On-chip path encoded photonic quantum Toffoli gate

Femtosecond laser direct writing (FLDW) provides an important technique for the fabrication of integrated photonic quantum chips, but the produced universal photonic quantum computation chips are still limited to two-qubit logic gates, such as the most commonly used controlled NOT (CNOT) gates encoded by path or polarization. Multiqubit logic gates can be decomposed into the combination of a series of single-qubit and two-qubit logic gates in principle, but the circuits become much more complicated to write.


As for the most important three-qubit Toffoli gate, its decomposition according to the traditional quantum circuit generally requires six CNOT gates plus ten various single-qubit gates. Not only its circuit is very complex, but also its success probability is extremely low, even the heralded scheme using six entangled photon pairs just reaches (1/4)6=1/4096.


To address this problem, the research group led by Prof. Yan Li's from the School of Physics at Peking University, China, cooperating with Prof. Xi-Feng Ren's Group from the CAS Key Laboratory of Quantum Information at University of Science and Technology of China, using 3D configuration to optimize the quantum circuit, have designed and demonstrated a path encoded photonic quantum Toffoli gate chip based on FLDW technique for the first time.


The research results are published in Photonics Research, Volume. 10, Issue 7, 2022 (Meng Li, Chu Li, Yang Chen, Lan-Tian Feng, Linyu Yan, Qian Zhang, Jueming Bao, Bi-Heng Liu, Xi-Feng Ren, Jianwei Wang, Shufeng Wang, Yunan Gao, Xiaoyong Hu, Qihuang Gong, and Yan Li. On-chip path encoded photonic quantum Toffoli gate[J]. Photonics Research, 2022, 10 (7): 1533-1542).


To reduce the circuit complexity, they utilize the probabilistic post-selected three-qubit controlled-controlled phase (CCZ) gate as the core to construct the Toffoli gate. By selecting path encoding and changing the target from the traditional two-level "qubit" into the three-level "qutrit", the circuit requires only two cascaded controlled phase (CZ) gates and three signal photons without auxiliary photon, and the success probability increases to 1/72.


Compared with the polarization encoded logic gate, it can also significantly shorten the chip length. Above all, it can fully take the advantages of the true 3D direct writing ability of FLDW to further upgrade the 2D circuit to a 3D one with more succinct configuration with only 10 directional couplers (Fig.1).


Fig.1 The circuit and experimental results of the path encoded three-qubit photonic quantum Toffoli gate fabricated by the FLDW technique. (a) The optimized 3D quantum circuit of the Toffoli gate with an overpass waveguide. (b) Micrograph of the coupling region of the directional coupler, whose interaction distance is 8 μm. (c) Micrograph of the overpass waveguide. (d) The experimental reconstructed truth table with the fidelity of 85.5%.


The key is to introduce a depth-varying 3D overpass waveguide to eliminate all undesired crossing and coupling with other waveguides, which are hard to avoid, so as to greatly improve the performance of the chip. What's more, the quantum interference in the chip happens no more than one time, instead of twice in the polarization encoded quantum Toffoli gate using bulk optical elements, so that it can achieve a relatively higher true-table fidelity, whose measured value is 85.5%.


In addition, they also demonstrate the potential in the fabrication of the path encoded four-qubit controlled-controlled-controlled NOT (CCCNOT) gate with two overpass waveguides, which further highlights the advantage of 3D quantum circuits (Fig.2).


Fig.2 The circuit and experimental results of the path encoded four-qubit photonic quantum CCCNOT gate fabricated by the FLDW technique. (a) The optimized 3D quantum circuit of the CCCNOT gate with two overpass waveguides. (b) Theoretical output power distribution for each single port input. (c) Experimental output power distribution. The similarity of the experimental and theoretical values is 99.2%.


Prof. Yan Li believes that by using the true 3D capability of FLDW and combining the 3D path with multiple degrees of freedom of photons such as polarization and orbital angular momentum, it is expected to further simplify the quantum circuit structures, reduce the photon resource requirements, and realize more complex and powerful 3D photonic quantum computation chips.