Questions tagged [quantum-gate]

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

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Syndrome extraction in bit-flip code using stabilizers

I'm trying to understand how syndrome extraction in bit-flip code works. I've been reading Quantum Error Correction: An Introductory Guide, and I was wondering how the syndrome extraction part in this ...
Hamed's user avatar
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What is the purpose of the Cirq gate cirq.measure?

Can you tell me more about the cirq.measure gate ?
Andlan Zhang's user avatar
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Diffuser's hadamard logic in equal superposition with negative phases

This is with reference to the question here: How to understand intuitively the Grover diffusion operator? Overall it makes sense on how H^n of the diffuser logic creates the |000..0> from an equal ...
GRK's user avatar
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Hilbert space of n qubits always has a decoherence free subspace if n is even?

I've heard that a subspace of an $ n $ qubit Hilbert space is called decoherence-free if it is not affected by errors of the form $ g^{\otimes n} $ where $ g \in SU(2) $. Let $ \textbf{2} $ denote the ...
Ian Gershon Teixeira's user avatar
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How to figure out the action of a circuit form its effect on logical operators?

I am looking at the following circuit from "The Heisenberg Representation of Quantum Computers" by Daniel Gottesman. I understand how the circuit acts on the logical operators. I understand ...
am567's user avatar
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How can i label input and output ports of my QuantumCircuit in qiskit?

I made quantum circuits as quantum gates then later used these gates in a larger circuit. Here, the input ports of the block (which is the gate) are labelled by integers but i want to custom label ...
Syed Shahmir Kazmi's user avatar
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1 answer
71 views
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How does one create a long range CNOT gate on a square grid of qubits using constant depth circuits?

In this talk, the speaker shows a bunch of data qubits on the top and ancilla qubits at the bottom that need to be linked by CNOT gates. The grid here is $n\times n$. The procedure is to swap the ...
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Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?

There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum ...
am567's user avatar
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How can we see on Cirq that Google Sycamore has 54 qubits?

Hello, can you explain how to see in Google Cirq that the figure above is a 54 qubits quantum computer ? thanks
Andlan Zhang's user avatar
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Algorithm to reveal properties of a random quantum permutation gate

Given a unitary $U$, which implements a random permutation $\sigma$, such that the input to the unitary permutes as here: $|v_1\rangle\otimes\ldots\otimes|v_n\rangle$ becomes $|v_{\sigma(1)}\rangle\...
schmector's user avatar
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What is the explicit action of the following circuit?

Would somebody please be able to explain the action of this circuit to me? (Taken from Arthur Pesah's blog post "Computing with Quantum Codes using Transversal Gates") I understand overall ...
am567's user avatar
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How does one realize quantum gates on actual quantum devices?

I am interested in understanding the process of implementing quantum gates on actual quantum hardware such as those developed by Google, IBM, and others. My current understanding is that each hardware ...
user185671631's user avatar
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Calculation of feasible operations for a certain set of primitive gates

Assume we have a set of primitive operations of a quantum processor. How can I determine the set of feasible operations or prove that a certain operation is not feasible? As an example, one could ...
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Implementing cphase gate on IonQ through Amazon Braket

I am implementing a VQE algorithm where I need controlled phase gate as part of ansatz circuit. I am using Amazon Braket service. Ionq processor however does not support c-phase gate or phase gate. ...
F1_light's user avatar
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1 answer
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Why is the first logical unitary gate in this example fault tolerant?

From Arthur Pesah's blog on "Computing with Quantum Codes using Transversal Gates", found here: https://arthurpesah.me/blog/2023-12-25-transversal-gates/ He gives the following examples of ...
am567's user avatar
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I would like to understand the meaning of applying permutation to a unitary matrix

$$U = \frac{1}{2} \begin{pmatrix} -1 & -1 & 1 & 1 \\\\ 1 & -1 & 1 & -1 \\\\ 1 & -1 & -1 & 1 \\\\ 1 & -1 & 1 & 1 \end{pmatrix}$$ $$P = \frac{1}{...
junghyunHa's user avatar
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Encoding boolean function in a quantum circuit

Let $U_f$ be the quantum gate such that $| x \rangle | y \rangle \mapsto | x \rangle |y\oplus f(x) \rangle$, where $x$ is some bit string of size $n$, $|y\rangle$ is a qubit, and is $f$ is some ...
joeren1020's user avatar
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Qiskit bad unitary decomposition

I want to decompose a two-qubit unitary gate $U$, $$U = e^{-i \cdot \frac{t}{2} \cdot Z_1 \cdot Z_2}\,,$$ where $t$ is an angle. I already know the right decomposition but Qiskit gives me an ...
Daniele Trisciani's user avatar
4 votes
2 answers
381 views

What unitary commutes with all local Pauli operators?

