Quantum Error Mitigation as a Universal Error Reduction Technique: Applications from the NISQ to the Fault-Tolerant Quantum Computing Eras

In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient computational power of classical decoding units. Here, we integrate quantum error correction and quantum error mitigation into an efficient FTQC architecture that effectively increases the code distance and T-gate count at the cost of constant sampling overheads in a wide range of quantum computing regimes. For example, while we need 10(4) to 10(10) logical operations for demonstrating quantum advantages from optimistic and pessimistic points of view, we show that we can reduce the required number of physical qubits by 80% and 45% in each regime. From another perspective, when the achievable code distance is up to about 11, our scheme allows executing 10(3) times more logical operations. This scheme will dramatically alleviate the required computational overheads and hasten the arrival of the FTQC era.

Automated summary

In the early stages of fault-tolerant quantum computing, limitations in quantum devices and classical decoding units restrict the available code distance and magic state count. This study integrates quantum error correction and quantum error mitigation into an efficient architecture, effectively increasing the code distance and T-gate count at the cost of constant sampling overheads. Experimental results show a reduction in the required number of physical qubits by 80% and 45% in different regimes. Additionally, when the achievable code distance is around 11, the scheme allows for more than 10(3) times the number of logical operations.