174 research outputs found
Surface code quantum computing by lattice surgery
In recent years, surface codes have become a leading method for quantum error
correction in theoretical large scale computational and communications
architecture designs. Their comparatively high fault-tolerant thresholds and
their natural 2-dimensional nearest neighbour (2DNN) structure make them an
obvious choice for large scale designs in experimentally realistic systems.
While fundamentally based on the toric code of Kitaev, there are many variants,
two of which are the planar- and defect- based codes. Planar codes require
fewer qubits to implement (for the same strength of error correction), but are
restricted to encoding a single qubit of information. Interactions between
encoded qubits are achieved via transversal operations, thus destroying the
inherent 2DNN nature of the code. In this paper we introduce a new technique
enabling the coupling of two planar codes without transversal operations,
maintaining the 2DNN of the encoded computer. Our lattice surgery technique
comprises splitting and merging planar code surfaces, and enables us to perform
universal quantum computation (including magic state injection) while removing
the need for braided logic in a strictly 2DNN design, and hence reduces the
overall qubit resources for logic operations. Those resources are further
reduced by the use of a rotated lattice for the planar encoding. We show how
lattice surgery allows us to distribute encoded GHZ states in a more direct
(and overhead friendly) manner, and how a demonstration of an encoded CNOT
between two distance 3 logical states is possible with 53 physical qubits, half
of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure
A silicon-based surface code quantum computer
Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems
Fault-tolerance thresholds for the surface code with fabrication errors
The construction of topological error correction codes requires the ability
to fabricate a lattice of physical qubits embedded on a manifold with a
non-trivial topology such that the quantum information is encoded in the global
degrees of freedom (i.e. the topology) of the manifold. However, the
manufacturing of large-scale topological devices will undoubtedly suffer from
fabrication errors---permanent faulty components such as missing physical
qubits or failed entangling gates---introducing permanent defects into the
topology of the lattice and hence significantly reducing the distance of the
code and the quality of the encoded logical qubits. In this work we investigate
how fabrication errors affect the performance of topological codes, using the
surface code as the testbed. A known approach to mitigate defective lattices
involves the use of primitive SWAP gates in a long sequence of syndrome
extraction circuits. Instead, we show that in the presence of fabrication
errors the syndrome can be determined using the supercheck operator approach
and the outcome of the defective gauge stabilizer generators without any
additional computational overhead or the use of SWAP gates. We report numerical
fault-tolerance thresholds in the presence of both qubit fabrication and gate
fabrication errors using a circuit-based noise model and the minimum-weight
perfect matching decoder. Our numerical analysis is most applicable to 2D
chip-based technologies, but the techniques presented here can be readily
extended to other topological architectures. We find that in the presence of 8%
qubit fabrication errors, the surface code can still tolerate a computational
error rate of up to 0.1%.Comment: 10 pages, 15 figure
How to test the "quantumness" of a quantum computer?
We discuss whether, to what extent and how a quantum computing device can be
evaluated and simulated using classical tools.Comment: Submitted 12.10.201
A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales. They are strategies for space-time trade-offs, going from slow computations using few qubits to fast computations using many qubits. Our schemes are based on surface-code patches, which not only feature a low space cost compared to other surface-code schemes, but are also conceptually simple~--~simple enough that they can be described as a tile-based game with a small set of rules. Therefore, no knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements
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