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Nature Communications

Hidden two-qubit dynamics of a four-level Josephson circuit

Elisha Svetitsky, Haim Suchowski, Roy Resh, Yoni Shalibo, John M. Martinis, Nadav Y. Katz

Published Nov 25, 2014• 36 citations
Publisher
DOI
10.1038/ncomms6617

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We propose a scheme for simulating 3+1, 2+1, 1+1 Dirac equation for a free spin-1/2 particle with superconducting josephson circuits consisting of five qubits, four qubits, two qubits respectively. In 3+1D and 2+1D, the flux qubit1 driven by a resonant pulse is in the superposition state of its own two eigenstatesis, and it is used as a bus to induce the (blue)red-sideband excitation consisting of a magnetic pulse acting resonantly on two levels of the flux qubit2 and the energy levels of one phase qubit, which yields two (Anti)Jaynes-Cummings interactions with one driving pulse and reduces the damage of the driving pulses to the system consequently. Numerical results show that decoherence time is several times longer than transition time supposing set appropriate experimental parameters. Therefore experiments verifying the dynamics of electron and neutrino, such as Zitterberwung effect in 3+1, 2+1 and 1+1 dimensions, can be implemented by microelectronic chips composed of the qubits as artificial atoms.
We propose an experimental approach to {\it macro}scopically test the Kochen-Specker theorem (KST) with superconducting qubits. This theorem, which has been experimentally tested with single photons or neutrons, concerns the conflict between the contextuality of quantum mechnaics (QM) and the noncontextuality of hidden-variable theories (HVTs). We first show that two Josephson charge qubits can be controllably coupled by using a two-level data bus produced by a Josephson phase qubit. Next, by introducing an approach to perform the expected joint quantum measurements of two separated Josephson qubits, we show that the proposed quantum circuits could demonstrate quantum contextuality by testing the KST at a macroscopic level.
For a flux qubit considered as a two-level system, for which a hidden polynomial pseudo-supersymmetry was previously discovered, we propose a special time-dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close enough to its critical value, the external field frequency may be tuned in a way to keep the probability to detect a definite direction of the current circulating in a Josephson-junction circuit above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.