Quantum computation with realistic magic state factories

TL;DR

This paper provides a comprehensive resource assessment of magic state factories in surface code quantum computers, introducing new techniques and correcting prior undervaluations, with implications for scalable quantum computing.

Contribution

It offers the most detailed analysis to date, including new methods for error tracking, a subsystem code realization, and refined cost estimates for magic state factories.

Findings

Undervalued block codes of Bravyi and Haah identified

Fidelity estimates achieved without union bound

Magic state factory size can be as small as 6.3 million qubits

Abstract

Leading approaches to fault-tolerant quantum computation dedicate a significant portion of the hardware to computational factories that churn out high-fidelity ancillas called magic states. Consequently, efficient and realistic factory design is of paramount importance. Here we present the most detailed resource assessment to date of magic state factories within a surface code quantum computer, along the way introducing a number of new techniques. We show that the block codes of Bravyi and Haah [Phys. Rev. A 86, 052329 (2012)] have been systematically undervalued; we track correlated errors both numerically and analytically, providing fidelity estimates without appeal to the union bound. We also introduce a subsystem code realisation of these protocols with constant time and low ancilla cost. Additionally, we confirm that magic state factories have space-time costs that scale as a constant factor of surface code costs. We find that the magic state factory required for post-classical factoring can be as small as 6.3 million data qubits, ignoring ancilla qubits, assuming $10^{-4}$ error gates, and the availability of long range interactions.