Related papers: Dynamical Logical Qubits in the Bacon-Shor Code
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
2D compass codes are a family of quantum error-correcting codes that contain the Bacon-Shor codes, the $X$-Shor and $Z$-Shor codes, and the rotated surface codes. Previous numerical results suggest that the surface code has a constant…
Quantum states can quickly decohere through interaction with the environment. Quantum error correction is a method for preserving coherence through active feedback. Quantum error correction encodes the quantum information into a logical…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
Floquet codes define fault-tolerant protocols through periodic measurement sequences that drive a dynamically evolving stabilizer group. They provide a natural framework for hardware supporting two-qubit parity measurements but no unitary…
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the…
We develop a scheme for fault-tolerant quantum computation based on asymmetric Bacon-Shor codes, which works effectively against highly biased noise dominated by dephasing. We find the optimal Bacon-Shor block size as a function of the…
Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new…
We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both…
We study the fundamental limits on the reliable storage of quantum information in lattices of qubits by deriving tradeoff bounds for approximate quantum error correcting codes. We introduce a notion of local approximate correctability and…
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…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled…
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…
We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch…
Quantum error correction is essential for reliable quantum computation, where surface codes demonstrate high fault-tolerant thresholds and hardware efficiency. However, noise in single-shot measurements limits logical readout fidelity,…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…