Related papers: Topological error correcting processes from fixed-…
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…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Photonics provides a viable path to a scalable fault-tolerant quantum computer. The natural framework for this platform is measurement-based quantum computation, where fault-tolerant graph states supersede traditional quantum…
Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule.…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
We experimentally realized a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each associated with a Floquet winding number: a topological invariant. These bands are spin-momentum locked and…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
We consider the $\mathbb{Z}_2$ toric code, surface code and Floquet code defined on a non-orientable surface, which can be considered as families of codes extending Shor's 9-qubit code. We investigate the fault-tolerant logical gates of the…
Stabilizer channels are stabilizer circuits that implement logical operations while mapping from an input stabilizer code to an output stabilizer code. They are widely used to implement fault tolerant error correction and logical operations…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We propose a scheme to dynamically realize a quantum memory based on the toric code. The code is generated from qubit systems with typical two-body interactions (Ising, XY, Heisenberg) using periodic, NMR-like, pulse sequences. It allows…
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be…