Reliable confidence regions for quantum tomography using distribution moments
arXiv:2307.12823 · doi:10.1103/PhysRevA.109.032414
Abstract
Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum states with reliable confidence intervals. In this work we suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We approximate the probability distribution of the Hilbert-Schmidt distance between the target state and the estimation, which is given by the linear inversion, by calculating its two moments. We also present a generalization of this approach for quantum process tomography and deriving confidence intervals for affine functions. We benchmark our approach for a number of quantum tomography protocols using both simulation and demonstration with the use of a cloud-accessible quantum processor. The obtained results pave the way for the use of the suggested scheme for the complete characterization of quantum systems of various natures.
8 pages, 5 figures, 4 tables
References in corpus (13)
- Randomized Benchmarking of Quantum Gates
- Efficient quantum state tomography
- Direct Fidelity Estimation from Few Pauli Measurements
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Permutationally invariant quantum tomography
- Complete Characterization of Quantum-Optical Processes
- Quantum process tomography with coherent states
- Neural-network quantum state tomography
- Towards higher precision and operational use of optical homodyne tomograms
- Reconstructing complex states of a 20-qubit quantum simulator
- Tomography of a multimode quantum black box
- Estimating the precision for quantum process tomography
- Exploring postselection-induced quantum phenomena with time-bidirectional state formalism