Hu Chang-Kang, Wei Chao, Liu Chilong, Che Liangyu, Zhou Yuxuan, Xie Guixu, Qin Haiyang, Hu Guantian, Yuan Haolan, Zhou Ruiyang, Liu Song, Tan Dian, Xin Tao, Yu Dapeng
International Quantum Academy, Shenzhen 518048, China.
Southern University of Science and Technology, Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Shenzhen 518055, China.
Phys Rev Lett. 2024 Oct 18;133(16):160801. doi: 10.1103/PhysRevLett.133.160801.
Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method inspired by quantum overlapping tomography [Phys. Rev. Lett. 124, 100401 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.100401], which utilizes parallel measurements (PQST). In contrast to LQST, PQST significantly reduces the number of measurements and offers more robustness against shot noise. Experimentally, we demonstrate the feasibility of PQST in a treelike superconducting qubit chip by designing high-efficiency circuits, preparing W states, ground states of Hamiltonians, and random states, and then reconstructing these density matrices using full quantum state tomography (FQST), LQST, and PQST. Our results show that PQST reduces measurement cost, achieving fidelities of 98.68% and 95.07% after measuring 75 and 99 observables for six-qubit and nine-qubit W states, respectively. Furthermore, the reconstruction of the largest density matrix of the 12-qubit W state is achieved with the similarity of 89.23% after just measuring 243 parallel observables, while 3^{12}=531 441 complete observables are needed for FQST. Consequently, PQST will be a useful tool for future tasks such as the reconstruction, characterization, benchmarking, and properties learning of states.
通过对约化密度矩阵进行局部测量实现的量子态层析成像（QST，即局部量子态层析成像，LQST）是一种很有前景的方法，但对于大型系统而言变得不切实际。为应对这一挑战，我们受量子重叠层析成像[《物理评论快报》124, 100401 (2020)PRLTAO0031 - 900710.1103/PhysRevLett.124.100401]启发，开发了一种高效的量子态层析成像方法，该方法利用并行测量（PQST）。与LQST相比，PQST显著减少了测量次数，并对散粒噪声具有更强的鲁棒性。在实验中，我们通过设计高效电路、制备W态、哈密顿量的基态和随机态，然后使用全量子态层析成像（FQST）、LQST和PQST重构这些密度矩阵，证明了PQST在树形超导量子比特芯片中的可行性。我们的结果表明，PQST降低了测量成本，对于六量子比特和九量子比特W态，分别在测量75个和99个可观测量后，保真度达到了98.68%和95.07%。此外，仅测量243个并行可观测量后，就实现了对12量子比特W态最大密度矩阵的重构，相似度达到89.23%，而FQST则需要3^12 = 531441个完整的可观测量。因此，PQST将成为未来诸如态的重构、表征、基准测试和性质学习等任务的有用工具。
