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Annalen der Physik

All‐Resonance Controlled‐Phase Gate on Two Nonlocal Nitrogen‐Vacancy Center Ensembles Assisted by a Superconducting Quantum Circuit

Hai‐Peng Wu, Yan‐Mei Li, Ming‐Jie Tao, Ming Hua

Published Jun 10, 2021• 2 citations
Publisher

Abstract

Abstract The realization of universal quantum logical gates on nonlocal nitrogen‐vacancy center ensembles (NVEs) is a basic task for universal quantum computing with NVEs. In contrast to previous works on the construction of gates, a one‐step all‐resonance scheme is proposed to construct a controlled‐phase gate on two nonlocal NVEs that are coupled to different superconducting transmission line resonators connected by a superconducting transmon qubit. The gate can be easily realized using only one step. Moreover, the all‐resonance operation allows the gate to be achieved within a short time. By considering the feasible parameters obtained in the experiments, this gate can be completed within 101 ns with a high fidelity of approximately 97.8%, which has reached the threshold of fault‐tolerance quantum computing.

DOI
10.1002/andp.202100063

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Annalen der Physik•Nov 4, 2018•10 citations
Abstract The realization of universal quantum logical gates on nonlocal nitrogen‐vacancy center ensembles (NVEs) is a basic task for universal quantum computing with NVEs. In contrast to previous works on the construction of gates, a one‐step all‐resonance scheme is proposed to construct a controlled‐phase gate on two nonlocal NVEs that are coupled to different superconducting transmission line resonators connected by a superconducting transmon qubit. The gate can be easily realized using only one step. Moreover, the all‐resonance operation allows the gate to be achieved within a short time. By considering the feasible parameters obtained in the experiments, this gate can be completed within 101 ns with a high fidelity of approximately 97.8%, which has reached the threshold of fault‐tolerance quantum computing.
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 a fast controlled-phase (cphase) gate on these NVEs, respectively. This hybrid quantum system is composed of two distant NVEs coupled to separated high-QQQ transmission line resonators (TLRs), which are interconnected by a current-biased Josephson-junction superconducting phase qubit. The fidelity of our state-transfer protocol is about 99.6399.63%99.63 within the operation time of 70.6070.6070.60 ns. The fidelity of our cphase gate is about 98.1598.15%98.15 within the operation time of 93.8793.8793.87 ns. Furthermore, using the cphase gate, we construct a two-dimensional cluster state on NVEs in a $n\ifmmode\times\else\texttimes\fi{}n$ 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.
We theoretically model and simulate the dynamics of a hybrid quantum system consisting of two non-local ensembles of nitrogen-vacancy center and a superconducting transmon qubit mediated by two transmission line resonators. We apply a time-dependent external field to enhance this system’s speed and fidelity to function as a controlled-phase gate. Our simulation result shows that a high-fidelity entangled state of two non-local NV spins is 92%. It is achievable under realistic parameter regimes within a timescale of 1.1 nanoseconds. Our result paves the way to improving potential quantum computing and sensing applications.
Abstract A one‐step scheme is presented to construct the controlled‐phase gate deterministically on remote transmon qutrits coupled to different resonators connected by a superconducting transmission line for an universal distributed quantum computing. Different from previous work on remote superconducting qubits, the present gate is implemented with coherent evolutions of the entire system in the all‐resonance regime assisted by the dark photons to robust against the transmission line loss, which allows the possibility of the complex designation of a long‐length transmission line to link lots of circuit QEDs. The length of the transmission line can reach the scale of several meters, which makes this scheme suitable for large‐scale distributed quantum computing. This gate is a fast quantum entangling operation with a high fidelity of about 99%. Compared with previous work in other quantum systems for a distributed quantum computing, under the all‐resonance regime, the present proposal does not require classical pulses and ancillary qubits, which relaxes the difficulty of its implementation largely.
We propose a scheme to construct the controlled-phase (c-phase) gate on distant transmon qutrits hosted in different resonators inter-coupled by a connected transmon qutrit. Different from previous works for entanglement generation and information transfer on two distant qubits in a dispersive regime in the similar systems, our gate is constructed in the resonant regime with one step. The numerical simulation shows that the fidelity of our c-phase gate is 99.5% within 86.3 ns. As an interesting application of our c-phase gate, we propose an effective scheme to complete a conventional square lattice of two-dimensional surface code layout for fault-tolerant quantum computing on the distant transmon qutrits. The four-step coupling between the nearest distant transmon qutrits, small coupling strengths of the distant transmon qutrits, and the non-population on the connection transmon qutrit can reduce the interactions among different parts of the layout effectively, which makes the layout be integrated with a large scale in an easier way.
The Toffoli gate is a three-qubit controlled-controlled-NOT gate, which plays a central role in quantum information processing and quantum computing. Recently, hybrid systems and hybrid quantum gates have attracted much attention. We propose an efficient scheme to implement a hybrid Toffoli gate with two nitrogen-vacancy center ensembles (NV ensembles) as the control qubits and a single superconducting flux qubit as the target qubit. This hybrid Toffoli gate is realized by employing two NV ensembles coupled to a superconducting qutrit. The hybrid Toffoli gate is constructed by a controlled-controlled-phase (CCPHASE) gate sandwiched between two Hadamard gates applied on the target qubit. Since the CCPHASE gate is realized using only a single-step operation and no conventional gate decomposition protocol is applied, the Toffoli-gate implementation is greatly simplified. Because the higher energy level of the flux qutrit is not populated, the decoherence of this level is greatly suppressed. In addition, our hybrid Toffoli gate can be used to generate a hybrid Greenberger–Horne–Zeilinger entangled state of a flux qubit and two NV ensembles. Numerical simulations demonstrate that high-fidelity implementation of a hybrid Toffoli gate is feasible within current experimental technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems.
Abstract High‐fidelity universal quantum gates are crucial in quantum computing. Three high‐fidelity universal quantum gates, namely the hybrid controlled NOT gate, the hybrid Toffoli gate, and the hybrid Fredkin gate, on a flying photon qubit and diamond nitrogen‐vacancy (NV) centers, assisted by low‐Q single‐sided cavities, are presented. Errors due to the imperfection of the practical input–output process are detected to improve the fidelity of these quantum gates, which therefore relaxes the requirement on their implementation, since strong coupling is no longer mandatory. In addition, quantum gates have the advantage that they can work faithfully even when the resonant condition among the NV center, the photon, and the cavity is not strictly satisfied, or the NV centers are not identical. The performance and success probability of these quantum gates are analyzed, finding that these schemes are feasible with current technology.