Quantum compilation and circuit optimisation via energy dissipation
Tyson Jones, Simon C. Benjamin · arXiv (Cornell University) · 2018
We describe a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. A|in> = B|in>. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies 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 optionally a gate elimination phase to compress the circuit. We use a recently introduced imaginary-time technique derived from McLachlan's variational principle. If the template for B is too shallow for perfect recompilation then the method will result in an approximate solution. As a demonstration we successfully recompile a 7-qubit circuit involving 186 gates of multiple types into an alternative form with a different topology, a far lower two-qubit gate count, and a smaller family of gate types. We test the scaling of our algorithm on up to 20 qubits, recompiling into circuits with up to 400 parameterized gates, and incorporate a novel 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.