Questions tagged [quantum-gate]
For questions regarding usage, performance, implementation, application or theory related to quantum gates
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How to construct a quantum gate producing 1 if r divides x, 0 otherwise?
If you have two registers in the state $\frac{1}{2^{n/2}} \sum_{x = 0}^{2^{n/2} - 1} |x\rangle |0\rangle$, how could you construct a gate that produces a superposition of states $|x\rangle|1\rangle$ ...
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2answers
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What happens when I input two qubits starting at state $|00\rangle$ into a hadamard gate
I was watching the following video https://www.youtube.com/watch?v=IrbJYsep45E
And around 3 minutes in, they do an example computation with two qubits. The qubits started off in the state $|00\rangle$...
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1answer
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Solving a circuit implementing a two-level unitary operation
The circuit below implements the following two-level unitary transformation:
$\tilde{U}$ is a unitary matrix: $\tilde{U} = \left[\begin{matrix} a & c \\ b & d \end{matrix}\right]$
where $a, ...
1
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1answer
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Applying Group Leaders Optimization to Quantum Belief Systems
Context: I am particularly interested in quantum cognition & would like to use a tool like pyZX to perform the following types of optimizations.
In Preparing a (quantum) belief system they "...
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2answers
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How does the stated Pauli decomposition for $\operatorname{CP\cdot A\cdot CP}$ arise?
I'm having a bit of trouble understand @DaftWullie's answer here.
I understood that the $4\times 4$ matrix $A$
$$ \frac{1}{4} \left[\begin{matrix}
15 & 9 & 5 & -3 \\
9 & 15 & 3 &...
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3answers
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What is the matrix for the operator that implements a function to tell the parity of its argument?
$\newcommand{\qr}[1]{|#1\rangle}$ I gave myself the task of building an operator that implements the following function: $f(0) = 0$, $f(1) = 1$, $f(2) = 1$, $f(3) = 0$. I restricted myself to $x$ up ...
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What's an example of building a circuit $U_f$ that implements a simple function $f$?
I'd like to be able to program simple functions into simulators such as QCL. I read that any function $f$ can be implemented, but I don't know how to get say a unitary matrix that implements $f$.
$\...
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2answers
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Why does a rotation of $\pi/2$ on $|1\rangle$ yield $i|1\rangle$?
$\newcommand{\q}[2]{\langle #1 | #2 \rangle}
\newcommand{\qr}[1]{|#1\rangle}
\newcommand{\ql}[1]{\langle #1|}$
It seems $V(\pi/2, \qr{1}) = i \qr{1}.$ I didn't expect that. To me $\qr{1}$ points ...
4
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1answer
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Understanding the Group Leaders Optimization Algorithm
Context:
I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
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3answers
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Calculating measurement result of quantum swap circuit
Consider the following circuit, where $F_n$ swaps two n-qubit states.
If the inital state is $|0\rangle \otimes |\psi\rangle \otimes |\phi\rangle = |0\rangle|\psi\rangle|\phi\rangle$, the state ...
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2answers
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Simulation vs Construction of Fredkin gate with Toffoli gates
I'm working my way through the book "Quantum computation and quantum information" by Nielsen and Chuang. (EDIT: the 10th anniversary edition).
On chapter 3 (talking about reversibility of the ...
6
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3answers
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$R_z$ gate representations
Why is the $R_z$ gate sometimes written as:
$$
R_{z}\left(\theta\right)=\begin{pmatrix}1 & 0\\
0 & e^{i\theta}
\end{pmatrix},
$$
while other times it is written as:
$$
R_{z}\left(\theta\...
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0answers
45 views
Simulating Read only QRAM (constructing an oracle)
In many algorithms an array that stores a classical data or quantum data is crucial. The QRAM (quantum random access memory) that stores classical data in the circuit has been done. My question ...
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1answer
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Applying CNOT With Local Operations and Two EPR Pairs
Suppose Alice and Bob hold one qubit each of an arbitrary two-qubit state $|\psi \rangle$ that is possibly entangled. They can apply local operations and are allowed classical communication. Their ...
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1answer
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How to apply the outer product operator?
$\newcommand{\q}[2]{\langle #1 | #2 \rangle}
\newcommand{\qr}[1]{|#1\rangle}
\newcommand{\ql}[1]{\langle #1|}
\renewcommand{\v}[2]{\langle #1,#2\rangle}
\newcommand{\norm}[1]{\left\lVert#1\right\...
