A Regular Representation of Quantum Circuits

TL;DR

This paper introduces an ICM quantum circuit representation using initializations, CNOT gates, and measurements, facilitating optimization of teleportation-based, fault-tolerant quantum circuits.

Contribution

It proposes a canonical ICM representation for quantum circuits that include teleportation, aiding in optimization for fault-tolerant quantum computing.

Findings

ICM representation simplifies circuit optimization.

It provides a canonical form for teleportation-based circuits.

Enhances fault-tolerant quantum circuit design.

Abstract

We present a quantum circuit representation consisting entirely of qubit initialisations (I), a network of controlled-NOT gates (C) and measurements with respect to different bases (M). The ICM representation is useful for optimisation of quantum circuits that include teleportation, which is required for fault-tolerant, error corrected quantum computation. The non-deterministic nature of teleportation necessitates the conditional introduction of corrective quantum gates and additional ancillae during circuit execution. Therefore, the standard optimisation objectives, gate count and number of wires, are not well-defined for general teleportation-based circuits. The transformation of a circuit into the ICM representation provides a canonical form for an exact fault-tolerant, error corrected circuit needed for optimisation prior to the final implementation in a realistic hardware model.