Surface code implementation of block code state distillation

TL;DR

This paper presents a surface code implementation of block code state distillation, comparing its efficiency to traditional methods and finding limited overhead reduction in practical scenarios.

Contribution

It provides an explicit surface code implementation of block code state distillation and evaluates its overhead relative to existing techniques.

Findings

Block code distillation can produce multiple improved states from fewer inputs.

Overhead reduction is typically less than a factor of three in practical cases.

Traditional methods may still be more efficient in many scenarios.

Abstract

State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states |A>=(|0>+e^{i\pi/4}|1>)/\sqrt{2} produced a single improved |A> state given 15 input copies. New block code state distillation methods can produce k improved |A> states given 3k+8 input copies, potentially significantly reducing the overhead associated with state distillation. We construct an explicit surface code implementation of block code state distillation and quantitatively compare the overhead of this approach to the old. We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.