Related papers: Universal Quantum Computation with Continuous-Vari…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and cubic-phase gate teleportation. The first…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However the question of how to obtain and process information about what errors have occurred in order to negate their effects has not…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For…
This set of lecture notes forms the basis of a series of lectures delivered at the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at Forschungszentrum Juelich, Germany. The first part of…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility,…
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models.…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is…
Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection and feed-forward, inclusion of ideal photon counting measurements overcomes this obstacle. These…
Quantized integrable systems can be made to perform universal quantum computation by the application of a global time-varying control. The action-angle variables of the integrable system function as qubits or qudits, which can be coupled…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…