Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates.
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How to realize the index shift operation in quantum circuit?
Can we realize the index shift in a quantum circuit as we do in a classic circuit?
$\forall$ $a,b,c \in \{0,1\}$, $\left|abc\right>\mapsto\left|bca\right>$
e.g. $\left|001\right>\mapsto \left|...
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Liouvillian Spectrum of Spin chains in qutip [closed]
Is it possible within qutip only to find the Liouvillian Spectrum of a xxz spin chain or I have to import some commands from other libraries such as scipy.linalg etc.
By finding the spectrum, I mean ...
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Small, distance 2 quantum codes with transversal Clifford group
Are there any small, distance 2 quantum codes with a transversal Clifford group? For example, the 7-qubit Steane code is distance 3 but has the full single-qubit Clifford group. Are there smaller ...
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Coding a hamiltonian in qiskit
I have a hamiltonian of the form:
$H=\sum_{i=1}^N Z_i Z_{i+1}-Z_NZ_1$
And another one as:
$H=-\sum_{i=1}^N X_i$
I need it to it for N terms.
I am a bit lost can anybody help. I tried looking for ...
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Improvements to MC-U on every subset
Let's say we have some uniformly random n-bit integer $x = x_0 + 2*x_1 + 4*x_2 \cdots$. And we have some commutative operation $+{y}$ implemented as the unitary $U(y)$, with identity element $0$, so $...
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Is it possible to approximately compile Toffoli using H and CSWAP?
Question:
Given all controlled-SWAP (CSWAP) and Hadamard (H) gates on 3 qubits, is it possible to approximately compile the Toffoli (CCX) gate?
Discussion
From basic simulations, it appears that all $\...
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Parameterized Gates [duplicate]
I am trying to create my own custom parameterized gate and then transpile it to the AerSimylatorGate. I have been able to create the virtual circuit but in the transpilation to the backend basis set ...
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What are the Error Reduction Factors for Shor’s EC, Knill’s Gadget, Steane’s Gadget, and Flag Gadgets?
Similar to how cat state gadgets make the number of errors $p$ into $(1-p)^m$ what do the aforementioned gadgets do? If not the error reduction, what is the threshold?
Even if it is a link to a ...
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Numerical values for the volume of qubits
This paper mentions the volume of qubit in equation (9) given by:
$$Q_0=U*C_1*T_o*n_p^{(2/3)}*(v_q)^{(2/3)}$$
where
$Q_0$ is the heat entering the chamber
$U$ is the heat transfer coefficient
$C_1$ ...
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Custom Quantum Gate equivalence to backend basis gate set
Hello I am using Qiskit and I have defined a custom gate which implements the array shown in the image:
This array is unitary and the function R(theta) works by tuning a continious variable into 0 of ...
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How is the computational power defined in Quatum Computing?
In classical data centers, the computational power is expressed as function of the number of executed tasks per second as follows :
$$P(\lambda)=P_{idle}+(P_{peak}-P_{idle})\cdot(\lambda/CPU_{capacity}...
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Transpilation error: CircuitError: 'The amount of qubit(0)/clbit(0) arguments does not match the gate expectation (2).'
I am trying to implement a algoritm that reduces the number of qubits required for MAXCUT optimization. I need to create a custom gate that encodes a diagonal unitary matrix where the diagonal ...
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Is the normaliser of the Clifford group the Clifford group itself?
The Clifford group is defined as the normaliser of the group of multi-qubit Pauli unitaries.
What is the normaliser of the Clifford group?
Since Paulis are themselves Cliffords, such a unitary in the ...
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How is $R_{ZZ}(\pi/2)$ gate maximally entangling?
IBM Qiskit website says $R_{ZZ}$ gate is maximally entangling at $\theta = \pi/2$.
But acting $R_{ZZ}$ on two qubits initialized as $ |00 \rangle $ still remains $ |00 \rangle $ so it is separable in ...
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Is the outcome of this quantum circuit correct and if so why?
