If there is no API, please let me know how to ungroup the custom gate after I made own ...
2 votes
1 answer
406 views

construction of Y gate from X,Z and H gates

As a part of textbook exercise, Y gate is to be constructed using H,Z and X-gates, just like we have $X = HZH$. is there some way/process/intuition to find such combinations or it is just like we need ...
2 votes
1 answer
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Quantum gates supported by qiskit

My question might look a little inappropriate and very basic but I want to know all the quantum gates of qiskit. The link https://qiskit.org/textbook/ch-states/single-qubit-gates.html#generalU gives a ...
2 votes
0 answers
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A path towards building quantum Computing graduation project for undergraduates

I need help. I'm a computer science student with a Data science major. I have a final graduation project this year. With that, I want to create a project in the Quantum computing field. I'm already ...
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How we can switch the digital multi-qubit gates to analog multi-qubit blocks?

What is the difference between the digital and Analog Quantum gate? and the multi-qubit gates involved in a VQE ansatz can be switched to analog multi-qubit blocks. so How we can switch the digital ...
1 vote
1 answer
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How to draw CCZ gate in IBM Quantum composer

How to draw CCZ gate in IBM Quantum Composer? There is no CCZ gate in quantum composer. In addition to this, please help me to draw the gate shown in below figure in quantum composer.
1 vote
1 answer
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ucry and ucrz gates in Qiskit

I just came across ucry and ucrz gates in Qiskit. It would be great if someone has experience of using it and can explain it with an example and also with a bit of Python code. I only know about the ...
0 votes
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I have two quastion about n-MCT gate decomose into Clifford+Zn

this figure from paper :New techniques for fault-tolerant decomposition of Multi-Controlled Toffoli gate can someone tell me why cir1 is different from cir 2 , can they all represent Toffoli? the ...
1 vote
1 answer
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Julia codes for unitary gate decomposition

I am looking for a way to decompose any given operator U into ZYZ rotations. And then plug the values back into ei∗α∗Rz(θ0)∗Ry(θ1)∗Rz(θ2), to 'recompose' the gate and check if the gate decomposed ...
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1 vote
2 answers
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What is more important, minimizing the number of gates, or the number of qubits?

I am new to the quantum world, and I have 2 circuits that measure cosine similarity between 2 binary vectors. One uses a swap test, the other uses something called a hyper-state generation procedure. ...

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