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arXiv:2210.10597

Refined quantum gates for ΛΛΛ-type atom-photon hybrid systems

Wu, Yi-Ming, Gang Fan, Fang‐Fang Du

Published Oct 19, 2022• 0 citations
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Abstract

High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level $Λ$-typle atom-cavity system, we present some refined protocols for realizing controlled-not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of our gates is encoded on a flying photon, and the rest qubits are encoded on the atoms in optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi-qubit CNOT, Fredkin and Toffoli gates with O(n) optical elements without auxiliary photons or atoms. Further, the simplest single-qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.

DOI
10.48550/arxiv.2210.10597

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High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level ΛΛΛ-typle atom-cavity system, we present some refined protocols for realizing controlled-not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of our gates is encoded on a flying photon, and the rest qubits are encoded on the atoms in optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi-qubit CNOT, Fredkin and Toffoli gates with O(n) optical elements without auxiliary photons or atoms. Further, the simplest single-qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.
Abstract High‐efficiency quantum information processing is equivalent to the fewest quantum resources and simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three‐level Λ‐type atom‐cavity system, the authors present some refined protocols for realizing controlled‐not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of gates is encoded on a flying photon, and the remaining qubits are encoded on the atoms in the optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi‐qubit CNOT, Fredkin, and Toffoli gates with optical elements without auxiliary photons or atoms. Further, the simplest single‐qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.
Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.
Universal quantum gates play a critical role in quantum information processing. Here, based on the scattering property of photons off single emitters in one-dimensional waveguides, we present some heralded protocols for realizing controlled-not, Toffoli, and Fredkin gates on hybrid systems. The control qubit of our gates is encoded on a flying photon, and the target qubits are encoded in the degenerate ground states of the emitter. In our schemes, the faulty scattering processes between emitters and photons caused by system imperfections can be transformed into the detection of photon polarization. That is, our three quantum gates are accomplished in a heralded way. Moreover, the quantum circuits for the three gates are versatile and compact, and no additional qubits are required. With current technique on manipulating the emitter-waveguide system, our protocols may be experimentally feasible. This work provides an effective avenue for implementing quantum logic gates.
Abstract Quantum gates designed with minimized resources overhead have a crucial role in quantum information processing. Here, based on the degrees of freedom (DoFs) of photons and Λ‐type atom systems, two high‐fidelity and low‐cost protocols are presented for realizing polarization‐spatial hyperparallel controlled‐not (CNOT) and Toffoli gates on photon systems with only two and four two‐qubit polarization–polarization swap (P‐P‐SWAP) gates in each DoF, respectively. Moreover, the quantum gates can be extended feasibly to construct 2m‐target‐qubit hyperparallel CNOT and 2n‐control‐qubit Toffoli gates required only 4m and 4n P‐P‐SWAP gates on ‐ and ‐photon systems, respectively, which dramatically lower the costs and bridge the divide between the theoretical lower bounds and the current optimal syntheses for the photonic quantum computing. Further, the unique auxiliary atom of these quantum gates can be regarded as a temporary quantum memory that requires no initialization and measurement, and is reused within the coherence time, as the state of the atom remains unchanged after the hyperparallel quantum computing.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only ddd PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.
We present two deterministic schemes for constructing a CNOT gate and a Toffoli gate on photon-atom and photon-atom-atom hybrid quantum systems assisted by bad cavities, respectively. They are achieved by cavity-assisted photon scattering and work in the intermediate coupling region with bad cavities, which relaxes the difficulty of their implementation in experiment. Also, bad cavities are feasible for fast quantum operations and reading out information. Compared with previous works, our schemes do not need any auxiliary qubits and measurements. Moreover, the schematic setups for these gates are simple, especially that for our Toffoli gate as only a quarter wave packet is used to interact the photon with each of the atoms every time. These atom-cavity systems can be used as the quantum nodes in long-distance quantum communication as their relatively long coherence time is suitable for multi-time operations between the photon and the system. Our calculations show that the average fidelities and efficiencies of our two universal hybrid quantum gates are high with current experimental technology.