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arXiv:2005.01991 · Frontiers of Physics

Distributed entanglement generation from asynchronously excited qubits

Tiantian Huan, Ri‐Gui Zhou, Hou Ian

Published Dec 24, 2021• 0 citations
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Abstract

The generation of GHZ states calls for simultaneous excitation of multiple qubits. The peculiarity of such states is reflected in their nonzero distributed entanglement which is not contained in other entangled states. We study the optimal way to excite three superconducting qubits through a common cavity resonator in a circuit such that the generation of distributed entanglement among them could be obtained at the highest degree in a time-controllable way. A non-negative measure quantifying this entanglement is derived as a time function of the quadripartite system evolution. We find that this measure does not stay static but obtains the same maximum periodically. When the qubit-resonator couplings are allowed to vary, its peak value is enhanced monotonically by increasing the greatest coupling strength to one of the qubits. The period of its peak to peak revival maximizes when the couplings become inhomogeneous, thus qubit excitation becoming asynchronous, at a relative ratio of 0.35. The study demonstrates the role of asynchronous excitations for time-controlling multi-qubit systems, in particular in extending entanglement time.

DOI
10.1007/s11467-021-1139-9

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The generation of GHZ states calls for simultaneous excitation of multiple qubits. The peculiarity of such states is reflected in their nonzero distributed entanglement which is not contained in other entangled states. We study the optimal way to excite three superconducting qubits through a common cavity resonator in a circuit such that the generation of distributed entanglement among them could be obtained at the highest degree in a time-controllable way. A non-negative measure quantifying this entanglement is derived as a time function of the quadripartite system evolution. We find that this measure does not stay static but obtains the same maximum periodically. When the qubit-resonator couplings are allowed to vary, its peak value is enhanced monotonically by increasing the greatest coupling strength to one of the qubits. The period of its peak to peak revival maximizes when the couplings become inhomogeneous, thus qubit excitation becoming asynchronous, at a relative ratio of 0.35. The study demonstrates the role of asynchronous excitations for time-controlling multi-qubit systems, in particular in extending entanglement time.
In a multi-partite system, the multipartite concurrence of the entire system differs from the sum of the bipartite concurrences of its components. For a system with an even number of components, the relation between them is described by a monogamy inequality that compares the bipartite concurrences of two subsystems comprising even-number components and those of two subsystems comprising odd-number components. The difference between the even and the odd clusterings is exactly quantified by a polynomial invariant. We study the dynamic evolution of the polynomial invariant on three superconducting qubits inhomogeneously coupled to a circuit cavity. We show that in this quadripartite system, the non-negativity of the degree-4 invariant holds strictly over time and vanishes periodically. The magnitude of the invariant increases monotonically with the absolute coupling strength while the period of the vanishing and revival maximizes when the couplings among the qubits are inhomogeneous, showing the benefit of asynchronous qubit excitations in extending entanglement time.
The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent GHZ and W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasi-lattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable GHZ state.
Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission lines is inhomogeneous and geometrically dependent on the circuit layout. We propose a projection-deformation method to give analytically the eigenstates of the quasi-particle excitation that arise in the quasi-lattice. We further show that, during the quasi-particle excitation, the distribution of multi-photon resonances between the resonator photon and the quasi-lattice is determined by the degree the quasi-lattice is deformed from a normal lattice. The multi-photon resonances lead to simultaneous generation of GHZ-type and W-type of multipartite entanglement states of the qubits, which is enhanced by the inhomogeneous interaction. Comparing the concurrence and the 3-tangle generated, we find that the totally non-separable GHZ entanglement is specifically increased, up to two orders of magnitude.
Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberger–Horne–Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for an arbitrary number of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of NNN-group qubits distributed in NNN cavities can be created via a three-step operation. The GHZ states of the NNN-group qubits are generated by using NNN-group qutrits placed in the NNN cavities. Here, ``qutrit'' refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for coupling the cavities. The operation time is independent of the number of qubits. The GHZ states are prepared deterministically because no measurement on the states of qutrits or cavities is needed. In addition, the third energy level of the qutrits during the entire operation is virtually excited and thus decoherence from higher energy levels is greatly suppressed. This proposal is quite general and can in principle be applied to create GHZ states of many qubits using different types of physical qutrits (e.g., atoms, quantum dots, NV centers, various superconducting qutrits, etc.) distributed in multiple cavities. As a specific example, we further discuss the experimental feasibility of preparing a GHZ state of four-group transmon qubits (each group consisting of three qubits) distributed in four one-dimensional transmission line resonators arranged in an array.
Dissipation is usually considered a negative factor for observing quantum effects and for harnessing them for quantum technologies. Here we propose a scheme for speeding up the generation of quantum entanglement between two coupled qubits by introducing a strong dissipation channel to one of these qubits. The maximal entanglement is conditionally established by evenly distributing a single excitation between these two qubits. When the excitation is initially held by the dissipative qubit, the dissipation accelerates the excitation re-distribution process for the quantum state trajectory without quantum jumps. Our results show that the time needed to conditionally attain the maximal entanglement is monotonously decreased as the dissipative rate is increased. We further show that this scheme can be generalized to accelerate the production of the W state for the three-qubit system, where one NH qubit is symmetrically coupled to two Hermitian qubits.