Direct Estimates and Confidence Intervals for Fidelity of Quantum States

Quantum mechanics is science's most detailed theory of the physical world, and fully exploiting quantum mechanics is enabling new technologies such as quantum computers. A fundamental requirement when building quantum systems is to verify that the experimentalist has actually built what they intended to build. For this reason, experimentalists test quantum systems by taking (inherently probabilistic) measurements.

The aim of this project is to process these measurements in a new way in order to give a more accurate and reliable estimate of how much the actual quantum state differs from the intended quantum state. This more reliable verification procedure is an important step in constructing fault-tolerant quantum computers, and as such, this project contributes toward creating useful quantum computers.

Thus the broader impact of the project includes the potential impacts of quantum computing, as well as generally contributing to the progress of science.

The technical goal of the project is to estimate the fidelity between two quantum states with high certainty; in particular, the proposed method produces a rigorous confidence interval within which the fidelity lies (within a desired probability of failure). The approach is novel in the field, as it uses a computationally constructed statistic, and is applied directly to the raw data without requiring data-averaging or full tomography.

The method has advantages over existing direct methods as well as over maximum likelihood tomography methods. The intellectual contributions of the proposed work will be showing that the certification problem fits inside a very specific existing statistical framework, deriving the estimators and solving related optimization problems, and extending both the theory and applications, e.g., to quantum channels and entanglement witnesses.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.