2
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1answer
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What quantum gate is XNOR equivalent to?
The standard way to implement a reversible XOR gate is by means of a controlled-NOT gate or CNOT; this is the "standard quantum XOR operation". Physics.Stackexchange
Is there a "standard quantum XNOR ...
5
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1answer
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How can I decompose a gate into $\{\mathrm{CNOT}, \mathrm{H}, \mathrm{P}(\theta)\}$?
I am working with the set $\{\mathrm{CNOT}, \mathrm{H}, \mathrm{P}(\theta)\}$
where $\mathrm{H}$ is the Hadamard gate, and $\mathrm{P}(\theta)$ is the phase gate with angle $\theta$.
I want to build ...
4
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1answer
122 views
Qutrit Teleportation
I'm working through Scott Aaronson's Quantum Information Science problemsets, and I'm having trouble with a specific problem. Specifically the following problem:
Here's what I've done: after applying ...
6
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1answer
51 views
How to say “apply CNOT on q-bit 1 controlled by q-bit 2”?
Say you have $2$ q-bits, namely $q_1, q_2$. What's the right language for saying apply CNOT on $q_1$ and $q_2$ where $q_1$ is the control bit and $q_2$ is the target?
For instance, can I say "apply ...
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1answer
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How would one implement a quantum equivalent of a while loop in IBM QISkit?
I'm writing a simple multiplication algorithm that uses the Quantum Fourier Transform to repetitively add a number (the multiplicand) to itself and decrements another number (the multiplier). The ...
3
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1answer
67 views
How to create a condition on only one classical bit when we have a total of 2 classic bits in the system
I am trying to make a quantum circuit with one qubit and 2 classical bits for each measurment in the system below:
I want to make condition on the first bit: if the first collapse to zero so x ...
6
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1answer
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Decomposition of arbitrary 2 qubit operator
As you know, universal quantum computing is the ability to construct a circuit from a finite set of operations that can approximate to arbitrary accuracy any unitary operation.
There also exist some ...
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2answers
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Symmetry in Conditional Phase Shift Gates and Realizing CNOT through HCZH
Why are conditional phase shift gates, such as CZ, symmetrical? Why do both the control and target qubit pick up a phase?
Furthermore, assuming that they are symmetrical, when using a CNOT gate as an ...
4
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1answer
44 views
What is the significance of recent demonstration of a passive photon–atom qubit swap operation?
In reference to this recent nature article: https://www.nature.com/articles/s41567-018-0241-6
Specifically, does this warrant a new type of gate?
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1answer
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Classical XOR gate in Quantum Circuit
Can we use classical XOR gate in a quantum circuit? Or are there any alternatives for XOR gate?
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Explicit Conversion Between Universal Gate Sets
I'm interested in the conversion between different sets of universal gates. For example, it is known that each of the following sets is universal for quantum computation:
$\{T,H,\textrm{cNOT}\}$
$\{H,...
9
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2answers
115 views
State of the art gate speeds and decoherence times
I am interested in the state of the art gate speeds and decoherence times for the qubit types I know are being pursued by companies presently:
superconducting qubits,
ion trap qubits,
photonic qubits....
10
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2answers
190 views
Automatic compilation of quantum circuits
A recent question here asked how to compile the 4-qubit gate CCCZ (controlled-controlled-controlled-Z) into simple 1-qubit and 2-qubit gates, and the only answer given so far requires 63 gates!
The ...
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6answers
234 views
How to construct a multi-qubit controlled-Z from elementary gates?
For the implementation of a certain quantum algorithm, I need to construct a multi-qubit (in this case, a three-qubit) controlled-Z gate from a set of elementary gates, as shown in the figure below.
....
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3answers
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What does it mean for a quantum computer to have $X$ qubits?
I want to preface with a disclaimer that I am a physicist with minimal knowledge of computer hardware. I have a solid understanding of quantum information from a theoretical standpoint but zero ...
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Just want to confirm: Do two CNOT gates cancel each other?
I see somewhere that this happens:
But I wonder if this is just identity.
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3answers
405 views
Advantange of Hadamard gate over rotation about the X axis for creating superpositions
When I look at most circuits (admittedly small sample as I'm a beginner), the Hadamard gate is used a lot to prepare a superposition from say the $\mid0\rangle$ state.
But upon a little reflection, we ...
