19,467 research outputs found
Topological cluster state quantum computing
The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007),
when viewed as a cluster state computation, features a 3-D cluster state, novel
adjustable strength error correction capable of correcting general errors
through the correction of Z errors only, a threshold error rate approaching 1%
and low overhead arbitrarily long-range logical gates. In this work, we review
the scheme in detail framing discussion solely in terms of the required 3-D
cluster state and its stabilizers.Comment: 11 pages, 20 figures, v2 substantially revised and simplified to
remove the need for prior exposure to cluster state quantum computin
Quantum picturalism for topological cluster-state computing
Topological quantum computing is a way of allowing precise quantum
computations to run on noisy and imperfect hardware. One implementation uses
surface codes created by forming defects in a highly-entangled cluster state.
Such a method of computing is a leading candidate for large-scale quantum
computing. However, there has been a lack of sufficiently powerful high-level
languages to describe computing in this form without resorting to single-qubit
operations, which quickly become prohibitively complex as the system size
increases. In this paper we apply the category-theoretic work of Abramsky and
Coecke to the topological cluster-state model of quantum computing to give a
high-level graphical language that enables direct translation between quantum
processes and physical patterns of measurement in a computer - a "compiler
language". We give the equivalence between the graphical and topological
information flows, and show the applicable rewrite algebra for this computing
model. We show that this gives us a native graphical language for the design
and analysis of topological quantum algorithms, and finish by discussing the
possibilities for automating this process on a large scale.Comment: 18 pages, 21 figures. Published in New J. Phys. special issue on
topological quantum computin
Generation of three-dimensional cluster entangled state
Measurement-based quantum computing is a promising paradigm of quantum
computation, where universal computing is achieved through a sequence of local
measurements. The backbone of this approach is the preparation of multipartite
entanglement, known as cluster states. While a cluster state with
two-dimensional (2D) connectivity is required for universality, a
three-dimensional (3D) cluster state is necessary for additionally achieving
fault tolerance. However, the challenge of making 3D connectivity has limited
cluster state generation up to 2D. Here we experimentally generate a 3D cluster
state in the continuous-variable optical platform. To realize 3D connectivity,
we harness a crucial advantage of time-frequency modes of ultrafast quantum
light: an arbitrary complex mode basis can be accessed directly, enabling
connectivity as desired. We demonstrate the versatility of our method by
generating cluster states with 1D, 2D, and 3D connectivities. For their
complete characterization, we develop a quantum state tomography method for
multimode Gaussian states. Moreover, we verify the cluster state generation by
nullifier measurements, as well as full inseparability and steering tests.
Finally, we highlight the usefulness of 3D cluster state by demonstrating
quantum error detection in topological quantum computation. Our work paves the
way toward fault-tolerant and universal measurement-based quantum computing
Redundant String Symmetry-Based Error Correction: Experiments on Quantum Devices
Computational power in measurement-based quantum computing (MBQC) stems from
symmetry protected topological (SPT) order of the entangled resource state. But
resource states are prone to preparation errors. We introduce a quantum error
correction (QEC) approach using redundant non-local symmetry of the resource
state. We demonstrate it within a teleportation protocol based on extending the
symmetry of one-dimensional cluster states
to other graph states. Qubit ZZ-crosstalk errors, which are prominent in
quantum devices, degrade the teleportation fidelity of the usual cluster state.
However, as we demonstrate experimentally, once we grow graph states with
redundant symmetry, perfect teleportation fidelity is restored. We identify the
underlying redundant-SPT order as error-protected degeneracies in the
entanglement spectrum
Architectural design for a topological cluster state quantum computer
The development of a large scale quantum computer is a highly sought after
goal of fundamental research and consequently a highly non-trivial problem.
Scalability in quantum information processing is not just a problem of qubit
manufacturing and control but it crucially depends on the ability to adapt
advanced techniques in quantum information theory, such as error correction, to
the experimental restrictions of assembling qubit arrays into the millions. In
this paper we introduce a feasible architectural design for large scale quantum
computation in optical systems. We combine the recent developments in
topological cluster state computation with the photonic module, a simple chip
based device which can be used as a fundamental building block for a large
scale computer. The integration of the topological cluster model with this
comparatively simple operational element addresses many significant issues in
scalable computing and leads to a promising modular architecture with complete
integration of active error correction exhibiting high fault-tolerant
thresholds.Comment: 14 Pages, 8 Figures, changes to the main text, new appendix adde
Cross-level Validation of Topological Quantum Circuits
Quantum computing promises a new approach to solving difficult computational
problems, and the quest of building a quantum computer has started. While the
first attempts on construction were succesful, scalability has never been
achieved, due to the inherent fragile nature of the quantum bits (qubits). From
the multitude of approaches to achieve scalability topological quantum
computing (TQC) is the most promising one, by being based on an flexible
approach to error-correction and making use of the straightforward
measurement-based computing technique. TQC circuits are defined within a large,
uniform, 3-dimensional lattice of physical qubits produced by the hardware and
the physical volume of this lattice directly relates to the resources required
for computation. Circuit optimization may result in non-intuitive mismatches
between circuit specification and implementation. In this paper we introduce
the first method for cross-level validation of TQC circuits. The specification
of the circuit is expressed based on the stabilizer formalism, and the
stabilizer table is checked by mapping the topology on the physical qubit
level, followed by quantum circuit simulation. Simulation results show that
cross-level validation of error-corrected circuits is feasible.Comment: 12 Pages, 5 Figures. Comments Welcome. RC2014, Springer Lecture Notes
on Computer Science (LNCS) 8507, pp. 189-200. Springer International
Publishing, Switzerland (2014), Y. Shigeru and M.Shin-ichi (Eds.
Synthesis of Topological Quantum Circuits
Topological quantum computing has recently proven itself to be a very
powerful model when considering large- scale, fully error corrected quantum
architectures. In addition to its robust nature under hardware errors, it is a
software driven method of error corrected computation, with the hardware
responsible for only creating a generic quantum resource (the topological
lattice). Computation in this scheme is achieved by the geometric manipulation
of holes (defects) within the lattice. Interactions between logical qubits
(quantum gate operations) are implemented by using particular arrangements of
the defects, such as braids and junctions. We demonstrate that junction-based
topological quantum gates allow highly regular and structured implementation of
large CNOT (controlled-not) gate networks, which ultimately form the basis of
the error corrected primitives that must be used for an error corrected
algorithm. We present a number of heuristics to optimise the area of the
resulting structures and therefore the number of the required hardware
resources.Comment: 7 Pages, 10 Figures, 1 Tabl
Topological code Autotune
Many quantum systems are being investigated in the hope of building a
large-scale quantum computer. All of these systems suffer from decoherence,
resulting in errors during the execution of quantum gates. Quantum error
correction enables reliable quantum computation given unreliable hardware.
Unoptimized topological quantum error correction (TQEC), while still effective,
performs very suboptimally, especially at low error rates. Hand optimizing the
classical processing associated with a TQEC scheme for a specific system to
achieve better error tolerance can be extremely laborious. We describe a tool
Autotune capable of performing this optimization automatically, and give two
highly distinct examples of its use and extreme outperformance of unoptimized
TQEC. Autotune is designed to facilitate the precise study of real hardware
running TQEC with every quantum gate having a realistic, physics-based error
model.Comment: 13 pages, 17 figures, version accepted for publicatio
- …