Robust quantum compilation and circuit optimisation via energy minimisation

Quantum 6, 628 (2022).

https://doi.org/10.22331/q-2022-01-24-628

We explore a method for automatically recompiling a quantum circuit $mathcal{A}$ into a target circuit $mathcal{B}$, with the goal that both circuits have the same action on a specific input i.e. $mathcal{B}{mid{in}rangle}=mathcal{A}{mid{in}rangle}$. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies $mathcal{B}$ as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If $mathcal{B}$ is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a $7$-qubit circuit involving $186$ gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is $robust$, finding that per-gate noise of up to $1%$ can still yield near-perfect recompilation. We test the scaling of our algorithm on up to $20$ qubits, recompiling into circuits with up to $400$ parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today’s prototypes, and more generally the method may enable `blind’ compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.

The code and resources used to generate our results are openly available online [1] [2]. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.