Related papers: Linear programming bounds for quantum channels act…
Efficient and realistic error decoding is crucial for fault-tolerant quantum computation (FTQC) on near-term devices. While decoding is a classical post-processing task, its effectiveness depends on accurately modeling quantum noise, which…
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…
Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Numerous quantum error-mitigation protocols have been proposed, motivated by the critical need to suppress noise effects on intermediate-scale quantum devices. Yet, their general potential and limitations remain elusive. In particular, to…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
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…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…