# 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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### How to exactly implement Trotter-Suzuki formula on quantum computer

Recently, I am studying some topics related to product formula, and I am curious about how to implement such formula on real quantum devices. The $(2k)$-th order product formula can be witten as \...
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### how can i find ground state of final hamiltonian

decompose the evolution operator into a sequence of steps using the Trotter-Suzuki formula unitary operator is the evolution operator from 0 to T , k is a large integer so that τ = T /k is a small ...
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### How can extract reduced dynamics of a bipartite system from unitary evolution in quite

Let us assume that I have a bipartite system $A\otimes B$ and an initial product state undergoing some evolution $H^{AB} = H^A+H^B+V^{AB}$, which is time independent. I want to simulate the reduced ...
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### Can we use quantum phase estimation to count how often we can walk from one Rubik's cube position to another?

Consider a state $\vert\psi\rangle$ as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" state. Here, with $8$...
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### Can I use the Lie product formula to simulate the Hamiltonian of an adjacency matrix by using the QPE to take Nth roots of permutation matrices?

I have gotten some great help recently on Hamiltonian simulation, and am interested in using Hamiltonian simulation to explore (classical) random walks on large graphs, but I'm running up against ...
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### Wick rotation of the Schrödinger equation

Studying the following paper: https://www.nature.com/articles/s41534-019-0187-2.pdf Trying to figure out how $E_T$ shows up from (1) and (2). Any suggestion or guidance would be appreciated. We ...
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### Is the square-root-of-SWAP for a pair of 4-dimensional qudits isomorphic to two square-root-of-SWAPS for two pairs of qubits?

This may be a very naïve question indicative of a lot of confusion, but I am trying to understand more about Hamiltonian simulation. I'm starting to intuit that the $n^{th}$-root-of-SWAP acting on a ...
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### Can we simulate the Hamiltonian for the Rubik's Cube with "nth-root of SWAP" gates?

I'm interested in, but confused about, local Hamiltonian simulation. I don't yet have enough intuition regarding even the approach set forth by Lloyd in 1997. I think Lloyd's recipe is to repeatedly ...
In this paper, it talks about the 2-local Hamiltonian in the form: $H = \sum_{(u,v)\in E} H_{uv} + \sum_{k \in v} H_k$ It also says the Ising model, Heisenberg model, XY model and QAOA are in the ...