We present a scheme for implementing locally a nonlocal N -target controlled–controlled gate with unit probability of success by harnessing two ( N +1)-qubit Greenberger–Horne–Zeilinger (GHZ) states as quantum channel and N qutrits as catalyser. The quantum network that implements this nonlocal ( N +2)-body gate is built entirely of local single-body and two-body gates, and has only (3 N +2) two-body gates. This result suggests that both the computational depth of quantum network and the quantum resources required to perform this nonlocal gate might be significantly reduced. This scheme can be generalized straightforwardly to implement a nonlocal N -target and M -control qubits gate.
We present a scheme for implementing locally a nonlocal N -target controlled–controlled gate with unit probability of success by harnessing two ( N +1)-qubit Greenberger–Horne–Zeilinger (GHZ) states as quantum channel and N qutrits as catalyser. The quantum network that implements this nonlocal ( N +2)-body gate is built entirely of local single-body and two-body gates, and has only (3 N +2) two-body gates. This result suggests that both the computational depth of quantum network and the quantum resources required to perform this nonlocal gate might be significantly reduced. This scheme can be generalized straightforwardly to implement a nonlocal N -target and M -control qubits gate.
We show how a nonlocal N-qubit controlled unitary gate can be implemented locally and effectively by using non-symmetric quantum channels. We construct respectively two quantum networks for realizing conclusively this nonlocal quantum gate. The first one hires (N–2) symmetric qubit-qubit Bell states and a non-symmetric qubit-qudit Bell state as quantum channels. The basic idea of this scheme is to use (N–2) additional levels of this qudit to “hide” certain computational states of (N–1) nonlocal control states from the conditional dynamics, which results in an effective nonlocal N-qubit controlled unitary gate design. In this scheme, however, either the number of the additional levels or that of 1-qudit gates needs to increase with N. The other one can improve significantly the local implementation of this nonlocal gate if we harness (N–1) non-symmetric qubit-qutrit Bell states as quantum channels. This scheme uses respectively (N–1) qutrits’s additional levels to expose one and only one initial computational state of (N–1) nonlocal control states to the conditional dynamics. In comparison with the first one, the procedure is greatly simplified, and the total gate time is reduced. The fact that the quantum network that does the proposed implementation is built entirely of local single-body and two-body gates, and has only (3N–4) two-body gates is notable.
Local implementation of a nonlocal d-dimensional quantum Toffoli gate is considered. We construct respectively two quantum networks for realizing this nonlocal quantum gate conclusively. The first one is based on Eisert’s insight but follow a different pathway which results in a nonlocal d-dimensional Toffoli gate design. This scheme involves a local d-dimensional three-body interaction, which does not appear naturally in physical system. The other one can improve significantly the local implementation of this nonlocal gate if the target node harnesses a qutrit as a catalyser. In its simplest form this quantum network that does the improved scheme is built entirely of local single-body and two-body elementary gates, and with only 3 two-body elementary gates at the target node. The latter is simpler but conclusive, and more efficient but with less resource, which will make it more feasible with the current experimental technology and more suitable for large-scale quantum network.
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 n target cat-state qubits. In this proposal, the gate is implemented with n 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.
In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.
Scalable long-distance quantum gates are essential for distributed quantum computation and scalable quantum networks. We propose an efficient scheme for implementing an n-qubit fan-out gate Cn (also known as a controlled-NOT-⋯-NOT gate) across spatially separated parties. Our protocol requires only a pre-shared n-qubit Greenberger-Horne-Zeilinger state, n local controlled-NOT (CNOT) gates, and feed-forward operations, thereby reducing both the CNOT and Hadamard gate counts by (n−2) when compared with the standard decomposition-based approach. We further develop two optical architectures to implement the heralded and post-selected n-photon fan-out gates, respectively. These schemes require fewer single photons resources and achieve higher success probabilities than their decomposition-based counterparts, representing significant improvements. The results indicate that our approach is experimentally feasible and pave the way toward practical long-distance quantum computation.
We show how a non-local quantum controlled-NOT (CNOT) gate with multiple targets can be implemented with unit fidelity and unit probability. The explicit quantum circuit for implementing the operation is presented. Two schemes for probabilistic implementing the operation via partially entangled quantum channels with unit fidelity are put forward. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different.