We propose a one-step scheme to implement a multiqubit controlled phase gate with one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. Selective qubit-qubit couplings are achieved by adiabatically eliminating the atomic excited states and photonic states, and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes are excited during the gate operation, leading to a useful step toward scalable quantum computing networks.
The family of
n-bit Toffoli gates, with the two-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a single-step implementation of arbitrary
n-bit Toffoli gates (up to a local change of basis), based on resonantly driving a single qubit that has a strong Ising coupling to
n other qubits. The setup in the two-qubit case turns out to be identical to the universal Barenco gate. The gate time and error are, in theory, independent of the number of control qubits, scaling better than conventional circuit decompositions. We note that our assumptions, namely, strongly coupling
n+1 qubits and a driving frequency that scales with
n, may break down for large systems. Still, our protocol could enhance the capabilities of intermediate-scale quantum computers, and we discuss the prospects of implementing our protocol on trapped ions, Rydberg atoms, and superconducting circuits. Simulations of the latter platform show that the Toffoli gate with two control bits attains fidelities of above 0.98 even in the presence of decoherence. We also show how similar ideas can be used to make a series of controlled-not gates in a single step. We show how these can speed up the implementation of quantum error correcting codes and we simulate the encoding steps of the three-qubit bit-flip code and the seven-qubit Steane code.
We present two efficient methods for implementing the Fredkin (controlled swap) gate with atoms separately trapped in an array of three high-
Q coupled cavities. The first proposal is based on large detuning interaction that the effective long-distance dipole-dipole-like interaction between two distributed target qubits is achieved by virtually excited qubits and cavities. The second one utilizes the selective resonant dynamics, which leads to a fast resonant interaction in a certain subspace while leaving others unchanged. Both schemes can achieve the standard form of the Fredkin gate in a single step without any subsequent single-qubit operation. The effects of decoherence on the performance of the gate are also analyzed in virtue of master equation, and the strictly numerical simulation reveals the average fidelity of the quantum gate is relatively high corresponding to the state-of-the-art technology.
Two schemes of implementing the Toffoli gate are proposed in an array of coupled cavities. In the first one, two classical laser fields with fixed Rabi frequency are used via quantum Zeno dynamics. While in the second scheme, the invariant-based inverse engineering is used to implement the Toffoli gate, which can drive the instantaneous eigenstates to evolve exactly under the Schrödinger equation. The strictly numerical simulations are given and the influences of cavity decay and spontaneous emission on the Toffoli gate operation are analyzed with master equation. The result shows that our schemes for the Toffoli gate are robust against the decoherence because of the short time needed.
We propose a potentially practical scheme to implement an approximate three-qubit Toffoli gate by a single resonant interaction in dissipative cavity QED in which the cavity mode decay and atomic spontaneous emission are considered. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the approximate phase gate can be implemented by only a single dissipative resonant interaction of atoms with the cavity mode. Discussions are made for the advantages and the experimental feasibility of our scheme.