# Questions tagged [hamiltonian-simulation]

Hamiltonian simulation is a class of algorithms that, given a Hermitian matrix A, output a quantum circuit implementing an approximation to the unitary exp[iAt].

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### Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{i\hat{H}t} |\psi\rangle$. Thank you for your answer.
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### How can I decompose a matrix in terms of Pauli matrices?

I need to see an example of how Hamiltonian, i.e. any Hermitian matrix, can be decomposed into a linear combination of Pauli matrices. I would prefer an option to do this in larger than 2 dimensions, ...
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### How to convert QUBO problem to Ising Hamiltonian?

According to paper Ising formulations of many NP problems an unconstrained quadratic programming problem $$f(x_1, x_2,\dots, x_n) = \sum_{i}^N h_ix_i + \sum_{i < j} J_ix_ix_j$$ can be expressed ...
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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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### Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?

This is a sequel to Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm and Quantum algorithm for linear systems of ...
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### Ground state energy estimation - VQE vs. Ising vs. Trotter–Suzuki

Disclaimer: I am a software engineer who is curious about quantum computing. Although I understand some basic concepts, theory and math behind it, I am by no means experienced in this domain. I am ...
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### VQE - How to get from expectation value to eigenvalue?

In VQE, for a single-qubit Hamiltonian, I can use a standard ansatz to make a state $\psi$ and use two products to compute the expectation value $\langle\psi|{\cal H}|\psi\rangle$. As I vary the ...
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### VQE Cirq example

Is my understanding correct that in this example the Hamiltonian measurement is not performed through measuring individual Pauli operators because all its terms are mutually commuting? So, for each ...
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### How are two different registers being used as "control"?

On page 2 of the paper Quantum Circuit Design for Solving Linear Systems of Equations (Cao et al.,2012) there's this circuit: It further says: After the inverse Fourier transform is executed on ...
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### Example of Hamiltonian Simulation solving interesting problem?

Hamiltionian Simulation (= simulation of quantum mechanical systems) is claimed to be one of the most promising applications of a quantum computer in the future. One of the earliest – and most ...
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### What is the correct sign in the unitary evolution operator of a beam splitter?

I'm a bit confused about which is the correct sign in the unitary evolution operator of a beam splitter. In paper Digital quantum simulation of linear and nonlinear optical elements author uses the ...
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### What Are The Most Promising Real-World Applications For Quantum Machine Learning

I know this has been asked before in different ways, however, I am interested in something with a degree of clarity and focus not found in other questions. What I am looking to get is a list of the ...
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Let's say I am given a Hamiltonian $H$, whose ground state is efficiently preparable. We know that $||H|| \leq 1$. Let that ground state be $|\psi_{0}\rangle$, with energy $E_{0}$. We also know that ...
I was trying to implement Trotterization for a $k$-local Hamiltonian simulation using qiskit. For this, say I want to apply $e^{\lambda \sigma^1_z \otimes \sigma^2_z \otimes \sigma^3_z}$ (this being ...