• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,075 questions , 2,226 unanswered
5,347 answers , 22,743 comments
1,470 users with positive rep
818 active unimported users
More ...

  Is there a standard way to translate an Hamiltonian into QC circuit?

+ 3 like - 0 dislike

I would like to calculate an observable's expectation value of a state, the ground state, or time evolution of a finite system with $N$ spins under an Hamiltonian $H$. 

For the sake of discussion assume $N=16$ so we can use IBM QC.

How to translate a given Hamiltonian into Quantum logic gates in order to simulate the system evolution or its statistics. 

If it makes life easier assume a local hamiltonian or any lattice based model such as an Ising model Hamiltonian:

H(\sigma) = - \sum_{\langle i~j\rangle} J_{ij} \sigma_i \sigma_j -\mu \sum_{j} h_j\sigma_j

As a side note, I was intrigued by this question which mentions Andre Lucas paper:
 Ising formulations of many NP problems and thought that it would be nice to know how to translate an hamiltonian to a QC circuit.

asked Nov 5, 2017 in Computational Physics by lopo (45 points) [ revision history ]
edited Dec 19, 2017 by lopo

An analogous question for quantum optical systems is answered in my paper 

U. Leonhardt and A. Neumaier, Explicit effective Hamiltonians for general linear quantum-optical networks, J. Optics B: Quantum Semiclass. Opt. 6 (2004), L1-L4.quant-ph/0306123

Maybe you can translate it to your setting.

I think you want the Solovay-Kitaev algorithm, see https://arxiv.org/pdf/quant-ph/0505030.pdf

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights