Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED

Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.Comment: 12 pages, 6 figures, 2 table

Quantum state transfer and controlled-phase gate on one-dimensional superconducting resonators assisted by a quantum bus

We propose a quantum processor for the scalable quantum computation on microwave photons in distant one-dimensional superconducting resonators. It is composed of a common resonator R acting as a quantum bus and some distant resonators $r_j$ coupled to the bus in different positions assisted by superconducting quantum interferometer devices (SQUID), different from previous processors. R is coupled to one transmon qutrit, and the coupling strengths between $r_j$ and R can be fully tuned by the external flux through the SQUID. To show the processor can be used to achieve universal quantum computation effectively, we present a scheme to complete the high-fidelity quantum state transfer between two distant microwave-photon resonators and another one for the high-fidelity controlled-phase gate on them. By using the technique for catching and releasing the microwave photons from resonators, our processor may play an important role in quantum communication as well.Comment: 11 pages, 4 figures, one colum

Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics

Based on a microwave-photon quantum processor with two superconducting resonators coupled to one transmon qutrit, we construct the controlled-phase (c-phase) gate on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect on the transmon qutrit by the first resonator and the resonant operation between the qutrit and the second resonator. This distinct feature provides us a useful way to achieve the c-phase gate on the two resonator qudits with a higher fidelity and a shorter operation time, compared with the previous proposals. The fidelity of our c-phase gate can reach 99.51% within 93 ns. Moreover, our device can be extended easily to construct the three-qudit gates on three resonator qudits, far different from the existing proposals. Our controlled-controlled-phase gate on three resonator qudits is accomplished with the assistance of a transmon qutrit and its fidelity can reach 92.92% within 124.64 ns.Comment: 9 pages, 5 figure

One-step implementation of entanglement generation on microwave photons in distant 1D superconducting resonators

We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs $r_j$ which are coupled to the quantum bus (another common resonator $R$) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quantum communication. To demonstrate the performance of this device, we propose a one-step scheme to generate high-fidelity Bell states on MPs in two distant SRs. It works in the dispersive regime of $r_j$ and $R$, which enables us to extend it to generate high-fidelity multi-Bell states on different resonator pairs simultaneously.Comment: 5 pages, 3 figure

From atomistic model to the Peierls-Nabarro model with γ\gamma-surface for dislocations

The Peierls-Nabarro (PN) model for dislocations is a hybrid model that incorporates the atomistic information of the dislocation core structure into the continuum theory. In this paper, we study the convergence from a full atomistic model to the PN model with $\gamma$-surface for the dislocation in a bilayer system (e.g. bilayer graphene). We prove that the displacement field of and the total energy of the dislocation solution of the PN model are asymptotically close to those of the full atomistic model. Our work can be considered as a generalization of the analysis of the convergence from atomistic model to Cauchy-Born rule for crystals without defects in the literature.Comment: 45 pages, 2 figure

Self-Erasing Network for Integral Object Attention

Recently, adversarial erasing for weakly-supervised object attention has been deeply studied due to its capability in localizing integral object regions. However, such a strategy raises one key problem that attention regions will gradually expand to non-object regions as training iterations continue, which significantly decreases the quality of the produced attention maps. To tackle such an issue as well as promote the quality of object attention, we introduce a simple yet effective Self-Erasing Network (SeeNet) to prohibit attentions from spreading to unexpected background regions. In particular, SeeNet leverages two self-erasing strategies to encourage networks to use reliable object and background cues for learning to attention. In this way, integral object regions can be effectively highlighted without including much more background regions. To test the quality of the generated attention maps, we employ the mined object regions as heuristic cues for learning semantic segmentation models. Experiments on Pascal VOC well demonstrate the superiority of our SeeNet over other state-of-the-art methods.Comment: Accepted by NIPS201

Quantum information processing on nitrogen-vacancy ensembles with the local resonance assisted by circuit QED

With the local resonant interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting coplanar resonator, and the single-qubit operation, we propose two protocols for the state transfer between two remote NVEs and for fast controlled-phase (c-phase) on these NVEs, respectively. This hybrid quantum system is composed of two distant NVEs coupled to separated high-Q transmission line resonators (TLRs), which are interconnected by a current-biased Josephsonjunction superconducting phase qubit. The fidelity of our state-transfer protocol is about 99.65% within the operation time of 70.60 ns. The fidelity of our c-phase gate is about 98.23% within the operation time of 93.87 ns. Furthermore, using the c-phase gate, we construct a two-dimensional cluster state on NVEs in n*n square grid based on the hybrid quantum system for the one-way quantum computation. Our protocol may be more robust, compared with the one based on the superconducting resonators, due to the long coherence time of NVEs at room temperature.Comment: 10 pages, 4 figure

Certification of Boson Sampling Devices with Coarse-Grained Measurements

A boson sampling device could efficiently sample from the output probability distribution of noninteracting bosons undergoing many-body interference. This problem is not only classically intractable, but its solution is also believed to be classically unverifiable. Hence, a major difficulty in experiment is to ensure a boson sampling device performs correctly. We present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. The procedure can be applied to certify the equivalence of boson sampling devices while ruling out alternative fraudulent devices. We perform numerical simulations to demonstrate the feasibility of the method and consider the effects of realistic noise. Our approach is expected to be generally applicable to other many-body certification tasks beyond the boson sampling problem.Comment: 8 pages including Supplemental Materials, 7 figures, 3 table

Classifying parafermionic gapped phases using matrix product states

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for $\mathbb{Z}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of $\mathbb{Z}_{p}$ parafermions without extra symmetry other than $\mathbb{Z}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the non-trivial simple $\mathbb{Z}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. But the spontaneous symmetry breaking phases correspond to the trivial semisimple $\mathbb{Z}_{p/n}$ graded algebras, which can be further reduced to the trivial simple $\mathbb{Z}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results deepen our understanding of topological phases in one dimension from the viewpoints of MPS.Comment: 12 pages, 1 figure, 2 tables, published versio

Matrix product states for topological phases with parafermions

In the Fock representation, we propose a framework to construct the generalized matrix product states (MPS) for topological phases with $\mathbb{ Z}_{p}$ parafermions. Unlike the $\mathbb{Z}_{2}$ Majorana fermions, the $\mathbb{Z}_{p}$ parafermions form intrinsically interacting systems. Here we explicitly construct two topologically distinct classes of irreducible $\mathbb{Z}_{3}$ parafermionic MPS wave functions, characterized by one or two parafermionic zero modes at each end of an open chain. Their corresponding parent Hamiltonians are found as the fixed point models of the single $\mathbb{Z}_{3}$ parafermion chain and two-coupled parafermion chains with $\mathbb{Z}_{3}\times \mathbb{Z}_{3}$ symmetry. Our results thus pave the road to investigate all possible topological phases with $\mathbb{Z}_{p}$ parafermions within the matrix product representation in one dimension.Comment: 10 pages, 4 figures, published versio