High-fidelity realisation of CNOT gate in Majorana-based optical platform

Abstract

We present the experimental realisation of a robust CNOT quantum gate using Majorana zero modes simulated on a photonic platform. Three Kitaev chains supporting Majorana zero modes at their endpoints are used to encode two logical qubits, and both intra-chain and inter-chain braiding operations are performed to implement the CNOT gate. While the topological encoding of quantum information in Majorana fermions does not offer full topological protection in our non-interacting photonic setting, it nevertheless exhibits a natural resilience to the dominant noise and decoherence effects present in the experiment. Consequently, the fidelity of the CNOT gate is significantly enhanced, surpassing 0.992 and addressing a key limitation in the path toward scalable quantum computation. These results represent a major advancement in topological quantum computing with Majorana fermions and underscore the potential of photonic platforms for realising high-fidelity quantum gates.

Figures (6)

• Figure 1: Theoretical schematic. a. Schematic diagram for achieving universal quantum computation. By combining simple single-qubit gates (Hadamard gate, S gate and T gate) with two-qubit CNOT gates, universal quantum computation can be realized. b. Worldline strands of the CNOT gate. Through the encoding of two logical qubits using six Majorana zero modes from A to F, the CNOT gate can be implemented via specific braiding operation between them. c. Kitaev three-chain model. The chain used to implement braiding operations of the CNOT gate consists of eleven fermions with six Majorana zero modes. Each spheres represents a Majorana fermion, and a pair of Majorana fermions (marked by the gray circle) consitudes a Dirac fermion. The ends of three Kitaev chains host Majorana zero modes, labeled as A-F.
• Figure 2: Experimental setup. Correlated photon pairs are generated through the type-II spontaneous down conversion process. The two photons are then sent to Side A1/A2 and Side B. The two fundamental operations for implementing the CNOT gate: intra-chain braiding and inter-chain braiding, are performed as follows: The collaborative effort of the device in Side A1 and Side B realizes the inter-chain braiding evolution, whereas the device in Side A2 and Side B collaborates to accomplish the intra-chain braiding evolution. Quarter-wave plate (QWP), half-wave plate (HWP), polarization beam splitter (PBS), periodically poled KTiOPO$_{4}$ (PPKTP), beam displacer (BD).
• Figure 3: Experimental reconstructed density matrix for intra-chain exchange and inter-chain exchange braiding operation. $\textbf{a}$. Real (Re) and $\textbf{b}$. imaginary (Im) parts of the process density matrix $\chi_{intra}=(I-iZ)/\sqrt{2}$ of intra-chain exchange braiding operation $\sigma_{1}$. $\textbf{c}$. Real (Re) and $\textbf{d}$. imaginary (Im) parts of the process density matrix $\chi_{inter}=(II-iXX)/\sqrt{2}$ of inter-chain exchange braiding operation.
• Figure 4: Experimental results for the input states and the corresponding output states after the action of the CNOT gate. $\textbf{a}$-$\textbf{d}$. Real parts of the input states $|00\rangle_{l}$, $|01\rangle_{l}$, $|10\rangle_{l}$ and $|11\rangle_{l}$ with the corresponding output states $|00\rangle_{l}$, $|01\rangle_{l}$, $|11\rangle_{l}$ and $|10\rangle_{l}$, respectively. $\textbf{e}$-$\textbf{h}$. Experimental results for entanglement generation through the CNOT gate. The real parts of the density matrix in measurement basis ($\textbf{e}$ and $\textbf{f}$) and logical basis ($\textbf{g}$ and $\textbf{h}$). The imaginary parts of these density matrix are too small thus not shown in the figure.
• Figure 5: Comparison of the input/output state fidelities under different basis. a. Input states from $|001\rangle_{m}$ to $(|011\rangle_{m}+|110\rangle_{m})/\sqrt{2}$ with their corresponding output states after the action of the CNOT gate in measurement basis. b. Input states from $|00\rangle_{l}$ to $(|01\rangle_{l}+|11\rangle_{l})/\sqrt{2}$ with their corresponding output states in logical basis.