I am very novice with quantum computing and try to understand it. I thought I was getting a handle on it until I built the quantum circuit (1) below. The app I used to build it allows me to measure ...
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Implementation of U3 and U1 gate in Qiskit-1.0
How do I implement those two gates in the new version of Qiskit? I have used RY and PhaseShift resp. but I don't know if it's correct or not.
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Is the group of single-qubit Clifford+$T$ unitaries solvable?
Let $G_k$ be the group of unitaries generated by the $H$ and $R_Z\left(\frac{2\pi}{2^k}\right)$ gates up to a global phase (i.e $G_k$ is a subgroup of $U(2)/U(1)$). Since $G_2$ is the group of single-...
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Is any multi-qubit unitary operation a rotation about a specific unit vector?
I understand that any single qubit unitary operation can be expressed as a rotation around a three dimensional unit vector. Is it possible to do the same for multi-qubit unitaries? Can I express an $n$...
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Fault-tolerant CNOT gates
The controlled-not gate
$$
CNOT = \begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \end{bmatrix}
$$
is important in many ...
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Do we really apply both single-qubit and two-qubit gates in the same layer in experiments?
I'm doing experiments using superconducting computers, and my question is as follows:
Performing quantum gates requires isolating the coupling between a target qubit and other neighboring qubits.
To ...
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Why do we use Z-gates in the following figure?
This is a picture of a 'T-gate gadget' and a proof for a circuit from “Quantum homomorphic encryption for circuits with low T-gate complexity” by Broadbent, Jeffrey (2015) (arXiv). My question is why ...
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Custom pulse with fake backend not running for Cross Resonance Pulse
I am trying to create a cross resonance pulse by driving the control qubit at a non resonant frequency. My code runs but does not stop running.
...
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What is the connection between an observable and a gate?
I am reading some introductory quantum mechanics and I don't understand the connection between an observable and a gate. I thought a gate just applies a rotation to a state while a measurement gives ...
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How do the Type I and Type II fusions work?
I am going through the original paper on Type I and Type II fusions. But I cannot understand how this is actually implmented. They say they start with
$$\frac{1}{2} |H,H\rangle+|V,V\rangle \otimes |H,...
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Intro book on classical and quantum computing by Thomas G Wong
Looking at his book, and am obviously new to studying this. Could someone help explain to me how the truth table is valid here?
To my understanding, when $C=0$, the circuit behaves like a reversible ...
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Can IBM Quantum hardware handle any CSWAP at all?
I am designing quantum algorithms where the quantum circuit uses CSWAP gates a lot. The result is very noisy on the quantum hardwares. So I designed really simple circuits to test whether it is indeed ...
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How to write Verilog code to describe a quantum system
I would like to ask everyone for some verilog code sources that implement quantum systems so I can refer to them
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What does it mean for a gate to "commute with a measurement"?
I think I understand intuitively what this means. For example, I can apply an $X$ gate and then perform a measurement in the $X$ basis and I will get the same post-measurement states as if I measured ...
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Are transversal entangling gates possible for stabilizer codes other than CSS?
It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304....
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What do symmetric 2-qubits gates look like?
A gate $U= (u_{ij})_{i,j= 1}^4$ is symmetric if the action of the gate is the same as the action of $Swap\ U\ Swap$ where the swap gate is $$Swap= \begin{pmatrix} 1 & 0 & 0 & 0 \\
0 & ...
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Mathematical expression of controlled Ry gate
"How can I describe the controlled Ry gate transformation on the ground state qubit using a mathematical formula similar to the one below, which is for the CNOT transformation?"
The example ...
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Why is the controlled-Z gate a symmetric gate?
I want to understand why this gate is symmetric.
Consider a two qubits circuit (q1, q2) with a gate CZ controlled by the first q1, then if q1 is in the state $(a, b)^T$ and q2 is the state $(c, d)^T$, ...
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unitary that transform $\sigma^x \pm \alpha \sigma^z$ into $\sigma^x$ and $\sigma^z$
Consider $\sigma^x \pm \sigma^z$, where $\sigma^x$ and $\sigma^z$ are Pauli $X$ and $Z$ matrices. Let unitary $U$ be a $\pi/4$ rotation matrix around $Y$-axis. Then,
\begin{equation}
U(\sigma^x + \...
