# Phase Gadget Synthesis for Shallow Circuits

## TL;DR

This paper introduces a novel phase gadget-based technique for optimizing quantum circuits, significantly reducing gate count and depth, demonstrated on quantum chemistry variational circuits.

## Contribution

It presents an efficient method to synthesize shallow circuits from phase gadgets using ZX-calculus, improving quantum circuit optimization.

## Key findings

- Significant reduction in gate count and circuit depth.
- Effective application to quantum chemistry benchmarking circuits.
- Enhanced circuit efficiency for practical quantum computations.

## Abstract

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.

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Source: https://tomesphere.com/paper/1906.01734