Improved magic states distillation for quantum universality

TL;DR

This paper enhances magic state distillation techniques to better identify states enabling universal quantum computation, sharpening the threshold between classically simulable and quantum-universal states.

Contribution

It improves existing distillation procedures for Hadamard magic states, establishing a clearer threshold for quantum universality based on state purity.

Findings

Achieved a sharper threshold for magic state distillation in the Hadamard direction.

Showed that preparing any non-stabilizer pure state with stabilizer operations yields universality.

Identified an open problem regarding the T direction separation.

Abstract

Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant stabilizer circuits. We improve the procedures of Bravyi and Kitaev in the Hadamard "magic" direction of the Bloch sphere to achieve a sharp threshold between those rho allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with stabilizer operations, gives quantum universality. It remains open whether there is also a tight separation in the so-called T direction.