  We give an overview of the circuit optimisation methods used by tket, a
compiler system for quantum software developed by Cambridge Quantum Computing
Ltd. We focus on a novel technique based around phase gadgets, a family of
multi-qubit quantum operations which occur naturally in a wide range of quantum
circuits of practical interest. The phase gadgets have a simple presentation in
the ZX-calculus, which makes it easy to reason about them. Taking advantage of
this, we present an efficient method to translate the phase gadgets back to
CNOT gates and single qubit operations suitable for execution on a quantum
computer with significant reductions in gate count and circuit depth. We
demonstrate the effectiveness of these methods on a quantum chemistry
benchmarking set based on variational circuits for ground state estimation of
small molecules.
