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Physical Review A

Heralded quantum gates for hybrid systems via waveguide-mediated photon scattering

Guo‐Zhu Song, Jin‐Liang Guo, Qian Liu, Hai‐Rui Wei, Gui‐Lu Long

Published Jul 20, 2021• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.104.012608

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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 Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.
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.
High-fidelity quantum logic gates are essential in quantum computation, and both photons and electron spins in quantum dots (QDs) have their own unique advantages in implementing quantum computation. It is of critical significance to achieve high-fidelity quantum gates for photon-QD hybrid systems. Here, we propose two schemes for implementing high-fidelity universal quantum gates including Toffoli gate and Fredkin gate for photon-QD hybrid systems, utilizing the practical scattering of a single photon off a QD-cavity system. The computation errors from the imperfections involved in the practical scattering are detected and prevented from arising in the final results of the two gates. Accordingly, the unity fidelity of each quantum gate is obtained in the nearly realistic condition, and the requirement for experimental realization is relaxed. Furthermore, the quantum circuits for the two gates are compact and no auxiliary qubits are required, which would also be the advantages regarding their experimental feasibility. These features indicate that our schemes may be useful in the practical quantum computation tasks.
Robust universal quantum gates with an extremely high fidelity hold an important position in large-scale quantum computing. Here, we propose a scheme for several robust universal photonic quantum gates on a two-or three-photon system, including the controlled-NOT gate, the Toffoli gate, and the Fredkin gate, assisted by low-Q single-sided cavities. In our scheme, the quantum gates are robust against imperfect process occurring with the photons and the electron spins in diamond nitrogen-vacancy (NV) centers inside low-Q cavities. Errors due to the imperfect process are transferred to some heralding responses, which may lead to a direct recycling procedure to remedy the success probability of the quantum gates. As a result, the adverse impact of the imperfect process on fidelity is eliminated, greatly relaxing the restrictions on implementation of various quantum gates in experiments. Furthermore, the scheme is designed in a compact and heralded style, which can increase the robustness against environmental noise and local fluctuation, thus decreasing the operation time, the error probability, and the quantum resource consumption in a large-scale integrated quantum circuit. The near-unity fidelity and not-too-low efficiency with current achievable experimental techniques guarantees the feasibility of the scheme.
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 entanglement systems based on qudits dilate high-dimensional (HD) state spaces and enhance resistance to loss in quantum information processing (QIP). To fully exploit this potential, effective schemes for generating HD entanglement are crucial. In this paper, we propose a flexible heralded scheme generating random four-dimensional (4D) two-qudit maximal entanglement for a hybrid photon-emitter system by entering different input ports. This approach can be further extended to prepare 4D nnn-qudit $(n\ensuremath{\ge}3)$ maximal entanglement utilizing the 4D single-qudit Zm(m=1,2,3){Z}^{m}(m=1,2,3)Zm(m=1,2,3) gate for the first qudit and Xm{X}^{m}Xm gate for the other qudits (except the second qudit). For the hybrid system, the first 4D qudit is encoded on the hybrid polarization-path states of a flying photon, while the second and subsequent 4D qudits are represented by two stationary emitters coupled to the respective 1D waveguide. The qudit-encoded hybrid HD entanglement offers advantages over economizing quantum resource without any auxiliary qudits and obtaining robust fidelities of various HD entanglement by the error-detected mechanism of the emitter-waveguide systems. Moreover, the proposed protocol can be spread to generate dDd\mathrm{D}dD nnn-qudit $(d\ensuremath{\ge}{2}^{p+1},$ $n,p=2,3,\ensuremath{\cdots})$ entangled states, further broadening its applicability in HD QIP.