Hello,
I have a Kraus operator ITensor, and I would like to apply it to a density MPO to implement a quantum channel:
\sum_i K_i \rho K_i^\dagger
As an example, let’s take \rho to be a 4 qubit MPO:
MPO
[1] ((dim=2|id=910|"Qubit,Site,n=1"), (dim=2|id=910|"Qubit,Site,n=1")', (dim=4|id=585|"Link,l=1"))
[2] ((dim=2|id=316|"Qubit,Site,n=2"), (dim=2|id=316|"Qubit,Site,n=2")', (dim=16|id=948|"Link,l=2"), (dim=4|id=585|"Link,l=1"))
[3] ((dim=2|id=195|"Qubit,Site,n=3"), (dim=2|id=195|"Qubit,Site,n=3")', (dim=4|id=23|"Link,l=3"), (dim=16|id=948|"Link,l=2"))
[4] ((dim=2|id=604|"Qubit,Site,n=4"), (dim=2|id=604|"Qubit,Site,n=4")', (dim=4|id=23|"Link,l=3"))
My Kraus operator applies to sites 2 and 3, and is therefore a 5-index ITensor: two indices for sites 2 and 3, two primed indices for sites 2 and 3, and one index for the virtual Kraus index. Here is an example:
ITensor ord=5 (dim=2|id=316|"Qubit,Site,n=2")' (dim=2|id=195|"Qubit,Site,n=3")' (dim=2|id=316|"Qubit,Site,n=2") (dim=2|id=195|"Qubit,Site,n=3") (dim=4|id=791|"Kraus")
NDTensors.Dense{ComplexF64, Vector{ComplexF64}}
To implement the channel, I initially tried apply(K, rho, apply_dag=true). This ran with no errors, but outputted a MPO with to indices taged as Link,n=1:
MPO
[1] ((dim=2|id=910|"Qubit,Site,n=1"), (dim=2|id=910|"Qubit,Site,n=1")', (dim=4|id=675|"Link,l=1"))
[2] ((dim=2|id=316|"Qubit,Site,n=2")', (dim=4|id=675|"Link,l=1"), (dim=2|id=316|"Qubit,Site,n=2"), (dim=16|id=50|"Link,n=1"))
[3] ((dim=16|id=50|"Link,n=1"), (dim=2|id=195|"Qubit,Site,n=3")', (dim=4|id=23|"Link,l=3"), (dim=2|id=195|"Qubit,Site,n=3"))
[4] ((dim=2|id=604|"Qubit,Site,n=4"), (dim=2|id=604|"Qubit,Site,n=4")', (dim=4|id=23|"Link,l=3"))
I subsequently get errors when running other functions on this MPO. Did I make a mistake here, or is there an alternative way to compute the quantum channel?
Thank you!
Roman