Related papers: Topological quantum error correction in the Kitaev…
We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the…
Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential…
We analyze propagation of quantum information along chiral Majorana edge states in two-dimensional topological materials. The use of edge states may facilitate the braiding operation, an important ingredient in topological quantum…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
The ground state of the Kitaev quantum spin liquid on a honeycomb lattice is an intriguing many-body state characterized by its topological order and massive entanglement. One of the significant issues is to prepare and manipulate the…
We calculate the topological entanglement entropy (TEE) for a three-dimensional hyperhoneycomb lattice generalization of Kitaev's honeycomb lattice spin model. We find that for this model TEE is not directly determined by the total quantum…
When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful…
The theoretical inception of the Kitaev honeycomb model has had defining influence on the experimental hunt for quantum spin liquids, bringing unprecedented focus onto the synthesis of materials with bond-directional interactions. Numerous…
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 prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through…
Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…
Homological quantum error correction uses tools of algebraic topology and homological algebra to derive Calderbank-Shor-Steane quantum error correcting codes from cellulations of topological spaces. This work is an exploration of the…
We analyse in detail the effect of non-trivial band topology on the area law behaviour of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model into 1D fermionic subsystems, we identify…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally…
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we…
Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements…