Related papers: Toric codes and quantum doubles from two-body Hami…
We derive an electron-vibration model Hamiltonian in a quantum chemical framework, and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
We present a solution of Kitaev's spin model on the honeycomb lattice and of related topologically ordered spin models. We employ a Jordan-Wigner type fermionization and find that the Hamiltonian takes a BCS type form, allowing the system…
Toric codes are error-correcting codes that are derived from toric varieties, which hold a unique correspondence to integral convex polytopes. In this paper, we focus on integral convex polytopes $P \subseteq \mathbb{R}^2$ and the toric…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial…
We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide…
Quantum simulation provides a powerful route for exploring many-body phenomena beyond the capabilities of classical computation. Existing approaches typically proceed in the forward direction: a model Hamiltonian is specified, implemented…
The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error…
We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing…
Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $\epsilon$. Typically, gadget constructions involve terms with large…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with…
In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin…