We show that topological edge states can be realized in a simple superconducting circuit composed of an inductively shunted flux qubit. The Josephson potential of that qubit forms ahoneycomb lattice similar to the case of graphene. The additional shunting element produces a quartic potential along one flux direction, which effectively creates a boundary in flux space. We map analytically the low-energy dynamics of the circuit to an extended Su–Schrieffer–Heeger (SSH) chain, in which a quartic potential is added to the usual SSH Hamiltonian. This mapping is confirmed by numerical simulations of the full superconducting circuit. We argue that chiral symmetry still holds for the edge states of the extended model around a chiral point in parameter space. Close to this point, we numerically find that edge states in our superconducting circuit are topologically protected against perturbations that obey chiral symmetry, as is the case for charge noise. Our results show that topological effects previously thought to occur in multi-qubit systems, such as protection against decoherence, can also be found in much simpler single superconducting qubits.
We present a flip-chip architecture for an array of coupled superconducting qubits, in which circuit components reside inside individual microwave enclosures. In contrast to other flip-chipapproaches, the qubit chips in our architecture are electrically floating, which guarantees a simple, fully modular assembly of capacitively coupled circuit components such as qubit, control, and coupling structures, as well as reduced crosstalk between the components. We validate the concept with a chain of three nearest neighbor coupled generalized flux qubits in which the center qubit acts as a frequency-tunable coupler. Using this coupler, we demonstrate a transverse coupling on/off ratio ≈ 50, zz-crosstalk ≈ 0.7 kHz between resonant qubits and isolation between the qubit enclosures > 60 dB.
The heavy fluxonium at zero external flux has a long-lived state when coupled capacitively to any other system. We analyze it by projecting all the fluxonium relevant operators intothe qutrit subspace, as this long-lived configuration corresponds to the second excited fluxonium level. This state becomes a bound-state in the continuum (BIC) when the coupling occurs to an extended state supporting a continuum of modes. In the case without noise, we find BIC decay times that can be much larger than seconds T1≫s when the fluxonium is coupled to superconducting waveguide, while typical device frequencies are in the order of GHz. We have also analyzed the noise in a realistic situation, arguing that the most dangerous noise source is the well-known 1/f flux noise. Even in its presence, we show that decay times could reach the range of T1∼10ms.
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamicsof two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with XX, YY and ZZ interactions, including ultra-strongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.
A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and onein which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form σy(a+a†), which complement the inductive σxi(a†−a) coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the σyσy, σzσz and σxσx type. Our theory explains all these interactions, describing them in terms of general circuit properties—coupling capacitances, qubit gaps, inductive, Josephson and capactive energies—, that apply to a wide variety of circuits and flux qubit designs.