Related papers: Homology, Hopf Algebras and Quantum Code Surgery
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…
In efforts to scale the size of quantum computers, modularity plays a central role across most quantum computing technologies. In the light of fault tolerance, this necessitates designing quantum error-correcting codes that are compatible…
By studying ``points of the underlying quantum groups''of coquasitriangular Hopf (face) algebras, we construct ribbon categories for each lattice models without spectral parameter of both vertex and face type. Also, we give a classification…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
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…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent…
Achieving practical quantum advantage on fault-tolerant quantum computers (FTQC) is fundamentally constrained by the substantial spatial and temporal overheads required to map logical operations onto physical hardware. Existing compilation…
Quantum heuristics have shown promise in solving various optimization problems, including lattice protein folding. Equally relevant is the inverse problem, protein design, where one seeks sequences that fold to a given target structure. The…