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Optical Materials Express

Femtosecond laser direct writing of an integrated path-encoded CNOT quantum gate

Qian Zhang, Meng Li, Yang Chen, Xi‐Feng Ren, Roberto Osellame, Qihuang Gong, Yan Li

Published Apr 19, 2019• 33 citations
Publisher

Abstract

Femtosecond lasers enable three-dimensional direct writing of waveguides inside bulk transparent materials and have been applied to the fabrication of integrated photonic quantum logic gates. Up to now, the controlled-NOT (CNOT) gate, the key two-qubit quantum gate, has been realized only for polarization-encoded photonic qubits, which consists of three partially polarizing directional couplers (DCs) or two polarizing DCs. In this work, we demonstrate the femtosecond laser direct writing of a path-encoded CNOT gate formed by five DCs all with precisely controlled splitting ratios and stable symmetric phases inside glass for the first time. The quantum CNOT operation is performed using single photons with an average fidelity higher than 0.98. This provides a novel venue for the fabrication of large-scale 3D quantum computation circuits based on femtosecond laser writing.

DOI
10.1364/ome.9.002318

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Femtosecond lasers enable three-dimensional direct writing of waveguides inside bulk transparent materials and have been applied to the fabrication of integrated photonic quantum logic gates. Up to now, the controlled-NOT (CNOT) gate, the key two-qubit quantum gate, has been realized only for polarization-encoded photonic qubits, which consists of three partially polarizing directional couplers (DCs) or two polarizing DCs. In this work, we demonstrate the femtosecond laser direct writing of a path-encoded CNOT gate formed by five DCs all with precisely controlled splitting ratios and stable symmetric phases inside glass for the first time. The quantum CNOT operation is performed using single photons with an average fidelity higher than 0.98. This provides a novel venue for the fabrication of large-scale 3D quantum computation circuits based on femtosecond laser writing.
Femtosecond laser direct writing (FLDW) technique has been widely applied for fabrications of various photonic quantum chips in glass, such as chips for quantum computation, quantum walk, quantum simulation and quantum metrology. Photonic quantum logic gates are the building blocks for the realization of linear optical universal quantum computation. Up to now, several photonic quantum logic gates have been fabricated by FLDW, such as polarization encoded Hadamard (H) gate, Controlled NOT (CNOT) gate, herald CNOT gate and path encoded herald Controlled phase (CZ) gate and CNOT gate. By combining several single-qubit and two-qubit gates together, the constructed quantum circuits can realize some special functions, such as generating entangled states and perform quantum computation algorithms. Based on the successful fabrication of path encoded CNOT gate by FLDW, we further realized the fabrication of photonic quantum chips by cascading one H gate and one CNOT gate at the control qubit to generate path encoded Bell states, whose fidelity of truth table can reach 97.60.3%. Further, we cascaded one H gate and two parallel CNOT gates at the same control qubit to generate path encoded GHZ states, but which need three photons. Both Bell states and GHZ states are important entangled photon resources, which are widely used in quantum communication and quantum computation, and both combinations of logic gates above can be applied in many quantum circuits, so this work is of great importance and lays the technical foundation for the FLDW of more complex and powerful photonic quantum computation chips.
Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 ± 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.
Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.