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arXiv:2010.14776 · Physical Review A

Realization of a deterministic quantum Toffoli gate with a single photon

Shihao Ru, Yunlong Wang, Min An, Feiran Wang, Pei Zhang, Fuli Li

Published Feb 11, 2021• 21 citations
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Abstract

Quantum controlled-logic gates, including controlled not gate and Toffoli gate, play critical roles in lots of quantum information processing schemes. We design and experimentally demonstrate deterministic Toffoli gate by utilizing orbital-angular-momentum and polarization degrees of freedom of a single photon. In addition, we generate Bell states by using the controlled not gate. The effective conversion rate of the Toffoli gate in our experiment is $(95.1\ifmmode\pm\else\textpm\fi{}3.2)%$. Furthermore, our experimental setup does not require any auxiliary photons and probabilistic postselections.

DOI
10.1103/physreva.103.022606

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Quantum controlled-logic gates, including controlled not gate and Toffoli gate, play critical roles in lots of quantum information processing schemes. We design and experimentally demonstrate deterministic Toffoli gate by utilizing orbital-angular-momentum and polarization degrees of freedom of a single photon. In addition, we generate Bell states by using the controlled not gate. The effective conversion rate of the Toffoli gate in our experiment is (95.1\ifmmode±\else\textpm\fi3.2)(95.1\ifmmode\pm\else\textpm\fi{}3.2)%(95.1\ifmmode±\else\textpm\fi3.2). Furthermore, our experimental setup does not require any auxiliary photons and probabilistic postselections.
We propose and experimentally demonstrate an optimized setup to implement quantum controlled-NOT operation using polarization and orbital angular momentum qubits. This device is more adaptive to inputs with various polarizations, and can work both in classical and quantum single-photon regime. The logic operations performed by such a setup not only possess high stability and polarization-free character, they can also be easily extended to deal with multi-qubit input states. As an example, the experimental implementation of generalized three-qubit Toffoli gate has been presented.
Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.
A Toffoli gate plays a critical role in many quantum algorithms due to its function as a building block, which is a fundamental element for feasible large-scale quantum computation. With the help of polarization, spatial, and temporal degrees of freedom (DOFs), a construction scheme of a nearly deterministic polarization Toffoli gate is proposed, where only two two-photon gates are required. The simple construction circuit together with available techniques and optical elements facilitate the realization of the scheme presented here. This construction scheme can be utilized as a reference for multiqubit quantum gates with multiple DOFs.
We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.
Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.