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2answers
169 views
How do you implement the Toffoli gate using only single-qubit and CNOT gates?
I've been reading through "Quantum Computing: A Gentle Introduction", and I've been struggling with this particular problem. How would you create the circuit diagram, and what kind of reasoning would ...
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Is there a tool that can give you the unitary representing a quantum circuit from just a string?
Say I have a string representing the operations of a quantum circuit.
I want to have the unitary operator representing it.
Is there a tool for doing so in Python or else?
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2answers
100 views
How do we code the matrix for a controlled operation knowing the control qubit, the target qubit and the $2\times 2$ unitary?
Having n qubits, I want to have the unitary described a controlled operation.
Say for example you get as input a unitary, an index for a controlled qubit and another for a target.
How would you code ...
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2answers
394 views
Incorrectly Calculating Probability Amplitudes for 3-qbit Circuit
I’m trying to calculate the probability amplitudes for this circuit:
My Octave code is:
...
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2answers
334 views
Possibility of a “reset” quantum gate
I wish to have a "reset" gate. This gate would have an effect to bring a qubit to the $\mid0\rangle$ state.
Clearly, such a gate is not unitary (and so I'm unable to find any reliable implementation ...
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2answers
162 views
Shorthand notation for the sign flip gate
I need to use the following matrix gate in a quantum circuit:
$$\text{Sign Flip}=\left[\begin{matrix}0 & -1 \\ -1 & 0\end{matrix}\right]$$
$\text{Sign Flip}$ can be decomposed as (in terms ...
5
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0answers
81 views
Number of gates required to approximate arbitrary unitaries
If I understand correctly, there must exist unitary operations that can be approximated to a distance $\epsilon$ only by an exponential number of quantum gates and no less.
However, by the Solovay-...
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1answer
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Practical implementation of Hamiltonian Evolution
Following from this question, I tried to look at the cited article in order to simulate and solve that same problem... without success. Mainly, I still fail to understand how the authors managed to ...
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Does conditional gate collapse controller's superposition?
I've created a simple circuit in Q-Kit to understand conditional gates and outputted states on each step:
In the beginning there is clear 00 state, which is the input
The first qubit is passed ...
5
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1answer
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Arbitrary powers of NOT and SWAP
The square-root of not and square-root of swap gates are often singled out for discussion of gates displaying important properties relating to quantum computers.
How do I define arbitrary (non-...
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2answers
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Is it possible to realize CNOT gate in 3 dimension?
CNOT gates have been realized for states living in 2-dimensional spaces (qubits).
What about higher-dimensional (qudit) states? Can CNOT gates be defined in such case? In particular, is this possible ...
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CNOT Gate on Entangled Qubits
I was trying to generate Greenberger-Horne-Zeilinger (GHZ) state for $N$ states using quantum computing, starting with $|000...000\rangle$ (N times)
The proposed solution is to first apply Hadamard ...
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1answer
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Doing maths with controlled-half NOTs
In Quantum Computation with the simplest maths possible there is a section titled "Doing maths with a controlled-half NOT" which covers a reversible-(N)AND circuit with controlled-half NOTs.
What ...
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3answers
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Toffoli gate as FANOUT
I was searching for examples of quantum circuits to exercise with Q# programming and I stumbled on this circuit:
From: Examples of Quantum Circuit Diagrams
- Michal Charemza
During my introductory ...
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0answers
134 views
Error: Simulation of “Quantum algorithm for linear systems of equations” for $4\times 4$ systems on Quirk (without SWAP) - Global phase
Following @DaftWullie's answer I tried to simulate the circuit given in Fig. 4 of the paper (arXiv pre-print): Quantum circuit design for solving linear systems of equations (Cao et al, 2012), on ...
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1answer
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SWAP gate(s) in the $R(\lambda^{-1})$ step of the HHL circuit for $4\times 4$ systems
Context:
On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit:
Schematic:
A brief schematic of what's actually ...
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2answers
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Matrix representation of continuous-variable gates
In the introduction to continuous-variable quantum computing by Strawberry Fields (Xanadu), it lists the primary CV gates (rotation, displacement, squeezing, beamsplitter, cubic phase) along with ...
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1answer
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How the joint state of these qubits is derived?
Can someone show to me the steps to derive the joint state at the bottom of this image, please?
I tried to follow his explanation but I didn't get the same results…
This is taken from the lecture ...
