We are improving the reliability of quantum information processing using methods such as error models, simulators for quantum error correction algorithms and new decoders for quantum error correction.
Quantum computers of the noisy intermediate-scale quantum computer (NISQ) era are prone to errors that render their computations unusable. For certain applications and algorithms, error mitigation is therefore essential. In the R-QIP project, we are investigating quantum error correction techniques to protect quantum computations from errors. To this end, we are starting with a review of the latest error correction solutions and developing system requirements and system models. We then plan to develop a simulation environment to validate these solutions.
Quantum computers promise to solve certain classes of problems exponentially faster than classical systems. However, quantum information is inherently prone to errors and information loss: while the actual quantum computation takes place within an environment that is almost entirely free from errors, the hardware required for quantum computing is error prone. Thus, for quantum computation to be feasible in practice, the information stored within the qubits must be protected. This requires the introduction of quantum error correction, which means representing logical (or information) qubits with a larger number of physical (or encoded) qubits. Thus, if some physical qubits are faulty, the remaining ones can be used to restore the logical qubits.
However, it is important that quantum error correction is as efficient as possible so that as many of the few available qubits as possible can be used for computational operations and not exclusively for error correction. Therefore, our goal is to make quantum computation more reliable and efficient in the future.
It is likely that the first full-scale quantum error correction codes will be realised soon. This would be a major step for the practical feasibility of quantum computers. However, the most common error-correction methods currently in use, known as surface codes, require an order of magnitude of 100 physical qubits to implement a single reliable logical qubit. The quantum computers of the near future, however, will only have a few hundred to a few thousand physical qubits. Applying surface codes to a quantum computer of this size will yield at most a few tens of logical qubits. This is too low a number for most applications.
Therefore, we want to investigate other quantum codes that require fewer physical qubits to implement a (reliable) logical qubit. Novel classes of quantum codes could significantly reduce this inefficiency, such as quantum low-density parity-check (QLDPC) codes or quantum polar codes. In practice, their performance has not yet been sufficiently investigated.