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arXiv:1802.10388 · Optics Express

One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications

Tong Liu, Bao-qing Guo, Chang‐shui Yu, Wei‐Ning Zhang

Published Feb 12, 2018• 47 citations
arXivHTMLPDF

Abstract

In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.

DOI
10.1364/oe.26.004498

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In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.
Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multitarget-qubit controlled-not gate with one superconducting (SC) qubit simultaneously controlling nnn target cat-state qubits. In this proposal, the gate is implemented with nnn microwave cavities coupled to a three-level SC qutrit. The two logic states of the control SC qubit are represented by the two lowest levels of the qutrit, while the two logic states of each target cat-state qubit are represented by two quasi-orthogonal cat states of a microwave cavity. This proposal operates essentially through the dispersive coupling of each cavity with the qutrit. The gate realization is quite simple because it requires only a single-step operation. There is no need of applying a classical pulse or performing a measurement. The gate operation time is independent of the number of target qubits, thus it does not increase as the number of target qubits increases. Moreover, because the third higher energy level of the qutrit is not occupied during the gate operation, decoherence from the qutrit is greatly suppressed. As an application of this hybrid multitarget-qubit gate, we further discuss the generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of SC qubits and cat-state qubits. As an example, we numerically analyze the experimental feasibility of generating a hybrid GHZ state of one SC qubit and three cat-state qubits within present circuit QED technology. This proposal is quite general and can be extended to implement a hybrid controlled-not gate with one matter qubit (of different type) simultaneously controlling multiple target cat-state qubits in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-level natural or artificial atom.
Compared with a qubit, a qudit (i.e., a ddd-level or ddd-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits that are different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with d=3d=3d=3. We propose a simple method to realize a hybrid quantum controlled-sum gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary logic gates for quantum computing with qutrits. Our proposal is based on circuit QED and operates essentially by employing a SC ququart (a four-level quantum system) dispersively coupled to a microwave cavity. The gate implementation is quite simple because it only requires a single basic operation. Neither classical pulse nor measurement is needed. The auxiliary higher energy level of the SC ququart is virtually excited during the gate operation, thus decoherence from this level is greatly suppressed. As an application of this gate, we discuss the generation of a hybrid maximally entangled state of one SC qutrit and one cat-state qutrit. We further analyze the experimental feasibility of creating such a hybrid entangled state in circuit QED. This proposal is quite general and can be extended to accomplish the same task in a wide range of physical system, such as a four-level natural or artificial atom coupled to an optical or microwave cavity.
Optimizing the physical realization of quantum gates is important to build a quantum computer. Fredkin gate, also named controlled-swap gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate P\mathcal{P}P of the quantum Fredkin gate in our experiment is (95.4±2.6)%(95.4\pm 2.6)\%(95.4±2.6)%. Besides, we find that a kind of Greenberger-Horne-Zeilinger states can also be prepared by using our quantum Fredkin gate, and the Mermin inequality test shows its quantum contextual characteristic. Our experimental design paves the way for quantum computing and quantum fundamental study in high-dimensional and hybrid coding quantum systems.
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.
One of the greatest challenges in modern science is the realisation of quantum computers which, as their scale increases, will allow enhanced performance of tasks across many areas of quantum information processing. Quantum logic gates play a vital role in realising these applications by carrying out the elementary operations on the qubits; a key aim is minimising the resources needed to build these gates into useful circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, e.g., single- and two-qubit gates, difficulties in scaling quantum systems to encode and manipulate multiple qubits has hindered demonstrations of more complex operations. This is exemplified by the classical Fredkin (or controlled-SWAP) gate [1] for which, despite many theoretical proposals [2,3] relying on concatenating multiple two-qubit gates, a quantum analogue has yet to be realised. Here, by directly adding control to a two-qubit SWAP unitary [4], we use photonic qubit logic to report the first experimental demonstration of a quantum Fredkin gate [5]. Our scheme uses linear optics and improves on the overall probability of success by an order of magnitude over previous proposals [2,3]. This optical approach allows us to add control an arbitrary black-box unitary which is otherwise forbidden in the standard circuit model [6]. Additionally, the action of our gate exhibits quantum coherence allowing the generation of the highest fidelity three-photon GHZ states to date. The quantum Fredkin gate has many applications in quantum computing, quantum measurements [7] and cryptography [8,9]. Using our scheme, we apply the Fredkin gate to the task of direct measurements of the purity and state overlap of a quantum system [7] without recourse to quantum state tomography.
Abstract Optimizing the physical realization of quantum gates is important to build a quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate P of the quantum Fredkin gate in our experiment is (95.4 ± 2.6)%. Besides, we find that a kind of Greenberger–Horne–Zeilinger-like states can be prepared by using our quantum Fredkin gate, and these nonseparale states can show its quantum contextual characteristic by the violation of Mermin inequality. Our experimental design and coding method are useful for quantum computing and quantum fundamental study in high-dimensional and hybrid coding quantum systems.