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What is Quantum error correction?

A technology that spreads the information of one logical qubit over many physical qubits and measures only clues to the errors (the syndrome), so that errors can be found and corrected during a computation. It must handle both bit-flip and phase-flip errors and requires the physical error rate to be well below a threshold.

Japanese name: 量子誤り訂正

Quantum error correction appears in 1 practice question across 1 topic, including Quantum Computing Hardware.

Field: Quantum Computing Hardware

How it differs from classical error correction

Classical error correction finds and fixes errors by copying data or adding parity bits. With qubits, unknown states cannot be copied (the no-cloning theorem), and measuring the data directly destroys the superposition. Instead, α|0⟩ + β|1⟩ is spread into an entangled state such as α|000⟩ + β|111⟩, and auxiliary qubits measure only whether the first and second qubits agree and whether the second and third agree. These results (the syndrome) reveal where a bit flipped, so the state can be restored without knowing α and β. Real codes are built to detect phase-flip errors at the same time.

Threshold and code distance

If the error rate of the physical qubits is below the threshold (roughly 1% for the surface code), making the code larger lowers the logical error rate exponentially. For the surface code, the logical error rate is roughly proportional to (p/p_th)^((d+1)/2), so each increase of the code distance d by 2 divides it by p_th/p. A rotated surface code uses d² data qubits and d² − 1 measurement qubits, 2d² − 1 physical qubits in total, per logical qubit: 1,249 for d = 25.

Implementation challenges

In superconducting surface codes, syndrome measurements are repeated about every 1 µs, so the decoder that infers error locations from the results must also keep running fast enough to keep up. FPGAs and dedicated circuits are used for this. Errors in which qubits leak into levels outside the qubit, such as |2⟩, and errors that strike many qubits at once, for example from radiation, differ from the independent errors that ordinary codes assume and need separate countermeasures. Fault-tolerant computation also needs steps that prepare special states for certain gates, which further increases the number of qubits required.

Try it: questions about Quantum error correction

Why can't quantum error correction directly use the classical approach of making three copies of the data and taking a majority vote?

  1. AAn unknown quantum state cannot be copied exactly (the no-cloning theorem), and measuring it to check its value destroys the superposition
  2. BA qubit takes only the two values 0 and 1, so a majority vote is meaningless
  3. CQubit errors are only bit flips, so they can be corrected by adding a single parity bit, without making copies
Show answer and explanation

Answer: A. An unknown quantum state cannot be copied exactly (the no-cloning theorem), and measuring it to check its value destroys the superposition

By the no-cloning theorem, there is no operation that copies an unknown quantum state α|0⟩ + β|1⟩ exactly onto another qubit. Measuring the qubits that hold the data directly would also destroy the superposition. Quantum error correction therefore spreads the information of one logical qubit over an entangled state of several physical qubits and uses auxiliary qubits to measure only clues to the errors (the syndrome), such as the parity of neighboring qubits. Qubit errors include phase flips as well as bit flips, and both must be detected.

FAQ

How many physical qubits does one logical qubit need?

It varies greatly with the type of code, the physical error rate and the target logical error rate. For the surface code with physical error rates of about 0.1%, estimates of several hundred to about 1,500 for practical computations are often used. Lower physical error rates reduce the number needed.

How does it differ from error mitigation?

Error correction fixes errors during the computation, so in principle long computations become possible, but it needs many physical qubits. Error mitigation estimates the effect of errors and corrects for it by post-processing the measurement results; it needs no extra qubits, but the number of measurements required grows quickly as circuits get larger, so it cannot be used for long computations.

Quantum error correction in the explanations

Questions that mention Quantum error correction (1)

  1. Why can't quantum error correction directly use the classical approach of making three copies of the data and taking a majority vote?

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Related terms

Qubit Quantum superposition Parity bit Decoherence Dilution refrigerator Ion trap Josephson junction NISQ Post-quantum cryptography Quantum entanglement

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