Nengkun Yu Leads $1M NSF Grant to Learn Quantum States With Simple Measurements in Collab with Cornell

Nengkun Yu, associate professor in the Department of Computer Science, is leading a $1M grant from the National Science Foundation (NSF) to study how much simple measurements can reveal about quantum systems. Stony Brook University will receive approximately $500,000, with the remainder going to collaborators at Cornell University. The project runs through June 2030.

Reading the output of a quantum system is not like opening a file. A measurement returns a random outcome whose odds depend on the system's state, so learning that state takes many identical copies, each measured and the results pooled. Flipping a biased coin once says little about its bias, and a single measurement says little about a quantum state. Even for one qubit, the basic unit of quantum information, measuring repeatedly in a single direction is generally not enough to reconstruct its state. The challenge is deciding which measurements to make and how many copies are needed.

Yu's approach focuses on Pauli measurements, among the simplest measurements available for a qubit. The experimenter chooses one of three directions, called X, Y and Z, measures each qubit separately and keeps the complete record of outcomes. More sophisticated measurements that act jointly on several qubits or several copies can cut the number of copies needed, but they make experiments far more demanding.

"We study Pauli measurements because we want to understand how far simple hardware can take us," Yu said.

Working with Jayadev Acharya of Cornell University and Cornell doctoral students Abhilash Dharmavarapu and Yuhan Liu (now at Rice University), Yu has identified those limits more precisely. The same four researchers wrote four previous papers on the topic. The first, "Pauli Measurements Are Not Optimal for Single-Copy Tomography," published at the 2025 ACM Symposium on Theory of Computing (STOC), showed that Pauli measurements are not optimal among all single-copy measurements for reconstructing a general quantum state.

A second paper, "Pauli Measurements Are Near-Optimal for Single-Qubit Tomography," posted on the arXiv preprint server, showed that when each qubit must be measured separately, Pauli measurements are nearly optimal, even when later choices adapt to earlier results. Two more arXiv preprints answer specific questions without reconstructing everything. "Near-Optimal Mixedness Testing with Pauli Measurements" establishes nearly matching bounds for testing whether a state is maximally mixed. "Sublinear Copies Suffice for Fidelity Estimation with Pauli Measurements" reduces the number of copies needed to estimate fidelity, a measure of how closely a prepared state matches a known target.

Yu called the second result the most surprising. "Pauli measurements can be significantly worse than a broader class of measurements while still being almost the best possible choice under a very natural experimental restriction," he said.

The lesson is that some limits can be overcome with better algorithms, while others require changing the measurement hardware.

The findings could help people building quantum computers check that a device works. An experimentalist may not need a full description of what a device produced, only how closely it matches the intended state, which is what fidelity estimation answers. The lower bounds help too, because they show when a large data requirement reflects a fundamental limit and not a weakness of one algorithm. But the work has limits. Fully reconstructing an arbitrary large quantum state still becomes exponentially more costly as qubits are added, and the results are mathematical guarantees that must be tested against real calibration and preparation conditions in the lab.

The Stony Brook funding will support graduate research assistantships, summer research support, collaboration visits and conference travel. Yu and Acharya meet weekly and visit each other during the summer. Acharya's work centers on information theory and statistical inference, while Yu approaches the same questions through quantum information and computing. Xuan Du Trinh, a Ph.D. student in computer science at Stony Brook, contributes to the project through his research on quantum learning and entanglement certification.

Next, Yu wants to determine when reconstructing an entire quantum state is necessary and when far less information answers the question, including which kinds of entanglement can be certified using simple measurements.

Yu described what success would look like by 2030. "I would consider success to mean having that kind of understanding for several important inference tasks, together with protocols whose assumptions and resource requirements are clear enough for experimental researchers to evaluate. Training students who can move comfortably between quantum information and statistical learning would also be an important part of that success," he said.

By: Harsha Venkatesha Gupta