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arXiv:2411.03762 · Physical Review A

Deterministic two-photon controlled- Z gate with the two-photon quantum Rabi model

Jia-Cheng Tang, Jin Long Zhao, Haitao Yang, Junlong Tian, Pinghua Tang, Shuai-Peng Wang, Lucas Lamata, Jie Peng

Published May 2, 2025• 3 citations
arXivHTMLPDF

Abstract

We propose a scheme for realizing a deterministic two-photon controlled-$Z$ (cz) gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign gate and subsequently we construct the cz gate following the Knill-Laflamme-Milburn scheme [Nature (London) 409, 46 (2001)]. We consider three different regimes: the strong-coupling regime, the perturbative ultrastrong-coupling regime, and the large-detuning regime. Our results indicate that the cz gate operates fast with high fidelity. We also show that the photonic state in the waveguide can be input into the circuit QED system through a variable coupler and released after interaction with almost the same waveform except for a $\ensuremath{\pi}$-phase shift. Our scheme offers a suitable approach for achieving fast and deterministic two-photon quantum gates via light-matter interactions.

DOI
10.1103/physreva.111.052601

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We propose a scheme for realizing a deterministic two-photon controlled-ZZZ (cz) gate based on variants of the two-photon quantum Rabi model, which is feasible within the framework of circuit QED. We begin by utilizing the two-photon interaction to implement the nonlinear sign gate and subsequently we construct the cz gate following the Knill-Laflamme-Milburn scheme [Nature (London) 409, 46 (2001)]. We consider three different regimes: the strong-coupling regime, the perturbative ultrastrong-coupling regime, and the large-detuning regime. Our results indicate that the cz gate operates fast with high fidelity. We also show that the photonic state in the waveguide can be input into the circuit QED system through a variable coupler and released after interaction with almost the same waveform except for a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift. Our scheme offers a suitable approach for achieving fast and deterministic two-photon quantum gates via light-matter interactions.
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state ∣ φ 〉 (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.
Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between copropagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multiphoton scattering response, we demonstrate that, in certain limits, this configuration induces a nonlinear π -phase shift between the polariton eigenstates of the system without distorting spectrally the wave packets. Then, we show how to harness this nonlinear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic setups with multiple chiral-edge modes, opening their use for quantum information processing, or in other setups where such chiral light-matter couplings can be effectively obtained, such as optical fibers or photonic-crystal optical and microwave waveguides.
The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light–matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one–two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields. Systems with strong photon-photon interactions enable advanced quantum optical applications as well as the study of highly correlated light-matter states. Here the authors report strong coupling between single- and two-photon states in a superconducting circuit, enabling a new regime of nonlinear quantum optics.
To resolve the intrinsic trade-off between the deterministic nature and scalability of controlled phase gate implementation in the linear optics regime, we propose a novel deterministic two-photon controlled phase gate scheme in chiral quantum nanophotonics. The essential ingredient here is that, a non-linear π-phase shift is imprinted during the photonic molecule generations. On one hand, the gate operates in a deterministic way without the assistance of probabilistic ancilla qubit measurement. On the other hand, the gate implementation is of low complexity to be highly scalable. To date, the chiral coupling is readily underpinned by the advent of directional emission technique. Potential implementation platforms include QD, superconducting qubit, Rydberg atom, or N-V center that is coupled to a PhC waveguide, transmission line, or optical fiber.
We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong-coupling regime and find that fundamental quantum-optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield a single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two-photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multiqubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.
In superconducting quantum circuits, decoherence errors in qubits constitute a critical factor limiting quantum gate performance. To mitigate decoherence-induced gate infidelity, rapid implementation of quantum gates is essential. Here we propose a scheme for rapid controlled-Z (CZ) gate implementation through energy-level engineering, which leverages Rabi oscillations between the ∣11⟩\left|11\right\rangle∣11⟩ state and the non-computational state in a tunable-coupler architecture. Numerical simulations achieved a 22 ns\mathrm{22~ns}22 ns nonadiabatic CZ gate with fidelity over 99.99%99.99\%99.99%. We further investigated the performance of the CZ gate in the presence of anharmonicity offsets. The results demonstrate that a high-fidelity CZ gate with an error rate below 10−410^{-4}10−4 remains achievable even with finite anharmonicity variations. Furthermore, the detrimental impact of spectator qubits in different quantum states on the fidelity of CZ gate is effectively suppressed by incorporating a tunable coupler. This scheme exhibits potential for extending the circuit execution depth constrained by coherence time limitations.