# 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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### 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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### Modifying Qiskit Hamiltonian

I'm fairly new to the Qiskit API. I was wondering if I could get some assistance with trying to implement our technique of projecting out a new Hamiltonian from the ground-state Hamiltonian. The ...
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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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### Constructing a time evolution operator $e^{it H}$ for $H^2=I$

Consider a Hamiltonian $H = \sigma_x \otimes \sigma_z$ Construct the time evolution operator $U(t) = \mathrm{e}^{-\frac{iHt}{\frac{h}{2\pi}}}$ [Hint:Write down the expansion of $\mathrm{e}^x$ and use ...
1 vote
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### Primer for Quantum Circuits and Optimization

I am interested in studying physical systems and trying to build circuits to simulate them. Now, of course, all the systems I could try to work with at simple, toy, systems - and that's fine. ...
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### Circuit of a very trivial thing

I am writing to double check that if have a hamiltonian of the form $H = I_1 \otimes I_2$, when I seek to find the unitary, $e^{-i\gamma I_1 \otimes I_2}$, there really is no need to convert this into ...
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### XX, YY, ZZ circuit representations?

Is there a good primer or set of lectures\examples that show entirely how to take a given matrix and developing a circuit that represents it. I am trying to implement a program to find the lowest ...
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### Strange Behaviour of MeSolve, McSolve

I'm using Qutip to plot some basic two level dynamics using hamiltonians with a temporal envelope defined as the sum of two error functions, designed to make it more representative of experimental ...
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### Openfermion to qiskit

Is there a direct way to go from an object generated in openfermion to objects usable in Qiskit. I can't find anything about any plugin. It's not too hard to translate into pyQuil and then to Qiskit ...
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### Proof that most Hamiltonian evolutions are not efficiently approximable by quantum circuits

How to rigorously prove that finite Hamiltonians (for $n$-qubit systems), in general, are not efficiently$\dagger$ simulable (in the Hamiltonian simulation sense) using $\mathrm{poly}(n)$ number of ...
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### Compiling the Pauli-Z operator to the Rz operator for Hamiltonian simulation

I saw a tutorial on this long ago, but lost it. I know that the Pauli-Z operator compiles to Rz, but how? Here are the steps I remember: First, we have to solve for $U(t)$ in the Schrodinger equation ...
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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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### 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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Maybe it is a naive question, but I cannot figure out how to actually exponentiate a matrix in a quantum circuit. Assuming to have a generic square matrix A, if I want to obtain its exponential, $e^{A}... • 829 9 votes 2 answers 830 views ### Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is$|\Psi_0\rangle$? This is a sequel to Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm and Quantum algorithm for linear systems of ... • 16.3k 20 votes 1 answer 917 views ### What are examples of Hamiltonian simulation problems that are BQP-complete? Many papers assert that Hamiltonian simulation is BQP-complete (e.g., Hamiltonian simulation with nearly optimal dependence on all parameters and Hamiltonian Simulation by Qubitization). It is easy ... 16 votes 1 answer 961 views ### Obtaining gate$e^{-i\Delta t Z}\$ from elementary gates

I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't ...
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