Research

"If you think you understand quantum mechanics, you don't understand quantum mechanics." - Richard Feynman

My research interests combines mathematics and quantum information to build verifiable quantum protocols and practical algorithms for near-term quantum devices. A key theme used throughout is uncovering and exploiting the (algebraic) structures, Cartan decompositions, and invariants to certify quantum behavior and optimize resources.

Non-local games

Non-local games (NLGs) are games between a finite number of players and a referee, where separated players answer questions without communicating. The win rate reveals whether their correlations are genuinely quantum. They're often used to certify entanglement and measurements in a device-independent way. Such an appliation is often called "self-testing," and are used as primitives for verification and cryptographic protocols. Some of the key challenges related to NLGs are scaling to larger games, noise-robusness, and determining which framework properly describes our universise. My work specifically focuses on developing algorithms to play NLGs and embedding a finite number of games into larger spaces, where qubit reductions are possible.

Summary	Publication	Pre-print
Play NLGs on several hardware platforms	Application-level benchmarking of quantum computers using nonlocal game strategies	arXiv
Construct a variational quantum algorithm to play a NLG	Pending: A Game-Theoretic Quantum Algorithm for Solving Magic Squares	arXiv
Play parallel NLGs and reduce necessary qubits to do so	Pending: Commuting Embeddings for Parallel Strategies in Non-local Games	arXiv

Trotterization

Trotterization (also known as Lie-Trotter/Suzuki products) is technique used to break down hard operator evolutions like $e^{t(A+B)}$ into products like $(e^{tA/n}e^{tB/n})^n$. The latter is simuable on (most) quantum hardware using native gates. Some of the main challenges are depth-accuracy tradeoffs, sensitivity to non-commutativity, and hardware constraints. My work develops structure-aware trotterization using Jordan products and Jordan algebras, which are commutative (and generally non=associative) operator structures.

Summary	Publication	Pre-print
Second-order Trotter formula and error estimates in Jordan-Banach algebras	Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras	arXiv
A “semicoherent” framework linking exact symmetries to ε-approximate quantum processes	Semicoherent symmetric quantum processes: Theory and applications	arXiv
Prove Suzuki-type approximations and error estimates for exponentiated sums in a JB-algebra setting	Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in JB-Algebras	arXiv

Expressiveness of quantum circuits

Quantum expressiveness quantifies how well a parameterized quantum model (circuit) can span the set of quantum states (unitaries). This is often done by using frame potentials, where values using the Haar measure indicate broader coverage of state (unitary) space. Some key challenges related to quantum expressiveness are that frame potentials are too expensive to estimate and that expressiveness often depends on the circuit architecture, making a uniform theory difficult to develop.

Summary	Publication	Pre-print
Connecting frame potentials, quantum expectations, and pairwise fidelities to characteristic functions of random variables	Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach	arXiv
More coming!

The role of entropy

Quantum entropies quantify uncertainty, correlations, and resources in quantum systems. Making them practical on real devices is tricky due to the nonlinearity of some of the entropic functions.

Summary	Publication	Pre-print
Outline theoretical security standards for quantum-classical interfaces (connections)	Entropy of the Quantum–Classical Interface: A Potential Metric for Security	No pre-print
A survey of (classical) data compression algorithms in the context of edge computing and emerging quantum compression techniques	Classical and quantum compression for edge computing: the ubiquitous data dimensionality reduction	No pre-print
A survey of several entropic measures in quantum information and their core mathematical properties	Quantum entropies	No pre-print