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Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is…
Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground state degeneracy (GSD) which can increase exponentially with system size. In this paper,…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum…
The most fundamental strings in high density color superconductivity are the non-Abelian semi-superfluid strings which have color gauge flux tube but behave as superfluid vortices in the energetic point of view. We show that in addition to…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
Ultracold fermions in a one-dimensional, spin-dependent, optical lattice are described by a non-standard Hubbard model with next-nearest-neighbour correlated hopping. Periodic driving of the lattice allows wide tuning of the system…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum…
We demonstrate that a high fidelity approximation to $| \Psi_b \rangle$, the quantum superposition over all bit strings within Hamming distance $b$ of the codewords of a dimension-$k$ linear code over $\mathbb{Z}_2^n$, can be efficiently…
We investigate the long-range statistical correlations, whereby discuss the nature of the undermining interacting/ noninteracting domains and associated phase transitions under variations of the quark mass and the mass scale that…
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the $q$-analogues of projective systems and blocking sets. We also illustrate how to associate a classical…
Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode's…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
We propose a scalable trapped-ion quantum-computing architecture that efficiently incorporates quantum error correction. The chip design exploits orthogonal qubit connectivity by assigning horizontal trap regions to transversal logical…
Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they…
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…
Superconductors are the only experimentally accessible systems with spontaneously broken gauge symmetries which support topologically nontrivial defects, namely string defects. We propose two experiments whose aim is the observation of the…
We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of…
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy, and fidelity per lattice site by using the infinite matrix…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…