ITensor / ITensor/ITensorMPS.jl

[ITensors] [ENHANCEMENT] Support for Trotterizing time dependent operators

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enhancement
Dominant language
Julia
Stars
85
Forks
27
Avg merge
22m
Merged PRs (30d)
1

Description

Currently we have the following interface for Trotterizing a time independent operator sum:

function H()
  H = Sum{Op}()
  for n in 1:(N-1)
    H += "X", 1, "X", 2
  end
  return H
end

# Number of time steps
n = 3

# Total time to evolve to
t = 0.5

# ∏ₙ exp(-im * t * H / n)
U = exp(-im * t * H; alg=Trotter{1}(n))

We need to add support for Trotterizing a time-dependent operator, for example:

function H(t)
  H = Sum{Op}()
  for n in 1:(N-1)
    H += cos(ω * t), "X", 1, "X", 2
  end
  return H
end

t = [0.1, 0.21, 0.32, 0.44]
time_step = diff(t)
n = length(time_step)

# Operator to exponentiate at each time slice
Hs = [-im * time_step[n] * H(t[n]) for n in 1:n]

# exp(-im * t1 * Hs[1]) * exp(-im * t2 * Hs[2]) * exp(-im * t3 * Hs[3])
U = exp(Hs; alg=Trotter{1}())

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  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by tracing the existing Trotter{1} implementation behind exp(H; alg=Trotter{1}(n)) and how exp accepts operator inputs. Determine how the interface should consume the time-slice vector Hs and preserve its ordering. Done means exp(Hs; alg=Trotter{1}()) supports the time-dependent example with the expected product of exponentials.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
backend
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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