Cross-platform verification

Cross-platform verification is a randomized-measurement protocol from Elben, Vermersch and colleagues in the Innsbruck ion-trap and theory groups for estimating the fidelity between quantum states prepared on two different, possibly remote, devices. No quantum link and no full tomography are required: the platforms exchange only classical descriptions of random unitaries and measurement outcomes. Its output is a pairwise fidelity between two specific preparations, a characterization result rather than a standalone device score.

How it works

Both devices prepare nominally the same state, apply the same random local unitaries (sampled from a unitary 2-design and shared classically), and measure in the computational basis. Cross-correlating the two outcome distributions estimates the overlap Tr(rho1 rho2), and the same data yield each state’s purity; the reported figure is the max-normalized overlap F_max = Tr(rho1 rho2) / max{Tr(rho1^2), Tr(rho2^2)}. The measurement budget scales as roughly 2^(bN) with b ≈ 0.6–0.8, far below the b ≥ 2 of full quantum state tomography but still exponential, so direct whole-state comparisons top out around 10–15 qubits; larger devices are compared through subsystem fidelities.

Strengths and limitations

The protocol’s distinctive move is cross-correlating two experimental datasets directly, where cross-entropy benchmarking scores a single device against an ideal classical simulation. Caveats: F_max is the max-normalized overlap, not the Uhlmann fidelity, and the two can differ for mixed states; results are relative to the partner device or simulation; and because the two experiments may be separated in time, drift between them enters the comparison. Like direct fidelity estimation, it trades tomographic completeness for a targeted estimate.

Notable results

The original paper, published as Phys. Rev. Lett. 124, 010504 (2020), measured experiment–theory fidelities of entangled 10-qubit trapped-ion states. Zhu et al. compared trapped-ion machines against IBM superconducting processors on 7- and 13-qubit Quantum Volume-style circuits (Nature Communications, 2022), and Zheng, Yu & Wang extended the method from states to arbitrary quantum processes (npj Quantum Information, 2023). The protocol ships as a worked example in the maintained RandomMeas.jl package (v0.3.1, April 2026; companion paper in Quantum 10, 2086).