We introduce an inductive n-qubit pure-state estimation method based on projective measurements on mn + 1 separable bases or m entangled bases plus the computational basis, with m ≥ 2. The method exhibits a favorable scaling in the number of qubits compared to other estimation schemes. The use of separable bases makes our estimation method particularly well suited for applications in noisy intermediate-scale quantum computers, where entangling gates are much less accurate than local gates. Our method is also capable of estimating the purity of mixed states generated by the action of white noise on pure states. Monte Carlo simulations show that the method achieves a high estimation fidelity. Besides, the fidelity can be improved by increasing m above 2. We experimentally demonstrate the method on the IBM’s quantum processors by estimating up to 10-qubit separable and entangled states. In particular, a 4-qubit GHZ is estimated with experimental fidelity of 0.875.

我们介绍了一种基于m n  + 1 个可分离碱基或m个纠缠碱基的投影测量以及计算基的归纳n -qubit 纯态估计方法，其中m ≥ 2。与其他估计方案相比，该方法在量子比特数方面表现出有利的缩放比例。可分离基的使用使我们的估计方法特别适用于嘈杂的中等规模量子计算机中的应用，其中纠缠门的准确度远低于本地门。我们的方法还能够估计白噪声对纯态的作用所产生的混合态的纯度。蒙特卡罗模拟表明该方法实现了高估计保真度。此外，可以通过将m增加到 2 以上来提高保真度。我们通过估计高达 10 量子位的可分离和纠缠态在 IBM 的量子处理器上通过实验证明了该方法。特别是，一个 4 量子比特的 GHZ 估计具有 0.875 的实验保真度。