Best free online application for making notes containing quantum computing...
This I hope, is not a trivial question. I am sure many like me struggle while making personal notes online and face difficulty in write linear algebra expressions & Dirac notations to explain...
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Matrix representation of any conditioned gate
Is there an algorithm explaining how to represent any gate in the matrix form?Suppose, the circuit is the following:where operator$ U = e^{iA\pi/4} = \begin{bmatrix} 0.35-0.85i & -0.35-0.15i...
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RZZ from CNOT and RZ
The following should represent an RZZ gate (source: https://pennylane.ai/qml/demos/tutorial_qaoa_maxcut.html)How do the CNOT and an RZ compute mathematically to the RZZ?$$ R_Z(\theta) = \begin{pmatrix}...
View ArticleIs there a way to write a generic low dimensional Clifford matrix?
Suppose I want to write a general $2\times2$ special unitary matrix in a given basis, I can write it as such:$$\begin{pmatrix} \alpha & -\overline\beta\\ \beta & \overline...
View ArticleHow to find the matrix representation of a given many-qubit Hamiltonian?
I have the following HamiltonianH = - Z1Z2 - Z2Z3 - Z1Z3 - 6(Z1 + Z2 + Z3)Here, Z1, Z2, Z3 represent the Pauli-Z operators acting on qubits 1, 2, and 3, respectively. The interaction terms Z1Z2, Z2Z3,...
View ArticleHow to build the quantum circuit corresponding to a given unitary matrix?
I have the following matrix for a circular quantum walkimport numpy as npT = np.array([[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0,...
View ArticleHow to implement the -I matrix using Pauli gates
I'm trying to build a quantum walk circuit. I have the C0 matrix as followsimport numpy as npC0 = np.array([[-1, 0], [0, -1]])As we can see, it's the (-)Identity matrix. How to build the -I matrix...
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How to mathematically represent the $CSWAP_{1 \rightarrow 0,2}$ gate?
The controlled-$SWAP$ gate represented in the circuit above can be written down by the following mathematical expression:$$CSWAP_{0 \rightarrow 1,2} = |0\rangle\langle0| \otimes I_{4 \times 4} +...
View ArticleCalculate the product state/quantum register back into its tensor product
So let's asume I have a product state/quantum register as a result of a tensor product of two qubits.Lets take a "hard" product state matrix like:$$\frac{1}{\sqrt{2}}\begin{bmatrix}\frac12 +...
View ArticleIn general, what is feasible quantum computation?
I don't really understand what is feasible quantum computation, in my book (Lipton and Regan's Quantum Algorithms via Linear Algebra) they said that:A quantum computation $C$ on s qubits is feasible...
View ArticleDetect if a given binary number belongs to a certain subset with an unitary...
I want to create an operator $A$ which, given three binary numbers, $a_1$, $a_2,a_3$, will detect whether $a_1a_2a_3$ (as a binary number) is in certain set of numbers (for example, detect whether...
View ArticleIs it possible to get the "symbolic" matrix operator associated with a...
Qiskit provides the qiskit.quantum_info.Operator class to get the unitary matrix operator from the corresponding quantum circuit, as in the following example:from qiskit import QuantumCircuitfrom...
View ArticleHow to convert a simple matrix into circuit? [duplicate]
Suppose you have an invertible matrix. How do you convert it into a circuit?Matrices have dimensions $2^n \times 2^n$, so a circuit representation is desirable.For example, the matrix below is a simple...
View ArticleHow to convert a basic matrix into a quantum circuit?
Classical gates are not invertible, but larger expressions made from those gates can be invertible. One example of an invertible function is the function $f(A,B,C) = X,Y,Z$:$X = A \ B \ | \ \neg B \...
View ArticleWhat is the general unitary matrix for two- and three-qubit states?
As pointed out in the QisKit tutorial here, for one qubit there exists a general unitary (see the expression for it in the previous link). I wonder if there exists equally unambiguous expressions for...
View ArticleExistence of Hamiltonians such that the time evolution unitary becomes identity
Can we always find a set of coefficients ${k_i}$ (where not every $k_i = 0$) for a given Hamiltonian $H = \sum k_i H_i$, such that the unitary operator becomes the identity operation: $e^{-iH} =...
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Toffoli Gate Matrices
Here are the different toffolis (or maybe one of them is toffoli and the others are very similar to toffoli gates)My question is:we know the matrix of the number 1 Toffoli:What are the matrices for...
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Show how the Bell state arises from the circuit with Hadamard and CNOT, using...
I understand that starting with,we can get to $\vert \Phi^+ \rangle$. First, we start with $\vert Q_1 \rangle \otimes \vert Q_2 \rangle = \vert 0 \rangle \otimes \vert 0 \rangle$ and then applying $H$...
View ArticleApplication of transformation $U_d$ that maps any qudit state to $|d-1\rangle$
When giving examples of universal gate sets in the paper Qudits and High-Dimensional Quantum Computing, the authors first define the transformation that maps any given qudit state to...
View ArticleGeneric circuit for signature matrix
Consider a set $ A = \{a_0,a_2,\ldots,a_{k-1}\} \subset [N] := \{0,1,\ldots,N-1\}$.Consider the diagonal matrix\begin{equation}R := I - 2 \sum_{a\in A} |a\rangle\langle a|,\end{equation}which is just a...
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