Related papers: Quantum Self-Correcting Stabilizer Codes
Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure…
Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as…
We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between…
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 present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act…
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 prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to…
In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a $\mathbb{Z}_N$ gauge theory with prime dimension $N$ coupled to dynamical matter can be expressed as a qudit…
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
We suggest a simple approach to populate photonic quantum materials at non-zero chemical potential and near-zero temperature. Taking inspiration from forced evaporation in cold-atom experiments, the essential ingredients for our low-entropy…
We review recent progress in the computation of leading quantum corrections to the energies of classical solitons with topological structure, including multi-soliton models in one space dimension and string configurations in three space…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
Recently, quantum classifiers have been found to be vulnerable to adversarial attacks, in which quantum classifiers are deceived by imperceptible noises, leading to misclassification. In this paper, we propose the first theoretical study…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
Quantum error correction is a solution to preserve the fidelity of quantum information encoded in physical systems subject to noise. However, unfavorable correlated errors could be induced even for non-interacting qubits through the…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.