Phase gadget synthesis for shallow circuits

Cowtan, Alexander and Dilkes, Silas and Duncan, Ross and Simmons, Will and Sivarajah, Seyon; Coecke, Bob and Leifer, Matthew, eds. (2019) Phase gadget synthesis for shallow circuits. In: Proceedings 16th International Conference on Quantum Physics and Logic. Electronic Proceedings in Theoretical Computer Science, 318 . Open Publishing Association, USA, 213–228. (

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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.


Cowtan, Alexander, Dilkes, Silas, Duncan, Ross ORCID logoORCID:, Simmons, Will and Sivarajah, Seyon; Coecke, Bob and Leifer, Matthew