Скачать или смотреть Marco F. Asiani (Warsaw University): Magic states are rarely the most important resource to optimize

Marco Fellous Asiani (Warsaw University): Magic states are rarely the most important resource to optimize

Concatenated fault-tolerant quantum computing has recently been shown to be able to outperform leading error-correction codes, such as the surface code, for well designed concatenated schemes. In our work, we propose a scaling approach to evaluate the qubit resources required by concatenated fault-tolerant quantum computing. Our approach gives closed-form expressions, which remain simple for multiple levels of concatenation, making it an ideal tool to compare and minimize the resource costs of different concatenation schemes. We then use it to study the resources required for normal and magic operations. Here, magic operations require the preparation, verification and injection of complicated states called "magic states", while normal operations do not. It is often expected that magic operations will dominate a computation's physical resource requirements (qubits, gates, etc.), although this expectation has been cast in doubt for surface codes. Our results show that this expectation is also wrong for typical concatenated codes, with magic operations rarely being costly. We give concrete examples for the concatenated 7-qubit scheme with Steane error-correction gadgets or a flag-qubits approach. While optimizations that affect all operations are naturally more effective than ones that affect only magic operations, the surprising conclusion of our work is that the former can reduce costs by several orders of magnitude whereas the latter contributes only marginal reductions. This is particularly surprising given the numerous works on optimizations that affect only magic operations.

Quantum Information and Quantum Computing Seminars CTP PAS
2025-25-06