Related papers: Approximate quantum error correction for generaliz…
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 describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we…
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
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…
Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental…
We propose local strategies to protect global quantum information. The protocols, which are quantum error correcting codes for dissipative systems, are based on environment measurements, direct feedback control and simple encoding of the…
Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
In this paper, we investigate the error correction of universal Gaussian transformations obtained in the process of continuous-variable quantum computations. We have tried to bring our theoretical studies closer to the actual picture in the…
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…
We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions).…