To control and measure the state of a quantum system it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect,photon-induced dephasing from measurement back-action, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multi-mode element — an artificial molecule — with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential non-linear modes, one of which is flux-insensitive and used as the protected qubit mode. The second mode is flux-tunable and serves via a cross-Kerr type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed.
For the efficient implementation of quantum algorithms, practical ways to generate many-body entanglement are a basic requirement. Specifically, coupling multiple qubit pairs at oncecan be advantageous and can lead to multi-qubit operations useful in the construction of hardware-tailored algorithms. Here we harness the simultaneous coupling of qubits on a chain and engineer a set of non-local parity-dependent quantum operations suitable for a wide range of applications. The resulting effective long-range couplings directly implement a parametrizable Trotter-step for Jordan-Wigner fermions and can be used for simulations of quantum dynamics, efficient state generation in variational quantum eigensolvers, parity measurements for error-correction schemes, and the generation of efficient multi-qubit gates. Moreover, we present numerical simulations of the gate operation in a superconducting quantum circuit architecture, which show a high gate fidelity of >99.9% for realistic experimental parameters.
Kitaev’s toric code is an exactly solvable model with Z2-topological order, which has potential applications in quantum computation and error correction. However, a direct experimentalrealization remains an open challenge. Here, we propose a building block for Z2 lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a π-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.