I was thinking about this problem of identifying a set of unitary operations (other than the identity operation) that commute with local pauli $\sigma_X$ and $\sigma_Z$ matrices, i.e. find $U$ such ...
Mohan's user avatar
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How would I write the equation for this circuit?

Would the equation for this circuit be: $$(H \otimes H) \cdot \text{CNOT} \cdot (H \otimes H)$$
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Spin Hamiltonian to Quantum Circuits and are there any group theory associated with the quantum circuits?

Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model ...
Jessica John Britto's user avatar
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1 answer
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How is the $\text{CNOT}$ gate equivalent to $\text{XOR}$?

This is a screenshot from my lecture: Why does the $\text{CNOT}$ here output $a ⊕ b$? Does the "$⊕$" operation even make sense for a quantum state?
Siddarth's user avatar
3 votes
1 answer
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Simulate an arbitrary stablizer circuit with only CNOT gates

It is claimed that Informally, this means that any stabilizer circuit can be simulated using CNOT gates alone; the availability of Hadamard and phase gates provides at most a polynomial advantage. ...
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Two qubit Pauli expectation value of $\underset{U}{\mathbb{E}}[U^{\otimes 2} (P_1 \otimes P_2)^{\otimes 2} U^{*\otimes 2}]$

I want to find a value for the expression: $$\underset{U}{\mathbb{E}}[U^{\otimes 2} (P_1 \otimes P_2)^{\otimes 2} U^{*\otimes 2}],$$ where $U$ is a two-qubit unitary operator chosen Haar randomly, $...
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How to implement a quantum_and() gate

I have encoder() and decoder() functions as follows: ...
Panky's user avatar
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2 answers
109 views

Implementing error correction (from physical qubit point of view)

I have worked with physical qubits, and I am fairly familiar with gates and sequences from initialisation to readout. I don't know much about error correction, and I love to learn how error correction ...
Rex's user avatar
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1 answer
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How can I use Quantum Shanon Decomposition for any $N \times N$ matrix?

I have a non-unitary and non-hermitian matrix of $16\times16$. I have used singular value decomposition to break that matrix into three matrices i.e. $A = UDV$, Where $U$ and $V$ are unitary but still ...
Syed Shahmir Kazmi's user avatar
3 votes
1 answer
296 views

Hadamard transform on state

I'm reading this paper and have a question about the computation to go from (3) to (4). Define the state $\vert\psi\rangle = \sum_b\alpha_b\vert b\rangle$. In (3), we have the state $$\sum_{b \in\{0,1\...
JRT's user avatar
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Silq Language - Custom quantum gate

Having a unitary matrix, is it possible to use it as a custom quantum gate using Silq quantum programming language? I found different documentation on the internet explaining how to do custom quantum ...
Danilo Berta's user avatar
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1 answer
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Reducing the text content inside a custom quantum gate in Qiskit

I have prepared a parameterized custom quantum gate in qiskit by converting a quantum circuit into a gate through QuantumCircuit.to_gate(). However, the text ...
user9043261's user avatar
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1 answer
57 views

Multi-qubit rotation using Quirk

I was wondering, how can one perform a multi-qubit rotation in Quirk? For example, if I want to simulate the magic-state distillation protocol, I need e.g. a $(IIZZZ)_{\pi/8}$ rotation of 5 qubits. Is ...
David Dentelski's user avatar
1 vote
1 answer
66 views

Implementation of classical control of multi-qubits gates multiple times

I am implementing classical control of gates multiple times. There is no issue if the gate is a local gate, such as an $X$ gate. However, it seems that if I append the control multi-qubits gates more ...
JiQing's user avatar
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2 votes
1 answer
104 views

Is there an "in place" Toffoli gate?

I am trying to implement the multiplication of a scalar in $\mathbb{Z}_2$ and a polynomial in $GF(2^n)$ in Qiskit. One naive method of implementation that I can think of is: ...
Ash Ketchum's user avatar
1 vote
1 answer
169 views

Process matrix of CNOT gate

The fig below is the process matrix of the CNOT gate from this paper: where the legend explains that red corresponds to $\frac14$, green to $-\frac14$ and white to zero. I know the $U_{CNOT} = \frac{...
karry's user avatar
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2 votes
1 answer
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Multi-control multi-target gate

I'm using qiskit for simulation. Suppose, I have 6 qubits with indices [0, 1, 2, 3, 4, 5] and I have an operator $U$ of size $4 \times 4$, such that it operates on ...
Марина Лисниченко's user avatar
1 vote
1 answer
65 views

Why there's an issue when a quantum gate is controlled in the same time by 0 on a qubit and 1 or 0 with a classical bit on Qiskit?

