Distributed quantum inner product estimation

Understand

As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers.

• This task is fundamentally distributed, as no quantum communication can be performed between the two physical platforms due to hardware constraints, which prohibits a joint SWAP test.
• In this paper we settle the sample complexity of this task across all measurement and communication settings.
• The essence of the task, which we call distributed quantum inner product estimation, involves two players Alice and Bob who have $k$ copies of unknown states $\rho,\sigma$ (acting on $\mathbb{C}^{d}$) respectively.