The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyze the parity gate (
P gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with
P gates and show that native networks simplify considerably the resources required for producing multiqubit entanglement, such as
n--Greenberg-Horne-Zellinger (GHZ) states. Other applications include a Bell-state analyzer and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin
n-GHZ state with linear elements (beam splitters and local spin flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct an alternative spin-controlled-
Z gate by using the mode degrees of freedom as ancill\ae{}.
We propose a simple method to realize a hybrid controlled–controlled-Z (CCZ) gate with two photonic qubits simultaneously controlling a superconducting (SC) target qubit, by employing two microwave cavities coupled to a SC ququart (a four-level quantum system). In this proposal, each control qubit is a photonic qubit, which is encoded by two arbitrary orthogonal eigenstates (with eigenvalues ±1, respectively) of the photon-number parity operator. Since the two arbitrary encoding states can take various quantum states, this proposal can be applied to realize the hybrid CCZ gate, for which the two control photonic qubits can have various encodings. The gate realization is quite simple because only a basic operation is needed. During the gate operation, the higher energy intermediate levels of the ququart are not occupied, and, thus, decoherence from these levels is greatly suppressed. We further discuss how to apply this gate to generate a hybrid Greenberger–Horne–Zeilinger (GHZ) entangled state of a SC qubit and two photonic qubits, which takes a general form. As an example, our numerical simulation demonstrates that high-fidelity generation of a cat–cat–spin hybrid GHZ state is feasible within current circuit QED technology. This proposal is quite general, which can be applied to realize the hybrid CCZ gate as well as to prepare various hybrid GHZ states of a matter qubit and two photonic qubits in other physical systems, such as two microwave or optical cavities coupled to a four-level natural or artificial atom.
We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle the initial single-mode squeezed vacuum (SMSV) state with the photon state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity or reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. Maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled-Z (CZ-) operation using the BS with the appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3. We also propose to use new continuous variable (CV) states of definite parity that could increase the success probability of generating maximal hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.