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### From QUBO problem to quantum circuit [duplicate]

Can you describe how to convert some QUBO problem $$f(x_1, ..., x_n) = \sum\limits_{1 \le i < j \le n} \alpha_{i,j} \, x_i \, x_j$$ into its equivalent quantum circuits? Is it preferrable to start ...
2k views

### Can arbitrary matrices be decomposed using the Pauli basis? [duplicate]

Is it possible to decompose a hermitian and unitrary matrix $A$ into the sum of the Pauli matrix Kronecker products? For example, I have a matrix 16x16 and want it to be decomposed into something ...
652 views

### Quantum circuit to implement matrix exponential

I want to build a circuit which will implement $e^{iAt}$, where $A= \begin{pmatrix} 1.5 & 0.5\\ 0.5 & 1.5\\ \end{pmatrix}$ and $t= \pi/2$. We see that $A$ can be written as, $A=1.5I+0.5X$. ...
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### Representation of rotation operators $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ about arbitrary axis for $3$ qubits

I was wondering in how to interpret and represent the operator $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ for a 3 qubit system in a circuit using qiskit. I was thinking I could just perform an ...
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### How can I simulate Hamiltonians composed of Pauli matrices?

Suppose I want to perform the time-evolution simulation on the following Hamiltonians: $$H_{1} = X_1+ Y_2 + Z_1\otimes Z_2 \\ H_{2} = X_1\otimes Y_2 + Z_1\otimes Z_2$$ Where $X,Y,Z$ are Pauli ...
447 views

### How to decompose a multi-target controlled gate?

I'm trying to replicate with qiskit the results of this paper in which basically they implement a quantum version of the Principal Component Analysis applying Quantum Phase Estimation algorithm in ...
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### In the HHL alghoritm, how can I transform my hermitian matrix into a unitary operator?

I'm studying the HHL algorithm and I'm trying to do an his implementation but, there are some points that I don't understand how I can transform my hermitian Matrix into its unitary operator? In ...
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### In quantum adiabatic simulation, is the $s$ in $(1-\frac{s}{T})H_{in}+\frac{s}{T} H_{cl}$ related to the $t$ in $e^{-iHt}$?

I just want to do a whole adiabatic calculation on quantum circuit. To prepare two Hamiltonian of $H_{initial}$ and $H_{classical}$ and solve $H_{classical}$ using adiabatic calc like quantum ...

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