Synthesis of isometries/fixed input states

[willsimmons1465]

The current examples for qfast all consider unitary synthesis. It would be useful to apply this to the case where we have more outputs than inputs, such as for arbitrary state synthesis or exploiting ancillas.

Several works in the compiling world have looked at using initial states of qubits to obtain small (asymptotically constant) reductions in circuit size. One recent example for reference: https://arxiv.org/pdf/2012.07711.pdf. Finding ways to exploit the under-constrained setting of isometry synthesis via qubit initialisation and unitary gates is difficult from a view of algebraic circuit rewriting but seems like something proper synthesis tools like qfast could handle easier.

Likewise, this would fit in very nicely with block-based constructions like QGo (https://arxiv.org/pdf/2012.09835.pdf) to simplify the blocks with some/all of their inputs being initialised qubits

[edyounis]

This is an awesome idea. The theory behind QFAST and QSearch can allow for this as well. We are currently packaging all of our software into one BQSKit compiler; I will transfer this issue when that repo is made public. We can continue the discussion then. Stay tuned for it, you can subscribe to our mailing list through our website for updates.