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Is every code with a universal set of transversal gates trivial?
The quantum repetition code is an $ [[n,1,1]] $ stabilizer code with stabilizer generators $ Z_iZ_{i+1} $ for $ i=1, \dots, n-1 $.
The Eastin-Knill theorem states that a $ d >1 $ code cannot have a ...
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Show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \right\rangle$ is unitary [duplicate]
I am reading Quantum Computation and Quantum Information by Chuang and Nielsen and they claim that it is easy to show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \...
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Do magic states only work for CSS codes?
Magic states are used to obtain universal fault tolerant quantum gates.
The process involves distilling high quality magic states from many lower quality magic states using a state distillation ...
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Doing Quantum State Tomography on a custom-made gate with Qiskit Pulse
In this simple example I took the Qiskit CX gate, obtained the pulses' schedule and then tried to do Tomography on that. In theory, everything should run smoothly (I think) but I get this "error&...
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How can I measure qutrits in the X basis using cirq?
I attempted to create a custom measurement class which, in my case, allows us to go from the z basis to x basis using a hadamard gate transformation, and then we measure wrt that new basis. However, ...
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Why focus on T gates and not some other single qubit rotation R making Clifford + R universal?
Background: In many error correction codes in particular the surface code, the Clifford operations generated by the S,H and CNOT are transversal for quantum computation (meaning that these logical ...
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Single bit teleportation for Hadamard gate
The circuit in Figure 13.7 of Gottesman's book https://www.cs.umd.edu/class/spring2024/cmsc858G/QECCbook-2024-ch1-15.pdf
shows how to take the magic state $ T | + \rangle $ and use single bit gate ...
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Universal gate set for the $ [[15,1,3]] $ code
The $ [[15,1,3]] $ triorthogonal code implements transversal $ T $. Since it is a CSS code, two blocks will also have a transversal $ CNOT $ gate. To get a universal gate set all that is required is ...
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Transpile not working properly for decomposing single qubit gates into Rx Ry and Rz
I used the above code to decompose hadamard gate into RxRyRz but i am getting wrong angles which on multiplying don't match hadamard gate . Interestingly when i am using inbuilt hadamard hate using q....
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How to determine the single-qubit gate if we know an initial and corresponding final state [closed]
HOW TO FIND A QUANTUM GATE IF WE KNOW THE INITIAL AND FINAL SINGLE QUBIT STATES? I tried thinking by using projection vectors like ket 0 goes to ket I, then we can take the ket 0 bra I, but the ...
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Decomposition of a quantum gate into Rx Ry Rz
Can we break any quantum 2 qubit gate as a product of Rx Ry and Rz gates if yes then please provide a python code to do so .
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Definition of fault tolerant gate gadgets
I am trying to understand fault tolerance for gate gadgets a bit better. Here Gottesman provides the following definition:
I generally understand this definition but I have two questions.
(1) Why is ...
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How to verify that a certain gate was applied to a quantum code
Suppose I have a quantum error correcting code $|\psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$, say the $[[7,1,3]]$ Steane code for concreteness.
Suppose there is a black box that either ...
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How do I perform measurements in the X basis for qutrits in cirq?
After applying the hadamard gate to a 0 state qutrit, I should be able to get it into the + state, but how do I then measure the circuit in the X basis as opposed to the computational basis?
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Hypothesis on faster-than-light communication
I'm having a hard time understanding why it is not possible to communicate faster than light with entangled qubits. Now, this is my hypothesis.
A and B have a pair of qubits, and 2 synced clocks at 12:...
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Is there a tool to decompose 4-Qubit unitaries (aka 16x16 matrices)?
I was wondering if there is a tool that can decompose such a matrix in gates on 4 qubits?
I found one for 3-qubit gates (9x9 matrices) in Cirq but nothing for bigger matrices.
(The matrix is not ...
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