Related papers: Quantum Error Correction in Loop Quantum Gravity
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a non-zero cosmological constant $\Lambda$ in this context has been a withstanding problem. Other approaches, such as Chern-Simons gravity, suggest…
In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing…
Consider a 2-D square array of qubits of extent $L\times L$. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…
In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
In the framework of loop quantum gravity (LQG), having quantum black holes in mind, we generalize the previous boundary state counting (gr-qc/0508085) to a full bulk state counting. After a suitable gauge fixing we are able to compute the…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding…
Given the non-graph-changing Hamiltonian $\widehat{H[N]}$ in Loop Quantum Gravity (LQG), $\langle\widehat{H[N]}\rangle$, the coherent state expectation value of $\widehat{H[N]}$, admits an semiclassical expansion in $\ell^2_{\rm p}$. In…
We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one…
Reducing errors is critical to the application of modern quantum computers. In the current Letter, we investigate the quantum error mitigation considering parametric circuits accessible by classical computations in some range of their…
Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom…
We evaluate quantum gravity corrections to the standard model Higgs potential $V(\phi)$ a la Coleman-Weinberg and examine the stability question of $V(\phi)$ at scales of Planck mass $M_{\rm Pl}$. We compute the gravity one-loop corrections…
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.…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…