1. Robust quantum compilation and circuit optimisation via energy minimisation
- Author
-
Tyson Jones and Simon C. Benjamin
- Subjects
Physics ,QC1-999 - Abstract
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 \cite{githubLink} \cite{mmaGithubLink}. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.
- Published
- 2022
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