How to avoid repetitive contraction of tensor networks for better performance

[ACE07-Sev]

TLDR; how to minimize the number of contractions and partitions in the optimization.

Greetings dear Dr. Gray,

Hope you are well. I recently released qmprs, which currently compiles MPS into quantum circuits using an analytical decomposition that yields a staircase circuit (layers of two-qubit gates). To improve fidelity, I contract the circuit’s output with the adjoint of the target MPS and perform environment tensor optimization.

The optimization steps are:

1. Iterate over gates and temporarily remove each from the tensor network (.partition()).
2. Contract the rest of the network to get a 4-leg environment tensor.
3. Apply SVD to extract a new unitary.
4. Replace the original gate with this new unitary.

This optimization is computationally heavy—around 95% of the runtime, with contractions and partitions being the main bottlenecks.

I observed that while optimizing gates in a given layer, the other layers remain unchanged. So instead of recomputing full contractions for each gate, we could precompute the contraction of the unaffected layers once per layer and reuse it, greatly reducing redundant work. This still has considerable redundancy, but this is what I have in mind as an idea for now.

Any insights would be greatly appreciated, especially if it could bring runtime back down to seconds or minutes.

Here is the link to the relevant snippet:
https://github.com/Qualition/qmprs/blob/main/qmprs/synthesis/mps_encoding/sequential.py#L395-L493

[ACE07-Sev]

[ACE07-Sev]

Resolved via using two MPS L and R and updating gradually.