anedumla commented 5 years ago

Abstract

The problem of Hamiltonian simulation can be described as, given a hermitian matrix H and a real number t, find a circuit for exp(iHt).

A widely used approach is to find a decomposition H = H_1 + H_2 +... + H_m such that we can find circuits for each exp(iH_j t), and then approximate exp(iHt) by a product of the exp(iH_j t) (i.e. by putting the smaller circuits in sequence) according to the e.g. Lie-Trotter and Suzuki formulae.

An example of such formula is

Here, the larger the M, the better is the approximation to exp(iHt) but also the longer the circuit gets. A solution is to run the algorithm m times, each time with a small M, e.g. for m = 3, M = 2, 3, 4. In each case we get a worse approximation that we would get with, say, M=10. However, the circuits are a lot shorter and the overall running time is shortened. Then, the results obtained in each run can be classically combined so that the lower error terms cancel and we get an approximation with the same accuracy that could be reached with the longer M=10 circuit.

The goal of the project would be to implement a circuit in-place version of the above with Qiskit. The idea itself and a description of the implementation is given in https://arxiv.org/pdf/1907.11679.pdf .

Paper 1 (for description of V): https://arxiv.org/pdf/1202.5822.pdf Paper 2 (for description of a_j): https://arxiv.org/pdf/1907.11679.pdf

Description

Members

@githubhandle
@githubhandle - Slack: @slackhandle email: example@example.com
Qiskit Coach: @anedumla

Deliverable

GitHub repo

boschmitt commented 5 years ago

I'm in, Bruno Schmitt, Computer Scientist (:

hoshitaro commented 5 years ago

I'm in, Shintaro Niimura, I'm not sure what I should call myself, but I have an optics background and I have a green sticker, may should have been yellow....

anedumla commented 5 years ago

I'm in, Shintaro Niimura, I'm not sure what I should call myself, but I have an optics background and I have a green sticker, may should have been yellow....

Great! :) I'm sitting at table 21 if you want to find me

hoshitaro commented 5 years ago

Thanks, I'll go there when everybody starts moving!