We propose an implementation of a twin paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.Comment: 6 pages, 3 figures. I. F. previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Present-day, noisy, small or intermediate-scale quantum processors-although far from fault tolerant-support the execution of heuristic quantum algorithms, which might enable a quantum advantage, for example, when applied to combinatorial optimization problems. On small-scale quantum processors, validations of such algorithms serve as important technology demonstrators. We implement the quantum approximate optimization algorithm on our hardware platform, consisting of two superconducting transmon qubits and one parametrically modulated coupler. We solve small instances of the NP (nondeterministic polynomial time)-complete exact-cover problem, with 96.6% success probability, by iterating the algorithm up to level two.

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We have observed period-tripling subharmonic oscillations in a driven superconducting coplanar waveguide resonator operated in the quantum regime, kBT hω. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, ω/2π ∼ 5 GHz, when driving the resonator with a current at 3ω, with amplitude exceeding an instability threshold. We observed three stable radiative states with equal amplitudes, phase-shifted by 2π/3 radians, red-detuned from the fundamental mode. The downconversion from 3ω to ω is strongly enhanced by near-resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.