Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland

Impurity models are a central constituent of embedding frameworks such as dynamical mean-field theory (DMFT) and the ghost Gutzwiller approximation (gGA), where they act as simpler auxiliary systems representing realistic materials. Because they are correlated, solving for their ground state and dynamics remains a many-body problem, but their electron correlations are usually confined to a small part of the system, which makes them amenable to approximate treatments. Norman Hogan discusses solvers being developed for multi-orbital impurity models, including quantum computing approaches, reduced basis methods and the intersection of the two. Efficient and reliable solvers make it possible to explore the phases of multi-orbital impurity models, which are interesting in their own right, and accelerate the most expensive step in embedding frameworks, offering a pathway toward functional materials design.

Xinzhao Wang presents a query-optimal algorithm for simulating a general Lipschitz-continuous time-dependent Hamiltonian. Its query complexity matches the known lower bound for time-independent Hamiltonian simulation, showing that time dependence incurs no asymptotic query overhead. The main ingredient is a one-query transducer that implements the target evolution given a catalyst state. A weighted combination of circuits that reuse the transducer different numbers of times removes the need to prepare the catalyst; the error from omitting the catalyst decays factorially, which yields the optimal dependence on precision. The same algorithm also admits a gate-efficient implementation that retains the optimal query complexity, with gate complexity linear in the query complexity up to logarithmic factors.

Useful quantum advantage requires efficient quantum algorithms as well as large-scale processors. In many practical problems the dominant resource costs come from a small set of computational primitives, and optimising them in the quantum setting is hard, partly because of a reversibility constraint absent from classical computation. Andi Gu presents an evolutionary framework in which large language models propose circuit designs and an independent evaluator verifies and scores them. On tasks spanning numerical computation, chemistry, optimisation, quantum simulation and number theory, the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art in seven of eight cases. In the eighth, the search finds a new reversible architecture for prime-field modular inversion that makes divsteps viable and substantially improves the Toffoli-qubit trade-off. The results open the way to evaluator-guided co-design of new algorithmic structures for quantum computation with LLMs.