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Register a new userRobust fault tolerance for continuous-variable cluster states with excess anti-squeezing
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The immense scalability of continuous-variable cluster states motivates their study as a platform for quantum computing, with fault tolerance possible given sufficient squeezing and appropriately encoded qubits [Menicucci, PRL 112, 120504 (2014)]. Here, we expand the scope of that result by showing that additional anti-squeezing has no effect on the fault-tolerance threshold, removing the purity requirement for experimental continuous-variable cluster-state quantum computing. We emphasize that the appropriate experimental target for fault-tolerant applications is to directly measure 15-17 dB of squeezing in the cluster state rather than the more conservative upper bound of 20.5 dB.
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A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.
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 universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely known for the simplicity on implementation, the efficiency in error correction and the compatibility with modern optical communication devices. However, recent work indicates that using homodyne detection will lead to poor tolerance of excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks. Here, we propose a homodyne detection protocol using the technique of quadrature phase shift keying. By limiting information leakage, our protocol enhances excess noise tolerance to a high level. Furthermore, we demonstrate that using homodyne detection performs better than heterodyne detection in quaternary-modulated continuous-variable quantum key distribution under the untrusted detector noise scenario. The security is analyzed by tight numerical method against collective attacks in the asymptotic regime. Results imply that our protocol possesses the ability to distribute keys in nearly intercity area. This progress will make our protocol the main force in constructing low-cost quantum secure communication networks.
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.
We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.
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