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Bulletin of the American Physical Society

Engineering high-order nonlinear dissipation for quantum superconducting circuits

Shantanu Mundhada, Alexander Grimm, Steven Touzard, Shyam Shankar, Zlatko Minev, Uri Vool, Mazyar Mirrahimi, Michel Devoret

Published Mar 14, 2017• 0 citations
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Generating non-Gaussian states and converting them into traveling wave packets is crucial yet challenging for scalable, fault-tolerant quantum computing. We present a hardware-efficient approach that simultaneously achieves both tasks by combining an engineered nonlinear dissipation with a linear transmission loss from a superconducting circuit to a waveguide. This combination of dissipative channels leverages low-order interactions to induce a high-order nonlinearity, enabling deterministic emission of a wide range of non-Gaussian, error-correctable states, such as Schrödinger cat states, Gottesman-Kitaev-Preskill states, and pair-cat states. We identify experimental superconducting-circuit platforms and realistic parameter regimes for our proposal.
Out-of-equilibrium driven nonlinear oscillators have attracted interest as a platform for tailoring Floquet Hamiltonian spectra and stabilizing quantum states for quantum information. However, it is usually ignored that the necessary parametric drive can amplify environmental fluctuations limiting applications. In this work, we capture this effect by computing the effective Lindbladian of a Kerr parametric oscillator beyond the rotating wave approximation. We find that the relevant dissipators depend strongly on the nonlinearity and the mean-photon number in the oscillator. In particular, we address recent measurements of the logical lifetime on a Schr\"odinger's-cat qubit stabilized by a parametric drive, thereby providing an explanation for the observed three-order-of-magnitude discrepancy between experimental data and an ordinary Lindblad treatment. Our systematic approach paves the path to treat dissipative effects in Floquet-engineered nonlinear quantum systems.
Engineering nonlinear dissipation through parametric interactions is a key ingredient in autonomous quantum error correction. In ``cat'' qubits bit-flip errors may be exponentially suppressed using two-photon driven dissipation, but spurious dissipative channels appear, in a process that is poorly understood. The authors turn to high-order perturbation theory and exact numerical diagonalization to classify the possible decay mechanisms that reduce the coherence of such a qubit, bridging the gap between the microscopic parameters of the circuit and the lifetimes of the modes. Furthermore, engineering constraints on the surrounding apparatus are identified, to reduce decoherence.