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Journal of Physics Conference Series

Local ontology for a dual-rail qubit

Paweł Błasiak

Published Mar 1, 2016• 0 citations
Publisher

Abstract

We show that quantum predictions for the dual-rail realisation of a qubit can be faithfully simulated with classical stochastic gates and particles which interact entirely in a local manner. In the presented model 'non-locality' appears only on the epistemic level of description.
DOI
10.1088/1742-6596/701/1/012024

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It is said about quantum interference that "In reality, it contains the only mystery". Indeed, together with non-locality it is often considered as the characteristic feature of quantum theory which can not be explained in any classical way. In this work we are concerned with a restricted setting of a single particle propagating in multi-path interferometric circuits, that is physical realisation of a qudit. It is shown that this framework, including collapse of the wave function, can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. 'Non-locality' in the model appears merely as an epistemic effect arising on the level of description by agents whose knowledge is incomplete. This result suggests that the real quantum mystery should be sought in the multi-particle behaviour, since single-particle interferometric phenomena are explicable in a classical manner.
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We show that encoding superconducting qubits as dual-rail or spin-locked transmons lets a metamaterial waveguide couple them all-to-all while suppressing the spurious entanglement that burdens shared-mode architectures, a step toward the non-local connectivity that quantum low-density parity-check codes require. In a bare-transmon architecture, the dispersive coupling between each populated mode and every idle qubit attached to it entangles spectators with the gate, and cancelling it by dynamical decoupling lengthens every gate. The encoding suppresses this coupling at the hardware level, from second to fourth order in the inverse qubit--mode detuning. A two-tone cross-resonance drive then generates a Mølmer-Sørensen interaction between encoded qubits, which we use for an entangling gate and a joint parity measurement, both selective and parallelizable through different modes. Simulating two dual-rail transmons sharing three resonators with a mode lifetime of 30 μ30\,μ30μs, we find that heralding transmon relaxation as erasure leaves a gate infidelity of 1.4×10−31.4\times10^{-3}1.4×10−3 at 152152152~ns, dominated by photon loss. Photon loss and mode crowding together bound the array size. The gate duration must exceed the inverse mode spacing, which shrinks as the array lengthens, while photon loss grows with gate duration. This bound grows linearly with the mode lifetime and with the inter-resonator coupling; at a lifetime of 150 μ150\,μ150μs, five times the simulated value, and a coupling of 808080~MHz, a 10−310^{-3}10−3 error budget admits 131313 qubits on 252525 resonators.