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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 ...
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### 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 ...
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### 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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### How can I convert exponentials of pauli matrices to circuits of this form in Qiskit?

For example the following circuit is for $e^{-i(Z\otimes Z\otimes Z)\Delta t}$ I know this can even be done without the ancilla qubit, having the CNOTs control the last qubit and applying an RZ on ...
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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 ...
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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 to perform a time evolution of a quantum state with Qiskit Aqua?

How can we perform a time evolution of a quantum state for a given Hamiltonian with qiskit Aqua operator flow? I'm interested in it due to its higher efficiency.
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### 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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### Question Regarding Simulating Hamiltonian With Quantum Circuit

There have been a few other questions about this section of Nielsen and Chuang, but when working through the output of the circuit, there are some inconsistencies that are probably due to some mistep/...
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### Simulating the Ising-like model as a quantum circuit

We are interested in simulating the 1d Ising model Hamiltonian using a Quantum Circuit (QC). A similar question was posted before with no answers. Here we will assume, for simplicity, 3 lattice sites ...
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### Is the cost Hamiltonian unitary in QAOA?

I am trying to implement QAOA and there are things I don't understand at all. The expansion of $H$ into Pauli $Z$ operators can be obtained from the canonical expansion of the cost-function $C$ by ...
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### Simulate Hamiltonians with Pauli operations (controlled time evolution)

I had a question last week regarding the simulation of Hamiltonians composed of the sum of Pauli products: How can I simulate Hamiltonians composed of Pauli matrices? I'm having a follow-up question: ...
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### Showing that $e^{i \sigma_z \otimes \sigma_z t} = \text{CNOT}(I \otimes e^{i \sigma_zt})\text{CNOT}$
While working on circuit construction for Hamiltonian simulation using this answer as reference, I'm unable to see how the following equation is true:  e^{i \sigma_z \otimes \sigma_z t} = \text{CNOT}...