Scalable estimation of pure multi-qubit states

TL;DR

This paper presents a scalable method for estimating pure multi-qubit states using a minimal number of measurement bases, suitable for noisy quantum computers, with demonstrated high fidelity in experiments and simulations.

Contribution

The paper introduces an inductive estimation method that scales linearly with qubits using separable or entangled bases, improving efficiency over existing techniques.

Findings

Achieves high fidelity (up to 0.88) for 10-qubit states with few measurement bases.

Successfully estimates 4-qubit GHZ states on IBM quantum processors with near 0.875 fidelity.

Demonstrates the method's practicality for noisy intermediate-scale quantum computers.

Abstract

We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. Monte Carlo numerical experiments show that the method can achieve a high estimation fidelity. For instance, an average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with $21$ separable bases. 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. We experimentally demonstrate the proposed method in one of IBM's quantum processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and entangled states achieve an estimation fidelity in the order of $0.85$ and $0.7$, respectively.