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arXiv:1308.0225 · Physical Review B

Engineering three-body interaction and Pfaffian states in circuit QED systems

Mohammad Hafezi, Prabin Adhikari, Jacob M. Taylor

Published Aug 18, 2014• 53 citations
arXivHTMLPDF

Abstract

We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics in the form of a synthesized magnetic field for the photon-like excitations of the system allows the implementation of a parent Hamiltonian whose ground state is the Pfaffian wave function. Furthermore, we show that the addition of the next-nearest-neighbor tunneling stabilizes the ground state, recovering the expected topological degeneracy even for small lattices. Finally, we discuss the implementation of these ideas with the current technology.

DOI
10.1103/physrevb.90.060503

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We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics in the form of a synthesized magnetic field for the photon-like excitations of the system allows the implementation of a parent Hamiltonian whose ground state is the Pfaffian wave function. Furthermore, we show that the addition of the next-nearest-neighbor tunneling stabilizes the ground state, recovering the expected topological degeneracy even for small lattices. Finally, we discuss the implementation of these ideas with the current technology.
Superconducting qubits provide a competitive platform for quantum simulation of complex dynamics that lies at the heart of quantum many-body systems, because of the flexibility and scalability afforded by the nature of microfabrication. However, in a multiqubit device, the physical form of couplings between qubits is either an electric (capacitor) or magnetic field (inductor), and the associated quadratic field energy determines that only two-body interaction in the Hamiltonian can be directly realized. Here, we propose and experimentally synthesize a three-body spin-chirality interaction in a superconducting circuit based on Floquet engineering. By periodically modulating the resonant frequencies of the qubits connected with each other via capacitors, we can dynamically turn on and off qubit–qubit couplings and further create chiral flows of the excitations in the three-qubit circular loop. Our result is a step toward engineering dynamical and many-body interactions in multiqubit superconducting devices, which potentially expands the degree of freedom in quantum simulation tasks.
We describe a method for engineering local k+1k+1k+1-body interactions (k=1,2,3k=1,2,3k=1,2,3) from two-body couplings in spin-12\frac{1}{2}21​ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit Abelian and non-Abelian anyon excitations. The most complex of these, with k=3k=3k=3, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model up to small corrections, and further, we describe the process by which one might create and manipulate non-Abelian vortices in these circuits, allowing for direct control of the system's quantum information content.
Encoding quantum information in quantum states with disjoint wave-function support and noise-insensitive energies is the key behind the idea of qubit protection. While fully protected qubits are expected to offer exponential protection against both energy relaxation and pure dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave functions are engineered to minimize their overlap while benefiting from a first-order-insensitive flux sweet spot. Taking advantage of a large superinductance ( L ∼ 1 μ H ), our circuit incorporates a resonant tunneling mechanism at zero external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states | 0 ⟩ and | 1 ⟩ are encoded in wave functions with parities 0 and 1, respectively, ensuring a minimal form of protection against relaxation. Two-tone spectroscopy reveals the energy-level structure of the circuit and the presence of 4 π quantum-phase slips between different potential wells corresponding to m = ± 1 fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation ( T 1 = 177 ± 3 μ s ) and dephasing ( T 2 E = 75 ± 5 μ s ) times not only demonstrate the relevance of our approach but also open an alternative direction toward quantum computing using partially protected fluxonium qubits. Published by the American Physical Society 2024
Nonpairwise multibody interactions have recently attracted much attention due to their promising applications in the realm of quantum information science and technology. In this work, we propose a method to synthesize a nonpairwise three-body interaction of superconducting qubits using a coupler qubit dispersively coupled to two spatially separated qubits and a microwave pulse. This interaction describes physical processes of an excitation from the coupler qubit to two spatially separated qubits and the reverse process. We show that the interaction can be utilized to deterministically generate three-body Greenberger-Horne-Zeilinger (GHZ) entangled states, transfer the state of the coupler qubit into a two-qubit entangled state, and construct three-qubit controlled-controlled-phase and Toffoli gates. Our proposal only requires a coupler qubit and a single-step operation; thus, the system architecture and method are quite simple. As examples, we numerically simulate the dynamics of the system, and the numerical results demonstrate that high-fidelity preparation of the proposed three-body GHZ entangled state and quantum gates is feasible with current superconducting circuit technology. This approach is general and applicable to a wide range of quantum systems.
We demonstrate that a triangular optical lattice of two atomic species, bosonic or fermionic, can be employed to generate a variety of spin-1∕21∕21∕2 Hamiltonians. These include effective three-spin interactions resulting from the possibility of atoms tunneling along two different paths. Such interactions can be employed to simulate particular one- or two-dimensional physical systems with ground states that possess a rich structure and undergo a variety of quantum phase transitions. In addition, tunneling can be activated by employing Raman transitions, thus creating an effective Hamiltonian that does not preserve the number of atoms of each species. In the presence of external electromagnetic fields, resulting in complex tunneling couplings, we obtain effective Hamiltonians that break chiral symmetry. The ground states of these Hamiltonians can be used for the physical implementation of geometrical or topological objects.
In the last two decades, a spectacular development in the superconducting qubits has been accomplished experimentally as well as theoretically. The main reason for that is the realization that superconducting qubits can play a crucial role in the emergent field of quantum information processing and quantum computing. The interaction of superconducting qubits with the quantized electromagnetic field leads to make the circuit quantum electrodynamics, inspired by cavity quantum electrodynamics. The field of superconducting qubits and circuit QED is fast growing and branching to diverse applications in multidisciplinary fields. This makes it harder for first-time readers to follow-up. Therefore, this article is targeting to introduce in an intuitive way the topic of superconducting qubit and circuit QED by giving all the mathematical background, Lagrangian formalism for electric circuits, interaction Hamiltonian, and contextual physical interpretation essential to anew scientists and engineers planning to be specialized in this field as well as portraying a wide vantage for higher studies through the suggested recommendation resulted from the simulated examples and written code based on Python packages and Qiskit software. In this article, the superconducting qubits, transmon and fluxonium, are reviewed after introducing the abstract definition of a quantum bit. Moreover, light-matter interaction in fluxonium qubit and quantization of transmission line resonator are discussed briefly. Some of the simulated systems such as the energy levels of fluxonium as a function of offset flux are presented. Finally, applications of superconducting qubits in quantum computing and other fields such as quantum transistors, quantum machines and metamaterials are discussed. Index Terms Superconducting qubits, circuit QED, quantum logic gate, fluxonium, transmon.