I'm doing a project for an internship related to quantum computing and I was trying to do this operation on Qiskit lab: ...
Thomas's user avatar
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1 vote
1 answer
66 views

Rotation angle of arbitrary two-qubit gates

Exponential representation of single-qubit gates For arbitrary single-qubit gate $U_{\mathbf{1}}$, we can express it in such a form $$ U_{\mathbf{1}} = e^{i\alpha}\exp[-i\frac{\theta}{2}\vec{v}\cdot\...
Yunzhe's user avatar
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-1 votes
1 answer
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Are any quantum circuit can be translated into a matrix [closed]

Given a quantum circuit, can we transform it into a Matrix. If the answer is yes - so practically, any quantum circuit is a presentation of matrix?
Avi's user avatar
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1 answer
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Magic state distillation of physical vs logical qubit

In the original paper by Bravyi and Kitaev, the distillation procedure takes 5 physical qubits, each prepared in a faulty T state. The qubits are in a product state, and error can be detected by ...
David Dentelski's user avatar
1 vote
1 answer
97 views

Decomposing a $4 \times 4$ unitary matrix into 2-level unitary matrices

I am studying how to decompose a $4 \times 4$ unitary matrix into multiple 2-level unitary matrices. I have found a total of six 2-level unitary matrices, and they are as follows. At this point, I ...
junghyunHa's user avatar
1 vote
1 answer
87 views

How do you work out the matrix for controlled-U operations?

I see this equations all over for controlled-U operations: $$ \left|{0}\right>\left<{0}\right| \otimes \mathbf{1} + \left|{1}\right>\left<{1}\right|\otimes U = \begin{pmatrix} \mathbb{1} &...
grepgrok's user avatar
4 votes
1 answer
244 views

Qiskit reverse_bits is not equivalent to swapping qubits

For three qubits, I thought swapping the first and third qubit is equivalent to vertically flipping the circuit. However, performing one and then the other in Qiskit returns two different operators, ...
Dylan VanAllen's user avatar
6 votes
1 answer
99 views

Which Clifford groups are 2-designs?

Let $ X $ be the $ q \times q $ shift matrix sending $ |y \rangle \mapsto |y+1 \rangle $ where the ket index $ y=0,\dots, q-1 $ is taken mod $ q $. Let $ Z $ be the diagonal $ q \times q $ clock ...
Ian Gershon Teixeira's user avatar
2 votes
1 answer
58 views

How to compute the gate matrix for an operation on qubits not next to each other

I have a quantum circuit with 4 input qubits, A, B, C, and D. A is at the top, D is at the bottom. If I wanted to do a CNOT between B and C and leave A and D alone, I know the gate matrix for this ...
Pro Q's user avatar
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1 vote
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W state Entanglement Breaks During $X$-Basis Measurement

I'm encountering a problem in my Qiskit simulation involving W-state entanglement. The issue arises when attempting to measure all three qubits in the $X$ measurement basis. Surprisingly, the ...
Rayhan Kabir's user avatar
-2 votes
1 answer
70 views

Measuring probabilities of 0 or 1 in a two qubit state

I'm preparing for my upcoming exam, I need to determine the probabilities with which Bob measures 0 or 1 and in both cases describe the state of Alice, this is my state: $$ |\psi\rangle =\frac{1}{\...
embe99's user avatar
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-2 votes
1 answer
124 views

Disentanglement of qubits from output of CNOT gate

Suppose we have a control qubit with initial state $\binom{a}{b}$ and a target qubit with initial state $\binom{c}{d}$.What a CNOT does is transform the state of the target qubit into: $\begin{pmatrix}...
Root Groves's user avatar
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1 answer
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IBM quantum composer possible bug?(state amplitudes of quantum circuit)

I have this quantum circuit: and from the IBM quantum composer I get this state amplitudes: I wanted to flip the target qubit and keep only its pure state however this is not what I am getting.I am ...
Root Groves's user avatar
3 votes
3 answers
173 views

Matrix representation of the qutrit gate analogous to Pauli-$X$ gate

What is the qutrit gate analogous to the $X$ gate for qubits, i.e. NOT gate? and what is the matrix representation of that gate? I have searched on the Internet but couldn't find anything related. ...
Root Groves's user avatar
1 vote
0 answers
22 views

How to represent the gates and the quibit states in the 'Hello Quantum' iOS game in IBM Quantum Learning graphical simulator

The Hello Quantum ios game developed by IBM has the X, Z, H and CZ gates manipulating a 2 qubit array (im not sure if array is the right word?). I want to know how I can represent the qubit states in ...
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