Related papers: Quantum error correction on infinite-dimensional H…
Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence…
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…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer.…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…
Given a completely positive map, we introduce a set of algebras that we refer to as its generalized multiplicative domains. These algebras are generalizations of the traditional multiplicative domain of a completely positive map and we…
A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Benchmarking the performance of quantum error correction codes in physical systems is crucial for achieving fault-tolerant quantum computing. Current methodologies, such as (shadow) tomography or direct fidelity estimation, fall short in…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…