Experimental sample-efficient quantum state tomography via parallel measurements

TL;DR

This paper introduces a parallel measurement-based quantum state tomography method that significantly reduces measurement requirements and enhances robustness, demonstrated on superconducting qubits with high fidelity.

Contribution

The paper presents a novel parallel quantum state tomography approach inspired by quantum overlapping tomography, reducing measurement costs for large quantum systems.

Findings

Achieved high fidelity in reconstructing 6- and 9-qubit W states with fewer measurements.

Successfully reconstructed a 12-qubit W state with substantially fewer observables than full tomography.

Demonstrated the method's robustness and efficiency on superconducting qubit hardware.

Abstract

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)], 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 tree-like 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 6-qubit and 9-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 $3^{12}=531441$ 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.