The **Quantum Error Correction (QEC) threshold** refers to the maximum error rate per quantum operation (gate, measurement, or qubit storage) that a quantum system can tolerate while still enabling fault-tolerant quantum computation. Below this threshold, errors can be corrected faster than they accumulate, ensuring that quantum computations can proceed accurately over long durations. ### Key Details: 1. **Error Rate Per Gate or Qubit**: - The threshold is often expressed as a fraction or percentage, such as 10^-2 (1%) or 10−3 (0.1%) - If the actual error rates in the system are below this value, quantum error correction codes can reliably correct the errors. 2. **Logical Qubit Reliability**: - Logical qubits are encoded using multiple physical qubits with error correction techniques. - As long as the error rates are below the threshold, increasing the number of physical qubits can exponentially improve the logical qubit's reliability. 3. **Dependency on QEC Codes**: - The threshold value varies based on the specific error correction code and the error model of the system. - For example, the **surface code** has a high threshold of around 1% error per gate, making it practical for many physical implementations. 4. **Physical vs. Logical Error Rates**: - Below the QEC threshold, logical error rates decrease as the size of the error correction code increases. - Above the threshold, errors proliferate, making error correction ineffective. 5. **Importance in Quantum Computing**: - The QEC threshold determines the feasibility of fault-tolerant quantum computation. - Achieving gate and qubit error rates below the threshold is a critical milestone for scaling quantum computers to solve real-world problems. ### Practical Example: For a system employing the surface code with a threshold around 1% - If the physical gate error rate is 0.5%, it is below the threshold, and error correction can effectively suppress logical errors. - If the error rate rises to 2%, the system would be above the threshold, and logical errors would accumulate uncontrollably, rendering the quantum computation unreliable. The QEC threshold underscores the importance of hardware fidelity and robust error correction in advancing scalable quantum computing.