Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have confined the state of a superconducting resonator to the quantum manifold spanned by two coherent states of opposite phases and have observed a Schrödinger cat state spontaneously squeeze out of vacuum before decaying into a classical mixture. This experiment points toward robustly encoding quantum information in multidimensional steady-state manifolds.

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3 with hints of additional states appearing at ν = 2p + 3/5, where p = −2, −1, 0, and 1. This sequence of states breaks particle-hole symmetry and instead obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.One Sentence Summary: Bilayer graphene exhibits a unique sequence of electron-hole asymmetric fractional quantum Hall states because of its twofold orbital degeneracy. The charge carriers in bilayer graphene obey an electron-hole symmetric dispersion at zero magnetic field. Application of a perpendicular magnetic field B breaks this dispersion into energy bands known as Landau levels (LLs). In addition to the standard spin and valley degeneracy found in monolayer graphene, the N = 0 and N = 1 orbital states in bilayer graphene are also degenerate and occur at zero energy (1). This results in a sequence of single-particle quantum Hall states at ν = 4M e 2 /h, where M is a nonzero integer (2).When the disorder is sufficiently low, the eightfold degeneracy of the lowest LL is lifted by electron-electron interactions, which results in quantum Hall states at all integer filling factors (3,4). The nature of these broken-symmetry states has been studied extensively both experimentally and theoretically, with particular attention given to the insulating ν = 0 state. Multiple groups have been able to induce transitions between different spin and valley orders of the ground states using external electric and magnetic fields, which indicates the extensive tunability of many-body states in bilayer graphene (6-9). The interplay between externally applied fields and intrinsic electron-electron interactions, both of which break the degeneracies of bilayer graphene, produces a rich phase diagram not found in any other system.Knowledge of the ground state at integer filling factors is especially important for investigating the physics of partially filled LLs, where in exceptionally clean samples, the charge carriers condense into fractional quantum Hall (FQH) states. The above-mentioned degrees of freedom as well as the strong screening of the Coulomb interaction in bilayer graphene are expected to result in an interesting sequence of FQH states in the lowest LL (10-15).Indeed, partial breaking of the SU(4) symmetry in monolayer graphene has already resulted in sequences of FQH states with multiple missing fractions (17-22).Experimental observation of FQH states, however, has proven to be difficult in bilayer 2 graphene. Hints of a ν = 1/3 state were first report...

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We have realized a new interaction between superconducting qubits and a readout cavity that results in the displacement of a coherent state in the cavity, conditioned on the state of the qubit. This conditional state, when it reaches the cavity-following, phase-sensitive amplifier, matches its measured observable, namely the in-phase quadrature. In a setup where several qubits are coupled to the same readout resonator, we show it is possible to measure the state of a target qubit with minimal dephasing of the other qubits. Our results suggest novel directions for faster readout of superconducting qubits and implementations of bosonic quantum error-correcting codes.

We present a protected superconducting qubit based on an effective circuit element that only allows pairs of Cooper pairs to tunnel. These dynamics give rise to a nearly degenerate ground state manifold indexed by the parity of tunneled Cooper pairs. We show that, when the circuit element is shunted by a large capacitance, this manifold can be used as a logical qubit that we expect to be insensitive to multiple relaxation and dephasing mechanisms.

Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO R -like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for protected qubits and quantum simulation.

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