Related papers: Quantum error correction realized by the renormali…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates…
Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
We study the approximate correctability of general algebras of observables, which represent hybrid quantum-classical information. This includes approximate quantum error correcting codes and subsystems codes. We show that the main result of…
A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.
This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose…
This paper shows that Knill-Laflamme condition, known as a necessary and sufficient condition for quantum error-correction, can be applied to quantum errors where the number of particles changes before and after the error. This fact shows…
In this paper we study systematically the Euclidean renormalization in configuration spaces. We investigate also the deviation from commutativity of the renormalization and the action of all linear partial differential operators. This…
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction…
The normalization of the quantum corrected action is resolving the equation divergent dependence of the cutoff towards the system apparent result in quantum gravity. Here we consider the normalization to Einstein R twice scalar action 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…
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
Recent studies of globally controlled structures have culminated in a theoretical demonstration that fault-tolerant quantum computation can be carried out on a one--dimensional chain with control over two global fields only. This required…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
By formulating the renormalization group as a quantum channel acting on density matrices in Quantum Field Theories (QFTs), we show that ground-state expectation values of observables supported on slow momentum modes can be approximated by…
This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013)] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random…