Dear Julia team,

I want to speed up repeated MPO-MPS multiplications by first stacking a bunch of MPOs (maybe lazily) and only then contracting them with the MPS, instead of contracting them one at a time.

I am not an expert, but it feels like this method will better suit a GPU processor, also.

My problem is to get the indices right… I get confused with the prime levels and my code has bugs that I can’t seem to fix on my own.

The solution mustn’t assume that the quantum systems are solely spin or bosonic, since in my system each quantum system contains both.

Hereby I attach a minimal code that I wrote to show what I am trying to achieve (and how badly my code is written, also). I emphasize that this code does not work, however, It shows what I want to compute- a series of MPOs that should be contracted simultaneously:

```
#This code takes an MPS of spins in the all-down state and flips them all one at a time
using ITensors
#State preparation
function surface_tensor(dimension)
tens = zeros(1, dimension)
tens[1, 1] = 1
return tens
end
function bulk_tensor(dimension)
tens = zeros(1, 1, dimension)
tens[1, 1, 1] = 1
return tens
end
function gs_product_state(s, N)
# Initial state's MPS representation
α = [Index(1, "α$n") for n in 1:(N-1)] # bond indices
ψgs = MPS(N)
for n in 1:N
if n == 1 # the first ion
ψgs[n] = ITensor(surface_tensor(dim(s[n])), α[n], s[n])
elseif n == N # the last ion
ψgs[n] = ITensor(surface_tensor(dim(s[n])), α[n - 1], s[n])
else # all the other sites
ψgs[n] = ITensor(bulk_tensor(dim(s[n])), α[n - 1], α[n], s[n])
end
end
return ψgs
end
#MPOs generation
σx = [0 1;1 0]
I2 = [1 0;0 1]
function σx_onsite(N, s, site_ind)
# Apply σx to the spin on site numbered by site_ind.
gate = MPO(s, [if n==site_ind σx else I2 end for n in 1:N])
return gate
end
# concatenate N gates with sequential σxs:
N = 2
s = [Index(2, "s$n") for n in 1:N] # site indices
ψ0 = gs_product_state(s, N) # Initialize the MPS
gates = ITensor[]
for n in 1:N
gate = σx_onsite(N, s(n), n)
append!(gates, gate)
end
ψ = apply(gates, ψ0)
```

Best,

Yotam