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Have you read Towards quantum chemistry on a quantum computer (Nature Chemistry 2010, or here in the arXiv version)? They present "a photonic implementation for the smallest problem: obtaining the energies of H$_2$ (the hydrogen molecule) in a minimal basis". In the figure S1 of the Supporting information there is an equivalence of the operations they ...


5

The question refers to the VQE, so let's start with this and Max_Cut; they can be built on the VQE. There used to be a vqe.ipynp but I can't find, look for an example. The VQE algorithm doesn't need much input. You can fill it with the paulis_dict. This could be a simple Z gate for finding the eigenvalues= -1. pauli_dict = { 'paulis': [{"coeff": {"imag"...


5

Since Google is one of, if not the, industry leaders in molecular simulation with quantum computers, their published work is a reasonable benchmark for what's presently within reach. As you probably know, a few years ago Google reported (commentary) successful electronic structure calculations for a Hydrogen atom, favoring the variational quantum ...


2

The answer arguably depends on the problem you wish to solve with your computation. More specifically, are you wanting to optimize near-term applications in the NISQ era, or are you wanting to build a fully scalable, fault-tolerant and universe quantum computer? For the latter, you need to think about error correction. Pretty much everything that will ...


2

Here's a fairly thorough overview: https://arxiv.org/abs/1308.6253 For completeness I'll include the paper from the comment: https://arxiv.org/abs/quant-ph/0108146


1

You are correct. There is a 1-1 mapping between the standard "molecular Born-Oppenheimer Hamiltonian" that you wrote down in 2nd quantized form, and the equivalent Jordan-Wigner spin Hamiltonian. That mapping is actually quite simple: $$\Large{a_j \iff \mathbf{1}^{\otimes {j-1}}\otimes \sigma^{+}\otimes \sigma ^ {z\otimes {N-j-1}}}$$ $$\Large{a_j^{\dagger}...


1

Which of these transitions will occur will be governed by the operation regime of the apparatus and laser. It might happen, for example, that state 3 is unfavorable due to selection rules or it only acts as an auxiliary state. The very first step according to the D.Vincenzo's criteria is to identify and isolate the Hilbert space of the system to work with. ...


1

You may be referring to works like Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator (arXiv version). However, I'd say that in general the prediction of reaction rates or transition rates will be much more difficult compared with this 3-qubit job. Note a large amount of chemistry happens either in solution or in the solid ...


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