Spin-Boson Quantum Phase Transition in Multilevel Superconducting Qubits.

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.

Universal control of a bosonic mode via drive-activated native cubic interactions.

Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.