Controlling distilleries in fault-tolerant quantum circuits: problem statement and analysis towards a solution

TL;DR

This paper investigates how the placement of distillation circuits affects the layout and resource efficiency of surface code fault-tolerant quantum circuits, proposing an initial algorithmic solution for optimization.

Contribution

It introduces the problem of distillery placement in surface code quantum circuits and analyzes trade-offs, providing a novel algorithmic approach for resource reduction.

Findings

Distillery placement impacts circuit layout and resource use.

Proposed algorithm improves resource efficiency in quantum circuit design.

Evaluation on addition circuits demonstrates potential resource savings.

Abstract

The failure susceptibility of the quantum hardware will force quantum computers to execute fault-tolerant quantum circuits. These circuits are based on quantum error correcting codes, and there is increasing evidence that one of the most practical choices is the surface code. Design methodologies of surface code based quantum circuits were focused on the layout of such circuits without emphasizing the reduced availability of hardware and its effect on the execution time. Circuit layout has not been investigated for practical scenarios, and the problem presented herein was neglected until now. For achieving fault-tolerance and implementing surface code based computations, a significant amount of computing resources (hardware and time) are necessary for preparing special quantum states in a procedure called distillation. This work introduces the problem of how distilleries (circuit portions responsible for state distillation) influence the layout of surface code protected quantum circuits, and analyses the trade-offs for reducing the resources necessary for executing the circuits. A first algorithmic solution is presented, implemented and evaluated for addition quantum circuits.