Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact

TL;DR

This paper introduces a systematic, online method for synthesizing topologically protected quantum circuits, focusing on efficient placement of magic state distillation boxes to minimize resource overhead.

Contribution

It presents a novel greedy scheduler for compact placement of distillation boxes and offers a software implementation for practical synthesis of topological quantum circuits.

Findings

Efficient placement of distillation boxes reduces overhead.

The proposed method is systematic and online, enabling dynamic circuit synthesis.

Software implementation demonstrates practical applicability.

Abstract

It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available online, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.