Related papers: No Strings Attached: Boundaries and Defects in the…
Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…
Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has…
Tree codes, introduced by Schulman, are combinatorial structures essential to coding for interactive communication. An infinite family of tree codes with both rate and distance bounded by positive constants is called asymptotically good.…
We introduce a class of gapped three-dimensional models, dubbed "cage-net fracton models," which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional…
We study a translation invariant spin model in a three-dimensional regular lattice, called the cubic code model, in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
Almheiri, Dong, and Harlow [arXiv:1411.7041] proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here we explore this connection further. We derive…
In this work, a coding technique called cost constrained Geometric Huffman coding (ccGhc) is developed. ccGhc minimizes the Kullback-Leibler distance between a dyadic probability mass function (pmf) and a target pmf subject to an affine…
The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…
We construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. The Hilbert spaces are related by isometric maps, which we define explicitly. We construct a…
The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
We develop the procedures of gauging and ungauging, reveal their operational meaning and propose their generalization in a systematic manner within the framework of quantum error-correcting codes. We demonstrate with an example of the…
We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various…
Topological quantum computing is believed to be inherently fault-tolerant. One mathematical justification would be to prove that ground subspaces or ground state manifolds of topological phases of matter behave as error correction codes…
A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…