How does quantum entanglement work and what are its applications in communication?

10 Ağu 06:27

Last year, as part of an internship, I worked on a superconducting-qubit setup where we aimed to implement the 9-qubit Shor code. The first step was to create three logical qubits from three physical qubits each, encoding \(|0_L\rangle = (|000\rangle+|111\rangle)/\sqrt{2}\) and \(|1_L\rangle = (|000\rangle-|111\rangle)/\sqrt{2}\). We used CNOT gates and Hadamard operations, applied via microwave pulse sequences on the transmon qubits. Next, we applied the syndrome measurement process: two separate parity measurements (Z and X syndromes) were performed using ancilla qubits, which were then immediately measured to identify bit and phase errors. The resulting syndrome data was evaluated classically, and the appropriate correction gate (X or Z gate) was applied in real time to the affected physical qubit. Experimentally, we employed three main techniques: (1) high-frequency microwave pulses calibrated at sub-nanosecond levels to minimize gate errors; (2) fast, dispersive measurements using a coupling resonator that read out the syndrome in less than 500 ns, ensuring the total error correction time remained well below the respective \(T_1/T_2\) times; and (3) dynamic error correction loops where the control system (FPGA) executed the correction gates immediately. In practice, we found that while the Shor code is highly robust against single bit and phase errors, the additional ancilla qubits and long gate sequences increase the overall decoherence time. Compared to more modern surface codes (e.g., the surface code), the Shor code is simpler to understand and implement but less scalable because it requires more physical qubits per logical qubit and has more complex error propagation. Still, it provides an excellent testbed for practically exploring the fundamental principles of quantum error correction.