Quantum Error Correction

Quantum error correction (QEC) and quantum error mitigation (QEM) are two different schemes to deal with noise in devices, which can cause errors in computation.

Quantum error correction methods use multiple physical qubits to represent a single logical qubit. Data is preserved by distributing the information across multiple qubits. Quantum decoders can then detect and correct any errors that occur during computation. Surface code is a popular QEC code.

By contrast, quantum error mitigation methods are employed to infer less noisy outcomes of quantum computations, rather than correcting them. This is often done by repeatedly running slightly different circuits and classically post-processing the results. As an example, zero noise extrapolation is a popular error mitigation method.

QEM methods provide a reduction in noise that can be useful in the NISQ (noisy intermediate-scale quantum) era, as restraints in quantum hardware can make full quantum error correction less feasible. However, for useful computation involving many qubits and deep circuits, full quantum error correction will be necessary.

Quantum error correction and fault-tolerant quantum computers are often informally used interchangeably. To experts the terms have slightly difference meanings.

Quantum error correction is a scheme for protecting information from noise in device.

Fault-tolerance builds on this. Fault-tolerant quantum computers also prevent errors from spreading during the error correction process or during a computation. It is a richer and broader subject.

To build a useful quantum computer, we really do need fault-tolerance and not just error correction. At Riverlane, we are really solving the fault-tolerance problem, but often just call out “quantum error correction” since this phrase is more commonly known by non-experts.

While improved quality and quantity of qubits are critical, that's only part of the equation.

Quantum error correction (QEC) is a multi-faceted problem. On the qubit side, we need physical qubit error rates below the QEC threshold with a low ‘QEC overhead’, that is the ratio between the number of physical and logical qubits.

Once we reach a qubit fidelity of 99.9%, we can introduce a set of classical QEC technologies to solve this complex, vast, real-time data processing problem.

As quantum computers scale, an additional layer of classical QEC solutions is required to tackle the increasing error numbers and types, addressing three broad challenges:

1.  Developing complex QEC codes: QEC involves sophisticated inference algorithms (QEC codes) to determine the most likely error that might have occurred given a specific syndrome value.
2.  Performing at fast speeds: each QEC round must be fast (<1μs) and deterministic (respond promptly at well-determined times) to avoid delays that lead to uncorrectable errors.
3.  Dealing with massive data volumes: these algorithms require an extremely high instruction bandwidth, scaling to 100TB/s – equivalent to a single quantum computer processing and correcting the equivalent of Netflix’s total global streaming data every second.

So, while high-quality qubits are essential, they’re only part of the solution.

Scaling quantum computers to their full potential demands a seamless integration of quantum and classical technologies.