Algorithms, logical architectures, and quantum simulation: three directions for advancing the reach of computation.
01 / MATHEMATICAL STRUCTURE
Quantum algorithms.
We investigate the relationship between a problem’s structure and the quantum operations that can expose it. Our focus is on explicit assumptions, precision requirements, and end-to-end computational cost.
Questions worth investigating
When does phase estimation offer a useful route to spectral information?
How much does state preparation change the cost of a proposed speedup?
Which observables provide useful answers without reconstructing an entire state?
Research objectives: reproducible circuit studies, complexity analyses, and comparisons against classical reference methods.
Useful computation requires more than a large register. Our architecture research examines the joint design of logical operations, error correction, decoding, and execution schedules.
Questions worth investigating
How do physical error assumptions change the required code distance?
Where do decoding latency and non-Clifford resources constrain throughput?
How do connectivity and compilation affect the depth of an application?
Research objectives: transparent resource estimates and architecture-sensitive comparisons, with assumptions separated from measured evidence.
Quantum systems are a natural subject for quantum computation. Our simulation research focuses on energy estimation and dynamics, beginning with models that can be checked against established classical calculations.
Questions worth investigating
Which active-space models retain the physics needed for a useful answer?
How should approximation, simulation, and measurement errors share an accuracy budget?
At what scale does a model become scientifically informative and classically demanding?
Research objectives: benchmark definitions, accuracy studies, and resource maps for selected Hamiltonian problems.
Our method connects theory, exact simulation, noise characterization, and hardware-aware experimentation. Each stage sharpens the question and informs the next: what is the right representation, what limits the calculation, and where can a different approach change the outcome.
Progress is measured in the quality of the evidence: a reproducible result, a tighter bound, a better resource estimate, or a clearer understanding of a method’s limits.