Quantum states are usually fragile which makes quantum computation being not as stable as classical computation. Quantum correction codes can protect quantum states but need a largenumber of physical qubits to code a single logic qubit. Alternatively, the protection at the hardware level has been recently developed to maintain the coherence of the quantum information by using symmetries. However, it generally has to pay the expense of increasing the complexity of the quantum devices. In this work, we show that the protection at the hardware level can be approached without increasing the complexity of the devices. The interplay between the spin-orbit coupling and the Zeeman splitting in the semiconductor allows us to tune the Josephson coupling in terms of the spin degree of freedom of Cooper pairs, the hallmark of the superconducting spintronics. This leads to the implementation of the parity-protected 0-π superconducting qubit with only one highly transparent superconductor-semiconductor Josephson junction, which makes our proposal immune from the various fabrication imperfections.
High-order topological insulator (HOTI) occupies an important position in topological band theory due to its exotic bulk-edge correspondence. Recently, it has been predicted that externalmagnetic field can introduce rich physics into two-dimensional (2D) HOTIs. However, up to now the theoretical description is still incomplete and the experimental realization is still lacking. Here we investigate the influence of continuously varying magnetic field on 2D Su-Schriffer-Heeger lattice, which is one of the most celebrated HOTI models, and proposed a corresponding circuit quantum electrodynamics (cQED) simulator. Our numerical calculation shows that the zero energy corner modes (ZECMs), which can serve as evidence of the high order topology of the lattice, exhibit exotic and rich dependence on the imposed magnetic field and the inhomogeneous hopping strength. Moreover, by exploiting the parametric conversion method, we can establish time- and site-resolved tunable hopping constants in the proposed cQED simulator, thus providing an ideal platform for simulating the magnetic field induced topological phase transitions in 2D HOTIs. Since the high-order topological phases of the proposed model can be characterized by the existence of the ZECMs on the lattice, we further investigate the corner site excitation of the lattice in the steady state limit. Our numerical results imply that the predicted topological phase transitions can be unambiguously identified by the steady-state photon number measurement of the corner sites and their few neighbors. Requiring only current level of technology, our scheme can be readily tested in experiment and may pave an alternative way towards the future investigation of HOTIs in the presence of magnetic field, disorder, and strong correlation.
Geometric phases are well known to be noise-resilient in quantum evolutions/operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, asthese quantum gates are actually induced by nonabelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario, by varying the amplitudes and phase difference of two microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.
Implementing holonomic quantum computation is a challenging task as it requires complicated interaction among multilevel systems. Here, we propose to implement nonadiabatic holonomicquantum computation based on dressed-state qubits in circuit QED. An arbitrary holonomic single-qubit gate can be conveniently achieved using external microwave fields and tuning their amplitudes and phases. Meanwhile, nontrivial two-qubit gates can be implemented in a coupled cavities scenario assisted by a grounding SQUID with tunable interaction, where the tuning is achieved by modulating the ac flux threaded through the SQUID. In addition, our proposal is directly scalable, up to a two-dimensional lattice configuration. In our scheme, the dressed states only involve the lowest two levels of each transmon qubits and the effective interactions exploited are all of resonant nature. Therefore, we release the main difficulties for physical implementation of holonomic quantum computation on superconducting circuits.
The concept of flat band plays an important role in strongly-correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsiclimitations in conventional condensed matter materials. Here we propose a circuit quantum electrodynamics simulator of the 2D Lieb lattice exhibiting a flat middle band. By exploiting the simple parametric conversion method, we design a photonic Lieb lattice with \textit{in situ} tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the immediate incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiments and may pave a new way towards the future realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall states without magnetic fields.
The implementation of holonomic quantum computation generally requires controllable and complicated interaction among addressable multi-level systems, which is challenging on superconductingcircuit. Here, we propose a scalable architecture for non-adiabatic holonomic quantum computation on a circuit QED lattice with hybrid transmon and photon encoding of the logical qubits in a decoherence-free subspace. With proper driven on the transmon, we can obtain tunable resonate interaction between the transmon and each of the resonators, which leads to arbitrary single-qubit operation on the encoded logical qubit. Meanwhile, for a nontrivial two-qubit gate, we only need resonate interactions among the three resonators from the two logical qubits, which can be induced by commonly coupled to a grounding SQUID with ac magnetic driven. More importantly, our scheme is achieved with all resonate interactions among the involved elements, and thus leads to quantum gates with very high fidelity. Therefore, our scheme opens up the possibility of realizing high fidelity universal holonomic quantum computation in solid-state system.
We propose a scheme of investigating topological photonics in superconducting quantum circuits. There are two major ingredients. The first is the synthesization of an artificial gaugefield on a circuit quantum electrodynamics lattice through the developed dynamic modulation approach. The flexibility of such parametric method leads to the effective \textit{in situ} tunable magnetic field for photons on a square lattice. The second, which is the main new ingredient of this paper, considers the detection of the topological phases of the photons. Our idea employs the exotic properties of the edge state modes which result in novel steady states of the lattice under the driving-dissipation competition. Through the pumping and the photon-number measurements of merely few sites, not only the spatial and the spectral characters, but also the momentums and even the integer topological quantum numbers of the edge states can be directly probed, which reveal unambiguously the topological nature of the photons on the proposed lattice. The physical implementation of our scheme is discussed in detail, where our results pinpoint the feasibility based on current level of experimental technology.
An exotic DIII model of one-dimensional p-wave spin-triplet superconductors with the ℤ2 topological phase protected by the time-reversal symmetry is simulated by an array of inductivelycoupled transmon qubits with tunable nearest-neighbor couplings and scalability. The anti-commutation relation between opposite spin components in the DIII model is realized by a novel dispersive dynamic modulation approach, while previous schemes consider only spinless fermions. Our detailed analysis reveals that distinctive topological phenomena can be visualized with the state-of-the-art technology in this superconducting-circuit array.
We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits,which can realize arbitrary single-qubit gate on the topological qubit. When two qubits are involved, the interface between the topological qubits and a microwave cavity can induce a nontrivial two-qubit gate, which can not be constructed based on braiding operations. The two interfaces, being tunable via an external magnetic flux, may serve as the building blocks towards universal quantum computation with topological qubits.