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Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…
Quantum computers have the potential to outperform classical computers for some complex computational problems. However, current quantum computers (e.g., from IBM and Google) have inherent noise that results in errors in the outputs of…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a…
Mitigation and calibration schemes are central to maximize the computational reach of today's Noisy Intermediate Scale Quantum (NISQ) hardware, but these schemes are often specialized to exclusively address either coherent or decoherent…
Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Describing a general quantum process requires an exponentially large…
The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…