John Preskill discusses the development of quantum error correction, which has enabled reliable quantum computation. Quantum error correction protects encoded quantum information from errors caused by environmental interactions. If the average error probability per quantum gate is below a critical threshold, arbitrarily long quantum computations can be performed reliably. A quantum computer with about 10^6 qubits and an error probability of 10^-6 per gate could be a powerful factoring machine. Quantum error correction is possible due to the ability to use entanglement to combat errors. The key concept is that errors can be detected and corrected without destroying the quantum information. The 7-qubit Steane code is an example of a quantum error-correcting code that can correct single errors. This code encodes one qubit of information using seven qubits and is based on the classical Hamming code. Quantum error correction requires fault-tolerant procedures to ensure that errors do not propagate. The laws of fault-tolerant computation include avoiding repeated use of the same bit, copying errors rather than data, verifying encodings, repeating operations, and using the right code. These principles ensure that quantum computations can be performed reliably. The accuracy threshold for quantum computation is determined by the error rate per gate. If the error rate is below a certain threshold, quantum computations can be performed with high fidelity. Concatenated codes, which involve multiple layers of error correction, can further reduce error probabilities. However, if the error rate is too high, coding may not help. The accuracy threshold is crucial for the feasibility of quantum computing, as it determines the minimum error rate required for reliable computation.John Preskill discusses the development of quantum error correction, which has enabled reliable quantum computation. Quantum error correction protects encoded quantum information from errors caused by environmental interactions. If the average error probability per quantum gate is below a critical threshold, arbitrarily long quantum computations can be performed reliably. A quantum computer with about 10^6 qubits and an error probability of 10^-6 per gate could be a powerful factoring machine. Quantum error correction is possible due to the ability to use entanglement to combat errors. The key concept is that errors can be detected and corrected without destroying the quantum information. The 7-qubit Steane code is an example of a quantum error-correcting code that can correct single errors. This code encodes one qubit of information using seven qubits and is based on the classical Hamming code. Quantum error correction requires fault-tolerant procedures to ensure that errors do not propagate. The laws of fault-tolerant computation include avoiding repeated use of the same bit, copying errors rather than data, verifying encodings, repeating operations, and using the right code. These principles ensure that quantum computations can be performed reliably. The accuracy threshold for quantum computation is determined by the error rate per gate. If the error rate is below a certain threshold, quantum computations can be performed with high fidelity. Concatenated codes, which involve multiple layers of error correction, can further reduce error probabilities. However, if the error rate is too high, coding may not help. The accuracy threshold is crucial for the feasibility of quantum computing, as it determines the minimum error rate required for reliable computation.