Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras

TL;DR

This paper proposes a method combining quantum error correction and mitigation to enhance fault-tolerant quantum computing, significantly reducing resource requirements and enabling more logical operations within limited hardware constraints.

Contribution

It introduces an integrated approach that increases effective code distance and T-gate count with constant sampling overheads, improving scalability of FTQC in early quantum devices.

Findings

Reduces physical qubit requirements by up to 80%.

Enables executing 1000 times more logical operations at code distance 11.

Dramatically decreases computational overheads for quantum advantage demonstrations.

Abstract

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.