In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states has attracted much attention recently. However,due to the operational difficulties in solid state materials, non-Abelian statistics has not been experimentally realized yet. The superconducting quantum circuits system is scalable and controllable, thus is a promising platform for quantum simulation. Here, we propose a scheme to demonstrate non-Abelian statistics of topologically protected zero energy edge modes on a chain of the superconducting circuits. Specifically, we can realize topological phase transition by varying the hopping strength and magnetic filed in the chain, and the realized non-Abelian operation can be used in topological quantum computation. Considering the advantages of the superconducting quantum circuits, our protocol may shed light on quantum computation via topologically-protected states.
Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulationand the intrinsic leakage of the encoded quantum information to non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here, we propose to implement scalable nonadiabatic holonomic quantum computation with decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighbouring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighbouring transmon qubits, and thus avoiding the leakage problem. In addition, our presented numerical simulation shows that high-fidelity quantum gates can be obtained, verifying the advantages of the robustness and scalability of our scheme. Therefore, our scheme provides a promising way towards the physical implementation of robust and scalable quantum computation.
Topological states of quantum matter %, originally discovered and investigated in condensed matter physics, have inspired both fascinating physics findings and exciting opportunitiesfor applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum simulation of topological matter is very important in deepening our understanding of these states. This requirement puts the quantum superconducting circuits system as a good option for mimicking topological materials, owing to their flexible tunability and fine controllability. As a typical example herein, we realize a Z2-type topological insulator featuring the quantum spin Hall effect state, using a coupled system of transmission-line resonators and transmons. The single-excitation eigenstates of each unit cell are used as a pseudo-spin 1/2 system. Time reversal symmetry of the system is proved, and the boundary of the topological phase transition is fixed in the phase diagram. Topological edge states are shown, which can be experimentally verified by detecting the population at the boundary of the plane. Compared to the previous simulations, this compositional system is fairly controllable, stable and less limited. Therefore, our scheme provides a reliable platform for faithful quantum simulations of topological matter.
The phase factor plays a vital role in modern quantum physics. Especially, geometric phases induced in quantum evolutions have the built-in noise-resilient character, and thus foundcomprehensive applications in many robust quantum manipulation tasks. Here, we propose a fast scheme to construct universal quantum gates on superconducting circuits with non-Abelian geometric phases using resonant interaction of three-level quantum systems. As the evolution state always fulfill the Schrödinger equation of the govern Hamiltonian, during the cyclic quantum evolution, there will be no nonadiabatic transitions from the evolution state to other states, i.e., the orthogonal states of the evolution state. Meanwhile, arbitrary single-qubit quantum gates can be implemented in a single-loop scenario by shaping both the amplitudes and phases of two microwave fields, resonantly coupled to a transmon qubit. Moreover, nontrivial two-qubit gates can also be realized with an auxiliary transmon simultaneously coupled to the two target transmons in an effective resonant way. In particular, our proposal can be compatible to various optimal control techniques, which further enhances the robustness of the quantum operations. Therefore, our proposal represents a promising way towards fault-tolerant quantum computation on solid-state quantum circuits.
Green-Horne-Zeilinger states are a typical type of multipartite entangled states, which plays a central role in quantum information processing. For the generation of multipartite entangledstates, the single-step method is more preferable as the needed time will not increase with the increasing of the qubit number. However, this scenario has a strict requirement that all the two-qubit interaction strengths should be the same, or the generated state will be of low quality. Here, we propose a scheme for generating multipartite entangled states of superconducting qubits, from a coupled circuit cavities scenario, where we rigorously achieve the requirement via adding an extra z-direction ac classical field for each qubit, leading the individual qubit-cavity coupling strength to be tunable in a wide range, and thus can be tuned to the same value. Meanwhile, in order to obtain our wanted multi-qubits interaction, x-direction ac classical field for each qubit is also introduced. By selecting the appropriate parameters, we numerically shown that high-fidelity multi-qubit GHZ states can be generated. In addition, we also show that the coupled cavities scenario is better than a single cavity case. Therefore, our proposal represents a promising alternative for multipartite entangled states generation.
Searching topological states of matter in tunable artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progresses on observingtopological phenomena have been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a spin version of the Su-Schrieffer-Heeger model and observe the topological magnon insulator states in a superconducting qubit chain, which manifest both topological invariants and topological edge states. Based on simply monitoring the time evolution of a singlequbit excitation in the chain, we demonstrate that the topological winding numbers and the topological magnon edge and soliton states can all be directly observed. Our work thus opens a new avenue to use controllable qubit chain system to explore novel topological states of matter and also offers exciting possibilities for topologically protected quantum information processing.
The implementation of nonadiabatic geometric quantum computation is promising since its robustness against certain types of noises. Meanwhile, it is also challenging due to the needof complex control on the quantum multiple and/or multi-level systems. Here, we propose to implement nonadiabatic geometric quantum computation on a two-dimensional square superconducting qubit lattice. In our construction of the geometric quantum gates, we merely adopt simple and experimentally accessible control over the quantum systems, which only involve their qubit states. Specifically, our scheme is achieved by parametrically tunable all-resonant interactions, which leads to high-fidelity quantum gates. Moreover, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspaces can also be implemented based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to construct the logical qubit. Therefore, our scheme possesses promising prospects for experimental implementation of geometric quantum computation.
The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions on multilevel quantum systems. Here we propose to implementthe nonadiabatic holonomic quantum computation with the conventional capacitive coupled superconducting transmon qubits, where a universal set of quantum gates is constructed with the help of the interaction to an auxiliary qubit rather than consulting to delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, which leads to high-fidelity gate operations. In this way, the distinct merit of our scheme is that we only use the two lowest levels of a transmon to form the qubit states. In addition, the auxiliary qubits are in their ground states before and after every gate operation. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.
Faithfully transferring quantum state is essential for quantum information processing. Here, we demonstrate a fast (in 84~ns) and high-fidelity (99.2%) quantum state transfer in achain of four superconducting qubits with nearest-neighbor coupling. This transfer relies on full control of the effective couplings between neighboring qubits, which is realized only by parametrically modulating the qubits without increasing circuit complexity. Once the couplings between qubits fulfill specific ratio, a perfect quantum state transfer can be achieved in a single step, therefore robust to noise and accumulation of experimental errors. This quantum state transfer can be extended to a larger qubit chain and thus adds a desirable tool for future quantum information processing. The demonstrated flexibility of the coupling tunability is suitable for quantum simulation of many-body physics which requires different configurations of qubit couplings.
Nodal-loop semimetal is one of the exotic gapless topological states of matter that are discovered recently. Here we propose an experimentally feasible scheme to simulate the three-dimensionaltopological nodal-loop semimetal bands in a one-dimensional circuit quantum electrodynamics lattice, by introducing two additional parameter dimensions. A unit-cell of the lattice consists of a transmissionline resonator coupled by a superconducting transmon qubit, and two of the dressed states in a unit-cell are used to simulate the spin-1/2 states of an electron. The neighboring transmission-line resonators are connected by a superconducting quantum interference device, and the effective hopping among them is induced by parametric coupling. Meanwhile, the two artificial dimensions are simulated by tunable Zeeman terms of the spins. The detection of the mimic nodal-loop bands is also discussed and is shown to be well within current technology. Therefore, our scheme provides a feasible way to explore nodal-loop semimetal bands and other topological bands of different spin-orbit coupling forms in this controllable artificial system.